One story we told in The Wages of Wins was about Tyson Chandler and Eddy Curry. The Chicago Bulls drafted each big man in 2001. Four years later – in the summer of 2005 – it was time to make a decision. Should the team re-sign Chandler and/or Curry to long-term extensions? In the end, both players signed very similar deals. In other words, the market said each player was about the same. As we noted in the book, though, it was pretty clear in 2005 (and even clearer today) that Chandler was by far the more productive player. In sum, the market over-valued what Curry did in 2005.
Ultimately it was New York, not Chicago, that was hurt by this over-valuation. Back in 2005 Curry was sent to the Knicks in a deal that ultimately netted Tyrus Thomas and Joakim Noah for the Bulls. Given how little Curry has actually done for New York (and again, this was expected in 2005), this was a good deal for Chicago.
This summer the Bulls once again faced a similar problem. On draft night in 2004 the team acquired both Ben Gordon and Luol Deng. This past summer Chicago had to decide – would it sign Gordon and/or Deng to long term deals?
According to the Chicago Sun-Times, each player was offered the same deal: $50 million for 5 years. And each player rejected the offer. So next summer the negotiations will open again, with each player now able to field offers from other teams. But as restricted free agents, both will not quite see the offers a free market might provide.
Whether or not either player is retained next summer is not the story today. The story – assuming the Sun-Times got the offers right – is that the Bulls regard each player as basically the same. Is that true?
Points Scored and the “Efficiency” Metrics
To answer this question we need to evaluate performance. The most commonly cited performance metric is points scored per game. Here is how much scoring each player has offered in his career:
Luol Deng
2004-05: 11.7
2005-06: 14.3
2006-07: 18.8
Career: 15.2
Ben Gordon
2004-05: 15.1
2005-06: 16.9
2006-07: 21.4
Career: 17.8
At every point in each player’s career, Gordon has proven to be the better player. At least, that’s true if all you look at is points scored per game.
What if we use a summary measure like NBA Efficiency (per 48 minutes) or John Hollinger’s Player Efficiency Rating (PER)?
Luol Deng
2004-05: 20.7, 14.2
2005-06: 22.3, 15.8
2006-07: 25.7, 18.7
Career: 23.4, 16.7
Ben Gordon
2004-05: 19.9, 14.9
2005-06: 19.0, 14.5
2006-07: 24.0, 18.2
Career: 21.1, 16.0
The average small forward offers a per 48 minutes NBA Efficiency mark of 20.3. The average shooting guard has a 19.6 value. Hollinger’s metric is constructed so that average is 15.0, although I am not sure that’s true for all positions.
Regardless, by these metrics each player was well above average in 2006-07 and has been above average for their respective careers. Still, Deng is rated as a better player, although the difference – especially with respect to PERs – is rather small. In sum, if PERs is the metric of choice, the identical $50 million offers might make sense.
Looking at Wins Produced
As noted last year, both NBA Efficiency and PERs over-value scoring. So how does our perspective change when we turn to measure that doesn’t have this bias? Yes, let’s now turn to Wins Produce and Wins Produced per 48 minutes [WP48].
Luol Deng
2004-05: 5.1, 0.147
2005-06: 10.9, 0.200
2006-07: 14.9, 0.232
Career: 30.8, 0.202
Ben Gordon
2004-05: -0.7, -0.016
2005-06: 1.0, 0.020
2006-07: 4.5, 0.081
Career: 4.9, 0.033
Okay, now we have a difference. Deng produced more wins his rookie season (his worst as a pro) than Gordon has produced his entire career. What explains such a discrepancy?
To see this, let’s turn to the individual stats.
Table One and Two: The Careers of Luol Deng and Ben Gordon
In each table, above average marks are in black, below average in red. And given this color code, we see that Gordon’s table just bleeds. Yes, he can score and get assists. But after these two activities on the offensive end, he is below average. Specifically, Gordon is below average with respect to rebounds, steals, blocked shots, turnovers, and personal fouls. Given all this red, it’s not surprising to see a below average Win Score (and as noted above, below average WP48 and Wins Produced).
Looking at Deng we see very little red. Deng is only below average in his career with respect to steals and assists. He is above average with respect to scoring, rebounds, blocked shots, turnovers, and personal fouls.
When we look at all the statistics, and we consider the value of these statistics in terms of offensive and defensive efficiency (which Wins Produced does), the choice for Chicago is clear. Luol Deng needs to be re-signed. And given how many wins he produces, $10 million per year is a bit low. A win – as noted in the Anderson Varejao piece – is worth at least $1 million (at least, I am pretty sure about this).
On the other hand, giving $10 million to Gordon is a bit too much. Yes, Gordon is developing into an average player. But $10 million per year is an above average wage. Unless Gordon suddenly develops into an all-around player (like Deng), the Bulls would be better off letting Gordon go and using some of his money to sign Deng.
Certainly what we see from each player in 2007-08 will ultimately make this decision. Perhaps Gordon will suddenly improve (possible, but unlikely). Or maybe Deng will get hurt (again, possible). As it stands in November, though, Deng should cash in next summer. Gordon probably will also, but I doubt he will ever generate enough wins (and revenue) to justify the deal he will sign in 2008.
- DJ
Our research on the NBA was summarized HERE.
The Technical Notes at wagesofwins.com provides more information on the published research behind Wins Produced and Win Score
Wins Produced, Win Score, and PAWSmin are also discussed in the following posts:
Simple Models of Player Performance
213 responses so far ↓
Okapi // November 7, 2007 at 6:55 am
I hate to revitalize this topic (and don’t want to see the comments thread digress from an interesting post on Deng/Gordon), but I still don’t see why residuals from time t-1 can’t be incorporated into a forecast for time t. (As would be built into an autoregressive moving avg model, etc.)
There was a Fed study that wanted to see how accurate GDP/inflation forecasts were. The benchmark to which forecasts were compared was a simple forecast in which last year’s GDP and inflation rates was used as a forecast for this year.
Along those lines, I think it reasonable to evaluate Wins Produced by comparing to a simple benchmark forecast. Kind of like what the Marcel projections do for baseball, just taking last year and regressing to the mean.
I don’t know what the shrill polemicist Rosenbaum is doing. But I think it reasonable to take last year’s team point differential and then allocate to players in accordance with minutes played. If players don’t switch teams you just project forward last year’s team performance. as a projection for this year’s team performance. And when they switch teams they are valued at their share (based on minutes) of the team’s performance from last year. No theory or anything is necessary to support this. If Wins Produced is a good scheme (in a predictive and not just descriptive sense) for determining each player’s contribution to the team performance then projections based on Wins Produced should be more accurate than simple projections where players just get an equal share (based on minutes) of the team performance.
Okapi // November 7, 2007 at 7:08 am
One last note … Models are arbitrary simplifications of reality. It seems people pile onto the comments thread of this blog and gratuitously criticize every simplification of reality made by this model. IMHO, it’s a very good model.
(e.g. An adjustment for garbage minutes could be easily– at least in theory– made with a win probability system overlaid upon wins produced. But it’s not as if the absence of that in wins produced is a refutation of wins produced. In the interest of simplicity and transparency the basic model can omit stuff like that.)
MattB // November 7, 2007 at 7:50 am
I am sold. Deng is clearly the more valuable player.
Of course I’ve never liked Gordon’s style of play. He’s got that attitude of a “pure scorer”, or in other words, he doesn’t feel it’s necessary to play both sides of the floor.
Nice piece
Oren // November 7, 2007 at 8:29 am
I must not understand your charts.
I can understand how if you compare Ben Gordon’s career averages to the average SGs that you can come to the conclusion that his performance so far in his career has been below average.
But from a GMs perspective, wouldn’t one have to consider that Ben Gordon has shown noticable improvement each year in points per attempt, assists and wins produced?
Why don’t you think that this would imply that we should expect further noticible improvement?
Rasta // November 7, 2007 at 9:49 am
Dave,
Good column. The format of comparing PPG and PER for each player really helps get the point across.
You briefly mentioned Eddy Curry, who was matched up last night against Marcus Camby. Check out the boxscore:
http://www.nba.com/games/20071106/DENNYK/boxscore.html
Curry 11-16 fg, 8 rbs, 24 pts
Camby 3-7 fg, 13 rbs, 9 pts
Win Score:
Curry 10.5
Camby 12.0
We can breakdown the Win Scores into components like this:
Curry
WS from shooting 5.5
WS from rebounding 8.0
WS from TOs -4.0
WS from other stats 1.0
TOTAL 10.5
Camby
WS from shooting -1.0
WS from rebounding 13.0
WS from TOs -1.0
WS from other stats 1.0
TOTAL 12.0
If we accept the logic that turnovers are a function of offensive attempts, we can combine WS from shooting and TOs into one line item.
Curry
WS from shooting and TOs 1.5
WS from rebounding 8.0
WS from other stats 1.0
TOTAL 10.5
Camby
WS from shooting and TOs -2.0
WS from rebounding 13.0
WS from other stats 1.0
TOTAL 12.0
So, what does this tell us? It tells us that Curry’s 15 point advantage is outweighed by Camby’s 5 rebound advantage, even though Curry had a huge advantage in FG%. To me, this fails the smell test.
In general, I’m a supporter of Win Score and Wins Produced, but I’m having a hard time wrapping my head around this problem.
Help me out.
Pete // November 7, 2007 at 10:18 am
Rasta, IIRC teams score 1 point per possession on average.
In ~18 shot attempts Curry generated 24 points, adding 6 pts to his team above an average showing. By turning the ball over 4 times he deprived his team of 4 expected points. Thus, as you call it, his WS from shooting and TOs is a couple points.
Repeating that exercise for Camby shows that Camby cost his team a couple pts with his shot attempts.
Remember, each rebound generates a renewed offensive possession so is worth (an expected) 1 point to the team. Camby’s 5 extra rebounds vs. Curry generated an extra 5 pts for his team, offsetting his shooting performance and motivating a better night than Camby had.
I really like Win Score, though I think rebounding is overemphasized (should it really be 1 point per rebound or should it be 1 pt per rebound over the average rate of rebounds for players at that position?).
dberri // November 7, 2007 at 10:31 am
Every player is compared to the average at his position. So rebounds are indeed compared to the average. This is one big reason Curry scores so low. Curry getting 7 rebounds per game would be great, if he were a point guard. But as center, playing Curry costs you rebounds.
Swyft // November 7, 2007 at 12:39 pm
Amen! I’ve always believed that Ben Gordon was overrated! He’s an above average player but not a 10 million dollar player!
Chris // November 7, 2007 at 1:04 pm
I was wondering who is the best nba player of all time, according to the numbers that you have produced using Wp48 or wins produced?
Chirstopher // November 7, 2007 at 2:04 pm
Rasta, roughly speaking you’re looking at an above average game for Curry and a below average game for Camby. If Curry brought that every night I believe folks here would embrace him a bit more. Also, project that 1.5 over the whole season to get a better picture.
vanveen // November 7, 2007 at 2:31 pm
“Curry getting 7 rebounds per game would be great, if he were a point guard. But as center, playing Curry costs you rebounds.”
there is no evidence that playing Curry at center costs a team rebounds. wins produced doesn’t provide an explanatory framework wherein such assertions can defensibly be made. in fact, the weighting of rebounds betrays a notable absence of such a framework, i.e. players receive full credit for rebounds their team would have captured without them over 95% (sometimes more) of the time. producing less rebounds than an average center does not mean you’re reducing the rebounding capture % or rebounding rate of your team (although that is one likely interpretation: see yesterday’s comments section).
perhaps a hypothetical will illustrate my point.
imagine a team composed of 5 players, all of whom are equally proficient at rebounding the ball. each player has the same rebounding radius. if there’s a rebound within their rebounding radius, their chances of capturing it are the same. we will call them C, PF, SF, SG, and PG.
just to make this really simple, let’s say the C and PF can each capture 80% of the team’s rebounding opportunities. each can capture 75% of the other’s. for whatever reason, the PF has greater incentive to capture rebounds than the C and the C often defers to the PF. at the end of a season the PF has captured over half of the rebounds in their overlapping area. he finishes the season with 13.6rpg and the C only has 6.4 rpg.
in the wins produced model the PF is producing more rebounds than the C and will be rewarded for his ’superior’ individual production even though he didnt increase his team’s rebounding efficiency. if we replaced the C with a clone of PF we wouldn’t get more rebounds – we’d only see a more equitable distribution of rebounds between players on the team.
that’s an extreme example, but the point is that Wins Produced cannot distinguish between different interpretations. Curry may be costing his teams rebounds or he may not be. C or ~C. we don’t know and WP can’t tell us.
Pete // November 7, 2007 at 2:50 pm
Vanveen, are you saying that you wouldn’t make a position adjustment? I don’t think that would give better results.
jon // November 7, 2007 at 2:53 pm
dberri wrote:
“But as center, playing Curry costs you rebounds.”
Unfortunately (for Wow), this is not true. As it is currently constructed, the WoW model says that if we replace Curry with an “outstanding” rebounder like Reggie Evans, the Knicks as a team would see a huge increase in their total team rebounds. Likewise, it implies that Jason Kidd, averaging 7 rebounds a game from the PG slot, will help the Nets become one of the best rebounding teams in the league.
This is simply not true. The fact is, the majority of Kidd’s rebounds will be “taken” from his own teammates. Empirically, we can see that the Nets surrendered more rebounds than they captured as a team last year.
Now let’s head back to Eddy Curry. Last year, the Knicks gave up 3182 rebounds as a team (league average 3386), and rebounded the ball 3558 times themselves. So your assertion that “Eddy Curry costs you rebounds” is simply unfounded. He contributes effectively to the overall rebounding level of his TEAM. The Knicks were, in fact, quite a good rebounding team.
Now, perhaps you think that this is an anomaly. Let’s look at another example. Ben Wallace is a player with a high WinScore, driven primarily by his superior rebounding numbers. But do the individual rebounding numbers translate into TEAM success? In 2005-2006, his last season with the Pistons, Wallace averaged 15.4 rebounds per 48 minutes (or, 11.3 in 35 minutes per game). As a team though, the Pistons surrendered 3350 rebounds while capturing 3322. They gave up about as many rebounds as they got.
What happened when Ben Wallace left? in 2006-2007, the Pistons captured 3322 rebounds and surrendered 3376, a net loss of 26 rebounds for the 82 game season. Now, perhaps Wallace was replaced with a player of similar quality, and that explains tiny difference. Well, in 05, Wallace averaged 35 minutes. The majority of those minutes were given to Chris Webber in 06. Webber averaged 29.7 minutes and 6.7 rebounds (or, 10.8 rebounds per 48). Based on individual rebounding numbers, we should expect a large decline in the team rebounding of the Pistons. But this was not the case.
Again, this is a major flaw with the way WoW is determined. It is also the reason why players like Reggie Evans and Tyson Chandler are given the highest win scores (higher than Tim Duncan!). The approach that SHOULD be taken is one that evaluates a player’s ability to rebound over the ‘replacement level’. In this way, we can see just how many net rebounds a team gains or losses when they replace a player who is traditionally bad at rebounding (like Eddy Curry, career average of 10.23 rebounds per 48 with a player who is traditionally good at rebounding, like Ben Wallace, career average of 16.35 rebounds per 48). I can GUARANTEE you that the team will not gain or lose 6.12 rebounds per game. Unfortunately, WoW makes this assumption and it just doesn’t jive with the reality of the NBA. The best and worst rebounding teams do not have such huge discrepancies between them, period.
To be honest, I suspect that the model in its current form would serve as a better prediction tool if it were to simply discount rebounding completely and focus on the other areas. It would still have flaws, but the most egregious of them would be removed.
jon // November 7, 2007 at 2:58 pm
vanveen’s comments are exactly spot on. at worst, curry costs his team 1-2 possessions per game. at best, tyson chandler gains his team 1-2 possessions per game. but the WoW model assigns huge differences in the productivity levels of the two players when it is not warranted.
dberri // November 7, 2007 at 3:23 pm
Jon and Vanveen,
If rebounds are simply taken from teammates, then a player’s rebounding numbers would fluctuate tremendously depending on teammates. We do not see that in the data. Rebounds are quite stable.
That being said, there are diminishing returns in the NBA. And we have estimated this effect. It is there, but not large.
I would also add that all you are saying applies even more to scoring. Shot attempts are also taken from teammates. Should we discount Iverson’s scoring because he took shots his teammates could have taken? When he left Philadlphia, team shot attempts didn’t change very much.
jon // November 7, 2007 at 4:31 pm
If we replace an 11r/48 player with an 18r/48 player, your model tells us that his team will be gaining 7 rebounds. This simply isn’t true. Where are the rebounds coming from? When teammates change, a team doesn’t surrender the difference in rebounds. Period. This is true across many, many samples. Where are the phantom rebounds coming from, if not their own teammates?
Rebounds are stable because one player generally takes it upon themselves to hustle (or pad their stats) and grab the ball. But if you replaced that player with someone who didn’t hustle, your team rebounds would not fall by nearly the amount WoW suggests. Again, look at the best rebounding teams in the NBA vs the worst teams in the NBA, season by season, for the last 30 years. The data doesn’t lie.
dberri // November 7, 2007 at 4:47 pm
Jon,
Not too be rude about this.. but between the two of us I am the only one to do a systematic study of how teammates impact teammates productivity.
And you still haven’t told me why rebounds bother you more than scoring.
Jed // November 7, 2007 at 5:01 pm
It seems to me that someone really needs to do a study on the ACS (Abrasive Comment Score) for posts on the WoW blog. This sort of research would let us answer questions like “If DB moved to a different website, what would the expected impact on its net snarkiness be?”
Kent // November 7, 2007 at 5:50 pm
Jed,
I think I remember Brad DeLong once posting on his blog that part of the reason Paul Krugman was so shrilly criticized was that Krugman (at the time) kept a web site where he answered critics back. I think DeLong said that if Tom Friedman published his e-mail address Tom Friedman would receive more criticism.
Let’s assume my recollection is correct and let’s ignore the issue of whether Krugman in fact deserve to be fervently criticized.
I think it’s great that dberri responds to commenters. I fear that it’s encouraging the abrasive commenters, though, and it won’t persist. Every single post now seems to spawn a sequence of comments devoted to the apotheosis of Rosenbaum.
Owen // November 7, 2007 at 5:55 pm
“If we replace an 11r/48 player with an 18r/48 player, your model tells us that his team will be gaining 7 rebounds. This simply isn’t true. Where are the rebounds coming from?”
Is that really what the model is saying? I don’t think so. You guys really aren’t making sense it seems to me.
In the previous thread Vanveen posted that exact comment, and Pete responded by saying.
“While this is indeed true, it’s not just true for rebounding. Scoring has a similar property: there are a limited number of scoring opportunities in a basketball game. If you replace the minutes of a 11pt/48min scorer with an 18pt/48min scorer you don’t get 7 more points per 48 minutes. As with rebounding, the more likely explanation is that his teammate’s are ceding scoring opportunities to him because he’s better at it.”
Why don’t we make this a discussion, and start by having you respond to Pete’s comment, and see where that takes us….
JLewis // November 7, 2007 at 7:03 pm
Jon and Vanveen,
Sticking with Dave’s point that only rebounding seems to bother you, can you really answer that you DO NOT believe that a team is negatively impacted by substituting a strong rebounder on their roster for a weak rebounder?
Your entire case is predicated on the belief that team rebounds don’t vary based off of team composition. If this were accurate why would a team pay a premium for a top rebounder on the free agent market when any old player would do?
You are saying that it doesn’t matter who the player is because even if we put you on the court it won’t affect net rebounds because someone else on the team will just go get the rebounds that a talented rebounder would have taken if they were in your roster spot. That is absurd in itself but then you take it further by implying that the guys getting a bunch of rebounds are just “padding their stats.”
Do you truly believe that collecting rebounds in the NBA is as simple as saying, “I think I want to pad my rebounding stats tonight, I’ll go track down all of the rebounds alloted to our squad?”
To put this to you another way, you are saying that team rebounding statistics are consistent from year to year so individual players don’t matter in accumulating the team total. The logical conclusion to that is to say that team rebounding is fixed, not variable. The Lakers will get X rebounds every year regardless of team composition. The Cavs will also get X number of rebounds each year regardless of team composition. In essence, the uniform collects the rebounds, the player wearing the uniform is irrelevant.
Therefore it’s pointless for GM’s to try to add strong rebounders to their roster because the uniform is responsible for net rebounds. They shouldn’t even try because net rebounds are basically fixed from year to year.
No one, no matter how dim and narrow minded, can accept this line of thinking.
This is before we even get to the question of what makes a team (the uniform) a good rebounding unit. Not all teams rebound at the same rate, but according to you their rate is fixed and can’t be affected by substitution of players. So what intrinsic to the franchise or uniform explains the differences in rebounding rates from team to team?
Until you understand the implications of your argument and are able to propose a superior (or even equivalent) alternative, try to tone it down. Asking questions of Dave about WoW is cool, disparaging the system with faulty logic is not.
Pete // November 7, 2007 at 7:04 pm
Owen, I would appreciate that very much. Thank you.
Pete // November 7, 2007 at 7:05 pm
JLewis, thank you for your post. Finally a voice of reason.
Jason // November 7, 2007 at 7:57 pm
Jon, your notion that Jason Kidd’s rebounds would otherwise be grabbed by teammates is unfounded. While replacing him with anohter player isn’t likely to cost the Nets all 7 of his rebounds,the data indicate that the Nets were a better rebounding team when he was in the game (+3.3% better actually, according to 82game.com) than when he was on the bench. What it indicates is that his presence in the game allowed the Nets to grab a greater number of the available rebounds than they would if he was not playing.
On average, there were 82 rebounds to be had in any game last season. You are correct that a player does not create rebounds, but how these 82 rebounds are apportioned between the two teams is not set in stone. It is a function of the rebounding abilities of both clubs. Kidd, according to the numbers, increased his team’s rebounding rate 3.3% over what they did when he wasn’t in the game. If we assume that the team was strictly average (which, as the position correction Dave uses, is the assumption) then the assumption is that the team averaged 41 rebounds a game. A 3.3% increase in rebounds equates to a change from a 41 rebounding to 42 or 43 a game. If the total number of rebounds in a constant, were the Nets to grab 43 a game, their opponent would slip to 39 a game so that the total number of rebounds in the contest did not change. That’s a net difference of 4 rebounds a game. Over the course of the game, 4 rebounds that an opponent would have pulled down went to the Nets when Kidd was in the game. This is not speculation. This is what the data actually shows actually happened based on the percent of available rebounds pulled down when he was in the game vs. when he was not in the game.
So how do these 4 extra rebounds did Kidd get?
Kidd got 7 rebounds a game in a bit less than 37 minutes. That’s about 9 rebounds per 48 minutes. I don’t have the exact number but if the average point guard pulls down 4 fewer over the course of a game, that means the average point guard pulls down about 5 rebounds per 48. I don’t have the actual numbers here. Dave, how close am I? If this is about what the average point guard really *does* pull down, then assigning the rebounds to Kidd outright is *completely* in line with the actual change in rebound rate seen with him in or out of the game. If so, this suggests that the position correction does a pretty good job of accounting for the difference and relating them to actual events.
Jason // November 7, 2007 at 8:02 pm
I’d add, it also suggests that if the value of a rebound from regression does linearly relate to probability of a win, at least in Kidd’s case, assigning him complete credit for all of his rebounds, without penalty and weighted exactly as WP weights is, is the correct thing to do as any opportunity cost is accounted for in position correction with the assumption of a standard position rate for a replacement player.
Tim // November 7, 2007 at 8:16 pm
According to the Chicago Tribune, Luol Deng turned down an increased offer of five years for $57.5 million.
http://chicagosports.chicagotribune.com/sports/basketball/bulls/cs-071104bulls,1,7494389.story?coll=cs-bulls-headlines
Gordon, on the other hand, has said that the Bulls never budged from their initial offer to him, which was apparently in the $50 million “range,” whatever that means. I would also note that all the trade rumors pointed to Deng as the player the Bulls did not want to trade, and Gordon as the player they offered. So I’m not sure Paxson’s thinking is that much different from yours.
What do you think of the $57.5 million for five years for Deng? Keep in mind that Deng is still a restricted free agent next year, so the Bulls also were offering him security against getting injured in the next two years, and demanded a discount for that security. It seems pretty reasonable to me, and perhaps if Deng had shown interest the Bulls would even have gone higher. At any rate, I’m quite confident that they will eventually sign Deng, while I am not so confident that they will sign Gordon.
Kent // November 7, 2007 at 8:19 pm
Jason, great rebounding analysis.
William // November 7, 2007 at 8:35 pm
JLewis at 7:03 wins “post of the thread”.
It’s remarkable how many of these so-called flaws are explicitly addressed in The Wages of Wins. Please stop splatter-painting criticism and read the book.
APBRmetrics // November 7, 2007 at 8:43 pm
Jason Collins averaged 4.9 defensive rebounds per 40 minutes last season, about 2.0 defensive rebounds per 40 minutes less than the typical big man.
Jason Kidd averaged 7.0 defensive rebounds per 40 minutes last season, about 3.9 defensive rebounds per 40 minutes more than the typical point guard.
One would expect that the on/off differential in defensive rebounding percentage would be bigger with Kidd on the court than with Collins on the court. But it is not. The on/off difference with Collins on the court is +5.6%, while it is a smaller +4.2% with Kidd on the court.
Why does the “terrible” defensive rebounding Collins appear to have a bigger effect on defensive rebounding than the super-rebounding Kidd.
Well, Collins blocks out and is great at keeping his man off of the offensive boards and he smartly allows Kidd to grab rebounds that he could grab. Why? Because Kidd then can start the fast break.
On average, players with good rebounding numbers do improve their team rebounding, but far less than the one-for-one assumption embodied in Wins Produced.
Jason // November 7, 2007 at 9:14 pm
Of course, this is also complicated by the fact that when Collins was in the game, the Nets surrendered a higher fg% meaning there were fewer available defensive rebounds to be had as a defensive rebound requires that someone misses a shot.
In terms of a predictive metric. Wins Produced does not require a 1 to 1 replacement for rebounds and does not make that assumption. It requires something close to a 1 to 1 replacement in *overall* productivity. If Collins helps grab a higher percentage of available defensive rebounds for the team, but while on the court there are both fewer rebounds to be had and more points surrendered and fewer points scored, then the *model* holds.
Of course a *complex* model taking into consideration all rates and covariation could factor in all of this. Perhaps that would be a better model. A good question though is whether or not a a simple model captures the end result accurately enough that predictions drawn from it are accurate. It does *not* require a 1 to 1 replacement in any particular statistic for this to be true. It merely requires that on average, the statistical variation between players *in sum* (as measured by the final statistic, not variation in any one variable) reaches an answer consistent with the outcome of games. This is an empirical argument that the minutia of any one player’s single statistical category does not address. In that sense, my example of Kidd is largely irrelevant in how nicely the numbers worked out . (I had not known ahead of time that it would work so well and used him merely because “Jon” had brought him up.) The relevance was in refuting what appeared to be “Jon’s” position that a gain in rebounds would come at the expense of teammates rather than for the benefit of the team. In Kidd’s case, the benefit was indeed seen by the team, almost completely in proportion to his abilities over the average player. I do not know how often this is true, but again, refuting that the ratio of a single component is not one to one is not a refutation of the correlation for the formulaic as a whole. This is reasonable basic statistical thinking and model making, Dan. Certainly you are aware of that, no?
Harold A. // November 7, 2007 at 11:11 pm
Incidentally, why does win scored assume 1:1 relation between individual rebounding and team rebounding?
Harold A. // November 7, 2007 at 11:21 pm
Cant’ the general relation be derived from looking at plus/minus?
As a shooting guard Jason Tananski averaged 8.3 rebounds per 48 mins last year. We could look at team rebounding when he was in the game and when he was on the sidelines. His 8.3 could be compared with the back-up point guard and then we could see the impact on overall team totals. If the backup point guard had 6 rebounds per 48 mins, then we could see if Jason’s incremental performance is really worth the full 2.3 pts. this exercise only has to be done once to back out how close to 1:1 the relation should be. We could just find average across the league and then apply that relation to all players. Instead of the default of 1:1 relation which is implicitly assumed.
Jason // November 8, 2007 at 12:29 am
I suspect that some people are dreadfully confused on what a model is, what a model is for and what models do and do not do.
I don’t think that the 1:1 relationship between delta-rebounds for team and any pair of individuals *is* an is an assumption of the model at all. It’s a testable observation, not an assumption. It’s also not something that the model actually predicts, though so hanging on it is specious.
The model for disarticulating a team’s stats and assigning win probabilities to player on that team does not rely on the individual statist. It relies on the aggregate being relatively constant. And again, *this is a testable prediction,* not an assumption. If the relationship between a player’s stats and the team’s performance were not closely linked, there would be little predictive value. It does not say that replacing a 10rpg player with a 5 rpg player (all other things equal about the players stats are the same) will result in a decrease in 5 rebounds per game for the team. It predicts that the net effect will be equivalent to turning the ball over 5 more times, or missing 5 more shots, or scoring 5 fewer points *OR* grabbing 5 fewer rebounds or some combination of these things that appear, empirically, to have the same effect on the probability of victory. It predicts that if a player is replaced by another player (at the same position) who grabs 5 fewer rebounds that *if* such a replacement results in an *increase* in team rebounds (which though unlikely, could happen if indeed Mr. Replacement does box out exceptionally well) that this is likely to be offset by changes in other categories having the net effect equal to a decrease in 5 rebounds.
If this is not the case, if a change in a player’s aggregate rating is not closely linked with the sum of the team’s stats (across statistical categories–a very, very important point that it seems no one is addressing or remembering) then the absence of predictive value will so indicate. In such a case, the metric will descend towards randomness for a player over time, player movement will not have predictive value for a team’s performance and/or team efficiency will have no bearing on team record. This last point is not really debatable. Team efficiency measures *are* related to wins and losses, rather closely, so the only remaining argument is whether measures of individual player efficiency are tightly related to the team overall or if there’s significant randomness and/or ‘intangibles’ not measured. Again, this is testable. It’s not something that gets settled with the mind experiments or loud shouting about who does or does not know something about the game. It’s an empirical excercise. Noise, if the model has no merit, is to be expected, given variables of other players with whom he plays or plays against. Anecdote cannot demonstrate this either way. “logical” arguments about who a player ‘takes rebounds from’ cannot demonstrate this either way.
I am repeating myself for effect because it seems to be a point many are missing: There are empirical tests of the statistical relationship between the model and its predictions. The tests are tests of the model and how well it performs.
There are many things that can be discusses as to why or why we would or would not expect the model to be true or not. Whether or not a change in the rebounding between any pair of players will result in that same change in the team’s total is one such argument, but it’s not a test of the model. While it’s easy to *assume* that the categories will be matched one for one, this is not a requirement nor does it necessarily follow that it will be the case. Indeed if the relative value in relation to changes in the probability of victory really are so similar, it seems entirely reasonable that this could be the case (and appeared to be so with the Kidd example) .
But it’s also reasonable that the difference could appear in the team totals of some other category, divvied up amongst other players. Lousier rebounder may not decrease team’s rebound total, but the model would suggest that if this is the case, something else must be giving, like more made baskets by the other team, more turnovers, something else of equal import to the overall probability of victory. And again, this is testable with data, not with anecdote.
Repetition again: Nowhere is there required to be a 1 to 1 relationship of any *particular* statistic. It requires that the net effect of a player (which Dave is measuring via the WP metric) be relatively constant. If it is not, then the model will fall apart and have no predictive value.
Whether or not the model’s predictive value holds does not rely on a strict relationship between a player’s *single* category statistical measure. Period. Any argument surrounding the single category cannot falsify the model. Period. If the model does not hold, these arguments may explain *why* the model does not hold, why expectations drawn from the individual components do not add up to the team results, but that, again, *why* is a different issue.
It is very important to differentiate between assumptions, predictions and observations. They do not mean the same thing. Criticizing something as an assumption when it is not has little meaning.
John G // November 8, 2007 at 2:04 am
I don’t think that the Bulls place the same value on Luol Deng and Ben Gordon (at least I’d hope not). Everything I’ve seen leads me to believe that they’ll do what it takes to keep Deng, and then offer some set amount to Gordon. Honestly, the only Bulls free agent I care about is Duhon, who I hope is history at the end of this year regardless of what *any* model tells me about his performance
.
Also, “vanveen” / “jon” should have the courtesy to post his comments under the same name. I’m glad that you agree with yourself, but it doesn’t add much to the discussion.
APBRmetrics // November 8, 2007 at 2:10 am
Jason, I agree that an example does not prove anything. Feel free to contact me if you want to continue the conversation, but I am being rude by posting here.
Harold A. // November 8, 2007 at 7:11 am
Excellent post by Jason at 12:29 a.m.
Pete // November 8, 2007 at 7:44 am
I think the proverb “a bird in a hand is worth two more on a bush” tells us something here. A point is a point already in your hand. A rebound is still in sitting in the bush so it is only the probability of a point. Relative to points maybe rebounds should be weighted a bit less. That being said Rosenbaum and his acolytes are overstating their case tremendously.
MattB // November 8, 2007 at 8:27 am
APBRmetrics – Don’t go private…the comments are 50% of the reason I come here
Jason // November 8, 2007 at 9:29 am
If this is to be a predictive model, the “bird in hand” issue is irrelevant. The model gets evaluated on how it relates a metric to actual team results. At this point, the points and rebounds (and fouls, assists, blocks, etc) are all “in hand”. These are the data that are already in. The scoring is done, the rebounding is done. It’s a matter of seeing how close the stats fall to the result.
For upcoming games (the predictive part), the issue is whether or not past results, or some *aspect* of past results will predict future results. There are no birds in hand at this point. Rebounds are not assumed to be points any more than points scored in previous games are assumed to be predictors of points scored in the future. There is only the possibility that past results will resemble future results or the possibility that it will not and whether or not past individual results will correlate with future team results or not. Whether the items measured in the past are points, rebounds, whatever, is not important as they relate to the games past, decided, measured, finalized, or in the future *if* the correlation holds and that doesn’t rely on the ‘logical’ arguments about whether the point is better than the potential point. Before the event (again, the predictive part) there are no points; they are as far “out of hand” as the points that may come as a result of rebounds.
The weight of the rebound was determined by regression, how past results showed a rebound influenced the probability of the end result of a game, just as the weight of a point was determined. It wasn’t based on how a rebound was likely to result in a point, though that it does on average explains *why* a point and an rebound seem to have the same influence.
But on to the issue of the weight of a rebound: Pete, you seem to be looking at a rebound in the model only in terms of what happens in the ensuing possession, presenting it as a future point for the team that got the rebound. This is not the right way to view it, IMHO. A defensive rebound means, unequivocally, that their was a defensive stop. It means that the other team *did not* score. They get a zero when the expectation, on average, is more than that. That stop, that zero for them is “in hand” just as much as a point on your own scoreboard is. In such a case, what it’s saying is that limiting the opposition from scoring a point is the same as scoring the point yourself in terms of the relative score. It is the relative score, not any one team’s point total in isolation, that determines the outcome of a game. The only way for this not to be true would be if defense didn’t matter.
Westy // November 8, 2007 at 11:36 am
Good posts, Jason.
And this is exactly what I think the issue is. You note, “If this is not the case, if a change in a player’s aggregate rating is not closely linked with the sum of the team’s stats …”
The question I have is not in regard to the aggregated team Win Score based simply on the box score statistics, but the breakdown within it. If each defensive rebound were shared by the team, would the predictions for the team change? No, not at all. So assign each DR a value of 0.6 for the player who gets it and each other player on the floor at that time 0.1 (to reflect the fact that their defense contributed to the missed shot). The team aggregate total changes not at all, but the individual win scores do substantially. The positional adjustment would become much less.
You note that, “The weight of the rebound was determined by regression, how past results showed a rebound influenced the probability of the end result of a game, just as the weight of a point was determined. ” This makes the case that for the team it makes this difference, but not that it should be wholly attributed to one player.
Also, it makes me wonder, how is a missed shot equal to a turnover when looking at expectations for future points scored after that activity occurs? It doesn’t seem probable that each missed shot equates to -1 point future performance when some percent of them are offensively rebounded and ultimately turned into baskets. Now a turnover obviously costs you a possession. But a missed shot only costs you a possession some high percent of the time.
As you note, the statistic only works if replacing a player like Ben Wallace with a lesser rebounder means an aggregate loss of statistics across all the categories to make up for the loss in rebounds. I am not sure this has been studied well enough to show this conclusively.
At very face value, say we were GM’s running a team. The point of WS is to show us which players should be valued more. Now to some extent, statistics that are 100% accurate could be counterintuitive, but as folks who watch a ton of basketball, a sniff test is appropriate. And I wonder, if we were starting the team we are running from scratch, would we choose Tyson Chandler or would we choose Tim Duncan?
Jason // November 8, 2007 at 1:02 pm
Each missed shot *doesn’t* equal one fewer future point. A missed shot means that an opportunity that on average *would have* resulted in a point, resulted in no points. It is a -1 below the expectations. A missed shot *always* costs you a possession unless it is followed by an offensive rebound. The absolute value of an offensive rebound and a missed shot are equal (empirically), which makes sense since the board negates the miss in terms of possession changing. The cost of the missed shot is identical in terms of the change of possession to the turnover. The only difference is that with a missed shot another *tracked* category can negate the effect of the miss. There is no reason to change the weight of the missed shot. If it is followed by the offensive rebound, the weight is corrected by another tracked stat.
I agree that there are issues with attributing the whole of the rebound to a single player. However, any arbitrary departure from attributing it all to the player needs to be justified. 0.6 (and 0.1 to all others)? Sure. Numbers add up, but does it do a better job of predicting the effect of removing or inserting that one player? But why the arbitrary 0.6?
The weight is an empirical question, but it seems that people are more interested in arguing it on philosophical grounds. But I would argue that the null is that the guy who got the rebound gets the credit. And in lack of any empirical data suggesting that a different weight works better, the null of assigning the value to the guy who did the work cannot be rejected. If the answer is that weighting it does a better job of explaining variation in performance based on lineups, then the weighting is better, we can reject the null and replace it. It would change the position correction as well and there would be a new distribution of ‘wins’ apportioned on the team, keeping the sum the same. And we can test this: Does the new apportionment work as a better predictive measure for the addition or subtraction of other players? Again, this is an empirical question.
Make the model and test is. See if it’s better. No one is stopping you. It may be a better model. I suspect it *could* be a better model, that there probably is a weight that will reduce the error in the measure, though I do not know how much the error will be reduced with the change.
But here’s an important consideration: When we deviate from assigning the full value of the stat to the player credited with it, it’s also a metric that can no longer be ascertained from the box score since the box score does not report who else was on the court. Yes, these data are now being tracked, but the model becomes much, much more complex. A more complex model may be more accurate, but is this increased accuracy in any way proportional to the increased complexity in such a way that the explanatory power substantially exceeds the noise?
Pete // November 8, 2007 at 1:33 pm
Jason,
Thanks for the very good explanations. I see now where my thinking was in error.
Pete // November 8, 2007 at 2:11 pm
Jason wrote The weight of the rebound was determined by regression, how past results showed a rebound influenced the probability of the end result of a game, just as the weight of a point was determined.
I don’t understand how that would work. How do you regress points scored against Points, Rebounds, Steals, Assists, Blocked Shots, Field Goal Attempts, Turnovers, Free Throw Attempts, and Personal Fouls? Everytrhing except points drops out!!!!!!! It collapsed into the Rosenbaum residual model!!!
Sean // November 8, 2007 at 2:26 pm
I can see where this article does a very good job of breaking down the differences between the two players. I don’t know many Bulls fans that would actually argue Gordon is a better player. But I think what these sort of metrics don’t due is properly assess a players value to a certain team.
Gordon scores at amongst the best rates for a player at his position. His defensive deficiencies and lack of ball handling (point guard) skills do hurt the team. However, on a team desperate for scoring, as the Bulls are, I think Gordon has more value than he would elsewhere.
Still I think the Bulls choices on their offers was based heavily on what they predict will be a market with more players than teams with cap space next summer. The Bulls are prepared to go up around $13mil/yr for Deng who would appear to be worth it. And then prefer to sign-n-trade Gordon (who will get overpaid) and a young player like Thomas or Noah for an inside scoring presence.
Westy // November 8, 2007 at 2:26 pm
Thanks for the response, Jason. Good dialogue.
In regard to the shots/OR’s. A couple small items. From a team perspective, they offset each other, and again you’re right, the aggregate isn’t affected. But from an individual player’s perspective, he’s no better off shooting the ball than handing it to his defender. That doesn’t seem like a fair valuation. We know that he helps his team more by getting a shot up off the rim that ‘could’ be offensively rebounded. He should at least be given credit for that. One further question, is the expected value of a possession begun by an offensive rebound also still approximately 1?
In regard to DR’s. Yes, 0.6 is entirely an approximation (the math is nice, eh?). I don’t know what exact weighting would, as you say, “[do] a better job of explaining variation in performance based on lineups.” However, and I think this is why some people think WS overvalues rebounds, the sense in watching basketball is that it isn’t 1.0. Every rebound Duncan grabs off a shot that’s missed due to Bruce Bowen’s defense should in some way individually be credited also to the defense. I agree, it makes the formula way more complex. However, we now have the ability to do this, and if it is indeed more accurate, that should be readily acknowledged as a disclaimer if the more complex valuation is not used.
We know that changing the individual valuation of defensive rebounds would substantially hurt certain players’ valuation (Wallace, Rodman, etc.) and the story told in WoW would need to be adjusted. While there is no doubt scoring is overvalued in the NBA, we should not make the same error the other way.
And you’re right, I could (should?) study this myself. Unfortunately, the time to post here versus the time to gather all the data, statistical packages, etc. necessary to do this part time are not close. As you say, is it worth the increased time? Not if by pointing something out, I can influence somebody else (who is paid to do it) to study it. Ha.
Owen // November 8, 2007 at 3:36 pm
Jason – You are the champion poster of all time.
A few further thoughts.
1. DB has addressed the notion reducing the value of rebounds for a player in “Do We Overvalue Rebounds.” He said then “I kept everything the same but I lowered the impact of a rebound to only 70% the value of a point.”changing the value of rebounds does not change your results. Clearly, the issue is not rebounds.”
2. I think that simplicity is a major point. It’s very easy to make models more complex, very hard to make them simple enough to understand, and still have them work very well. What’s that line, don’t let perfect be the enemy of the good…
Also, Westy, a possession by definition cannot begin with an offensive rebound. An offensive rebound can only continue a possession already underway.
Re Bowen and Duncan, I looked at the numbers on Bowen over at 82games and it’s a bit conflicted. He had amazing defensive +/- numbers last year, +9. But the year before he hurt his team on defense, they were 2.7 points worse.. That is sort of strange. You wouldn’t think that all -world defense could flip flop so much.
I don’t doubt that Renaldo Balkman is a great defender, as his +/- suggests. But he was the best rebounding small forward in the league, had the most blocks per minute I think, and was one of the league leaders in steals per minute.
Kent // November 8, 2007 at 3:58 pm
Here’s the seminal “Do we overvalue rebounds?” post that Owen references in his 3:36 comment —
http://dberri.wordpress.com/2006/11/09/do-we-overvalue-rebounds/
Jason // November 8, 2007 at 4:16 pm
In terms of putting up a missed shot vs. handing the ball over, there is only a difference *if* you and your teammates have the ability to grab a rebound. This cannot be taken for granted, but it’s measured and credit should be awarded to those players that do it well. If you are to weight the missed shot differently from the turnover, you are devaluing the offensive rebound or taking it for granted, making the assumption that it just happens some part of the time. (And anyone who follows the Warriors knows that rebounds cannot ever be taken for granted.)
If you do not devalue an offensive rebound while lowering the penalty for a missed shot, you are making a missed shot and an offensive rebound worth something positive, when the net effect is not positive, at least in terms of the measured change in the probability of victory. Since the data do not indicate that there is such a difference, this is not warranted either.
Jon Posner // November 8, 2007 at 4:23 pm
Here is my number 1 problem with your statistics. I am not saying you or John Hollinger are right, but with your metric, each player is not the sole reason of their specific wins produced. That is why when a team total is added, it comes close to the actual, which gives your credit formula. But, for example, your statistic discredits inefficient shooters (Bryant, Gordon, etc.) Both players, if they wanted to, could shoot a lot less and become more efficient shooters, and thus drive up their personal wins produced. But then, by not taking as many shots, this would force other players to shoot more then they want (and presumably make them less efficient scorers). So by Bryant and Gordon being inefficient shooters, they are driving up the efficiency of other players. For example, if Gordon started shooting less and Deng had to shoot more, would he really still be the same efficient shooter? Highly doubtful. That is why your individual metric does not work. It is impossible to tell whether the total of the Bulls wins produced would go up if Ben Gordon took less shoots and became a more efficient shooter. What I do know is that if he were to do this, Ben Gordon’s personal wins produced would rise.
Jon Posner // November 8, 2007 at 4:25 pm
Berri, I am very interested in your thoughts on this. Surely you have probably addressed this before, but I have not read all of your blog posts or comments so I don’t know if you have.
dberri // November 8, 2007 at 4:31 pm
Jon,
About 16 months ago we looked at the link between shot attempts and shooting efficiency and couldn’t find one. It is in a post about Allen Iverson.
By the way, I think comments do work better when I don’t comment. The discussion over the last 24 hours has been outstanding. Part of that is Jason has done an extremely good job explaining Wins Produced.
Jon Posner // November 8, 2007 at 4:53 pm
just in general, to get at what i am saying, and is basically the same problem people have with rebounds. You just can’t attribute an individuals statistics, as Berri does, to themselves. Yes, Chandler is a good rebounder, but his teammates do help him. With him being known for being a rebounder, his teammates almost rely on him for rebounds. For example, if Jason Kidd played on a team with Ben Wallace and Tyson Chandler, do you think he would put in the effort to get the amount of rebounds he does? Highly doubtful. But on a team like the Nets, with a weak rebounding front court, he goes and rebounds more. But on either team, Jason Kidd is the same player. He is still the same talent. Wins Produced does not measure the talent of a player, and does not say how good a player is. It just says how much his statistics contribute to team success. In basketball, a player’s skill level is determined by more then just statistics.
Mark // November 8, 2007 at 5:02 pm
The cost of the missed shot is identical in terms of the change of possession to the turnover. The only difference is that with a missed shot another *tracked* category can negate the effect of the miss. There is no reason to change the weight of the missed shot. If it is followed by the offensive rebound, the weight is corrected by another tracked stat.
I’ve got to agree with Westy, there may be no reason to change the weight of the missed shot when tracking a team, but logic does not hold for an individual. Certainly most models (and GMs) overvalue points and overvalue rebounds, but WS always appeared to push too far the other way. Jason’s explanations clearly shows why that would be true.
This would be an obvious and easy change to the model. I’m curious if the results would satisfy most critics of WS.
Westy // November 8, 2007 at 5:10 pm
Following up once more.
Owen,
1. What I am suggesting is that DR value remain the same at the team level, but its credit be apportioned differently individually. That would mean the equation would also include, in addition to the 0.7*rebounds, a factor for other players’ rebounds. It isn’t clear to me there could be a 0.99 correlation between what extreme rebounders (those most likely overrated) rate in these two scenarios. While position adjustments would change, and players would still be ranked against an average rebounder at each position, those players whose main reason for an exceptional WS was rebounds would suffer somewhat. Everyone would move closer to average with respect to rebounds. At the least, it seems to me it would remove an error at the extreme ends of the rebounding spectrums.
2. I totally agree, the model we’re starting from is indeed ‘good’. It tells the story that we all agree says scoring is overvalued. However, we should also not stop working to improve the measure (yes, simpler is preferred but not always possible) if we can. And especially if we recognize that a certain type of player is being overrated by this system.
3. I only meant, on a possession that includes an OR, is the estimated value still ~1.0 points or does it go up or down?
Jason,
I agree, it doesn’t work with the way the equation is set up at the team level unless the estimated value of a possession with an OR changes. But wouldn’t you agree that it may break down somewhat at the individual level? Thus, the net effect is that players whose main purpose is shooting are slightly demerited. That combined with the possibility that rebounders (who shooters are least likely to be) are slightly overrated pushes the valuation askew for players on the ends of these spectrums.
dustin // November 8, 2007 at 5:21 pm
I think Jon raised an interesting point.
When DB says Player A is better than Player B, what he really means is that Player A is more productive than Player B. Talent is difficult to quantify and/or measure. Kobe may be the most talented player, but he is not the most productive.
Jon Posner // November 8, 2007 at 6:14 pm
all i am saying is, a study would not show it. if allen iverson decided to be only a spot up shooter. For example, iverson decided not to handle the ball on his team, and would take a completely different role on his team, that would certainly effect his shooting efficiency. but he has the talents to be a ball hog, and because he in fact does have that talent, by keeping the ball in his hands, and by not allowing others to shoot as much, he is in fact keep other plays wins produced up. iverson is almost taking a personal hit on his statistics to keep up the statistics of his teammates, in terms of shooting efficiency and turnovers. just the attention he draws from other defenders that are not actually defending him while he has the ball helps out everybody else. if he consistently decided he would not as much (for a long period of time), other players numbers would go down. they would be guarded closer, as there would be no need to keep an eye on iverson as much. by being a ball hog/unefficient shooter, iverson is just keeping his teammates from doing worse damage. (i am not saying he does not overshoot, maybe the team would be better off if he was a little bit less of a ball-hog. But to a certain extent for sure, his usage and him shooting helps the team
Jon Posner // November 8, 2007 at 6:21 pm
and so yea, Kobe may not produce as many wins on the Lakers as Jason Kidd produces for the Nets. But that does not mean that Jason Kidd is a better player than Kobe. Kobe is in a situation where he can’t produce many “wins” according to these statistics. He is on a team where he is forced to be a ball-hog and is forced to shoot inefficiently. It is something that is his responsibility, as he is the only player on the Lakers who can really create their own shot besides Lamar Odom, but Lamar Odom is an injury riddled inconsistent player. I think the point I am making is that if you look at dominant guards, especially while playing with out a lot of talent around them (kobe, AI on the sixers), their wins produced will not be high, and their teammates will have higher wins produced then they deserve. Iverson and Kobe in those situations are forced to do more than is reasonable to avoid their own teammates screwing up instead of them. If they were to defer to their teammates and play more of a team game, their teammates would suffer in terms of Wins Produced
Jason // November 8, 2007 at 6:25 pm
Might it break down at an individual level? Sure. It might, but what you seem to be missing is the difference between an empirical question and a philosophical one, Westy.
Yes, it’s entirely possible that giving the entire credit of a stat for WP comps to the player credited in the box score misses something. I’m sure that in some cases it does. But how much? And do the other adjustments in the formula (the position correction, the teammate correction and the ‘team defense’ correction take care of most of this? Honestly, I don’t know, but and damn is this getting tiring to type: that’s an empirical question that can be answered by looking at the model and its predictions vs the predictions of a modified model. Speculative notions that the weights are wrong is just that: speculative notions. Saying that an adjustment at the extremes of rebounding abilities would reduce error assumes that there’s error at the extremes of rebounding ability. It presupposes the error but does not demonstrate such error. Saying that the model overrates a particular type of player is subjective without data indicating that these players are not really worth what the model says they are. Do you have evidence of this? Saying that the model is unfair to the designated scorer also presumes that their value must be higher. Shooters who just shoot and don’t do anything else *are* penalized. This penalty is only a problem in the model if a player’s inability to do anything else doesn’t hurt the team because others really do compensate for this. Again, do you have evidence of this?
Jon: your notion that Gordon shooting less to improve his own FG% would lower the FG% of others seems to suggest that the team has already found the optimum distribution of shooting, such that deviation from it would result in at best neutral if not less productivity overall. There’s not actually any evidence of this. It seems similar to the faulty argument that players just take rebounds away from teammates, that the optimum has already been found here as well.
While you can speculate that Gordon could easily shoot less and shoot better accordingly and speculate that others would certainly shoot worse as a result, be aware that you are speculating. This is quite a different thing than providing evidence. Again, there is a difference between empirical and the hypothetical.
As to the team stacked with rebounders: Dave *has* addressed this by noting that there is a diminishing returns issue. This is a known phenomenon (call it a problem if you wish) that may interfere with the predictive abilities at the high end. For the overall evaluation of the model as a useful tool, what is needed is some quantitative measure of how often this happens and how much it skews predictions. If the answer is “not much” and “not often” then it’s not enough to reject the model. It’s a word of caution for a team loaded with rebounders thinking they’d get full benefit from adding another one, but it doesn’t invalidate the model nor does it suggest that ‘correcting’ across the board strengthens the model across the board.
Dustin: what definition do you use for ‘talented’ then? Seems like if talent and productivity don’t mesh, talent doesn’t mean much. It ain’t a dance contest after all.
Jon Posner // November 8, 2007 at 6:34 pm
This is my last point, and I realize what I write is hard to understand and I am not doing a good job of getting my point across. When you look at a player like Tyson Chandler, his best skill is his rebounding. He is extremely limited offensively and he knows this. There is no point for him to save his energy on the defensive end for offense. So you better believe when the shot goes up, he is busting his ass to get that rebound. The same with Ben Wallace. The fact is, rebounding is just not as hard a skill as scoring. If Kobe Bryant wanted to, I believe he could be the best rebounding guard in the NBA (maybe except Jason Kidd). But if he spends all his effort trying to rebound, he is not maximizing his skills or doing what is best for the team. The team needs him to be a scorer, because simply no one else has his capabilities or talents as a scorer. This has to be considered when looking at the type of player he is. Rebounding just simply isn’t as hard as scoring. Scoring takes a lot of skill, and thus the best player on each is team is almost always the scorer. That is why scorers are paid the most. (I am not saying anybody could average the amount of rebounds that Chandler does, but in terms of actual difficulty, what Kobe Bryant is able to accomplish is much more difficult.)
dustin // November 8, 2007 at 6:41 pm
What do analysts/announcers mean when they say talented? Everyone has a different definition.
Outside of basketball it is easy to distinguish between talent and productivity. Talent is your ability, productivity is how you use it.
dustin // November 8, 2007 at 6:44 pm
Jon why do you think rebounding is easier than scoring.
IMO scorers are paid the most because it is easy to see its effect on winning games, i.e. you can’t lose a game if you score more points than the opposing team. You can lose a game if you outrebound the other team.
Jon Posner // November 8, 2007 at 6:51 pm
Productivity (wins produced) does not necessarily mean you are a good basketball player. All it shows is that given the circumstances, this is how your statistics effect the team as a whole. I will say, I have no statistical proof, but what Kobe does for the Lakers goes beyond his Wins Produced and statistics. It is also shown in the Wins Produced and statistics of his teammates. Basketball is a team sport, and I just don’t think wins can be individualized. What each player does on the court has an effect on each other, and I really don’t see how it is possible to decide who gets credit for the wins. I think this is proven right when Tyson Chandler is ahead of Tim Duncan. Who would you rather have on your team Jason, honestly? Chandler or Duncan?
Jon Posner // November 8, 2007 at 6:59 pm
Have you every played basketball? Putting a ball in a hoop while being guarded is much easier then catching a ball while being guarded. This is just simple, obvious knowledge. Desagan Diop is the perfect example. The guy had not played basketball really in his life until high school and clearly does not have many basketball skills. But right away he was able to learn rebounding. Because simply, there isn’t much to it. Use your body, thats about it. How has Diop’s scoring come along though in his learning curve of playing basketball?
Jon Posner // November 8, 2007 at 7:05 pm
and on the last note, i meant putting the ball in the hoop is harder
Harold A. // November 8, 2007 at 8:18 pm
Jon, If rebounding is so easy why doesn’t everyone do it? Also, inefficient point scoring does not help the team. there’s one thing everyone can do it and that is throw up shots and make only a small percentage!!!!!!!!
Harold Almonte // November 8, 2007 at 8:36 pm
As it was discussed time ago, these linear metrics suppose that the act of rebounding doesn’t have a cost, the cost is the opponent ofensive rebound, but nobody is penalized by that, scoring have a cost when an attempt is failed, but others stats supposedly not. If your man takes a rebound, you are not penalized.
Rebounds are part of the defense of the possession, the final part, not all the defense. when you regress to win, rebounds just take all the credits of the FGMissed, because the other defensive part (teammates part) is not boxscored.
There’s a relationship between DR and OR, given their probability of accomplishment, that makes DR less valuable than OR in about 2/3. This is another way to reach the belief that DR are not worth a whole possession (1 point), and even must be regressed apart. To say a DR=OR=R is an overrating.
Jon Posner // November 8, 2007 at 8:36 pm
Not true at all. I already said why Kobe does not try to be the best rebounder. He can’t waste his energy. And if anybody palyer on the lakers attempted to shoot as much as Kobe, I GUARANTEE they would much, much, much, less inefficient. Considering how much he shoots, he is fairly efficient. The more one shoots, inevitably the lower his percentage becomes.
Jon Posner // November 8, 2007 at 8:49 pm
here is an idea to adjust shooting efficiency- just throwing it out there, tell me what you think (and i am not a statistician and would not know exactly how to do this) … to compare Kobe’s shooting efficiency to Tyson Chandler’s is just unfair… Shooting efficiency should either be compared between only positions, or how much you score relative to your teammates. For example, Kobe’s shooting efficiency would only be compared to other shooting guards, or only to other leading scorers for teams. I think this might give people a better gauge of how well they shoot. Volume should be included when talking about how efficient someone is. It is a lot easier to go 1/1 then 25/25….
Jason // November 8, 2007 at 9:01 pm
Jon, you should be aware that your insistence that scoring is harder than rebounding is supported only by supposition. It is not a “fact” as you pretend it is. Your arguments would be better served if you learned the difference between fact (0r even evidence) and opinion.
I’m curious why you consider a guarantee that’s based entirely on your assertion to be worth anything at all. You appear to know that all things are not only as they already are, but it seems that no changes could possibly make things better. That’s a peculiar and lofty power there!
Sam Cohen // November 8, 2007 at 10:46 pm
I think Jon is trying to make the point that Dean Oliver makes in his book “Basketball on Paper.” In chapter 19, The Problem with Scorers, he includes a number of graphs showing how it appears many players have a better offensive rating (loosely speaking, offensive efficiency, but he defines it slightly differently) the lower the percentage of a team’s offensive possessions they use. Thus, players that can maintain high efficiency while also using a higher percentage of a team’s possessions help the team the most–both because they are doing well individually and because they are allowing their teammates to operate on the part of their “skill curve” that maximizes (or at least increases) their offensive efficiency.
I’m curious to know if the WoW look at efficiency vs. shot attempts looked into this aspect of the efficiency rating. (I’m not sure if a shot per minute analysis would get at this, although it seems like it might; I’m guessing that a shots per possession analysis would probably be better, but also be much harder to find the data for)
I have no idea how difficult it would be to add this “adjustment” to the model. I also have no idea if the same basic concept would be applicable to rebounding or other measured statistics.
Jason // November 9, 2007 at 12:08 am
I don’t doubt at all that there are players who, for whatever reason, do better as low-volume shooters than high volume shooters. What I doubt is that we routinely see teams performing at the top of their efficiency curve. Would the Lakers be better off if Kobe shot less? Dunno, but the assertion that they’d do worse if he shot less is that: an assertion.
The ad-hoc explanations for why a player shoots as much or as poorly or as well based on other players are just that: ad-hoc. This doesn’t mean that they’re wrong, but it does mean that they aren’t systematic analyses.
Guy // November 9, 2007 at 4:12 am
“Would the Lakers be better off if Kobe shot less? Dunno, but the assertion that they’d do worse if he shot less is that: an assertion. ”
Not really: http://www.82games.com/pelton13.htm
Westy // November 9, 2007 at 8:25 am
I suppose I can proffer one more comment.
Jason,
Of course what I’m suggesting is speculative. It requires empirical testing to show whether it’s a hypothesis with any validity. That said, I’m not convinced that the way it is has been shown accurate either. You say, “Speculative notions that the weights are wrong is just that: speculative notions. Saying that an adjustment at the extremes of rebounding abilities would reduce error assumes that there’s error at the extremes of rebounding ability. It presupposes the error but does not demonstrate such error.” But isn’t it just as much a leap that the weights are exactly right the way they are right now? You’re presupposing that there isn’t an error at the individual level.
Okay, I will just say what I would begin with if I were reformulating the weights more towards what we should expect them to actually be:
Obviously DRs and ORs need to be split at the individual level.
A player’s valuation would include a factor of 0.6*DR plus 0.1*(other DRs while they’re on the floor). As well, each player would get 0.9*OR plus 0.1*(the shots they took that actually resulted in an OR). Missed shots would still be -1.0. This would reward players who take the kind of shots that actually result in ORs not just every shot attempt. Now, might the values instead be 0.7, 0.075 and 0.95, 0.05? Maybe, but shaking that out would be a valuable upgrade to the WS system.
Note that the team valuations remain the same and the ability of the team totals to predict wins remains unchanged. The goal of this would be to improve the individual rankings based on WS.
I like the WS system and its simplicity. But this change, while adding mild complexity, would seem to greatly add to the individual predictive power. Sure, the ’story’ might not be as interesting if Iverson and Bryant were rated slightly higher and Wallace and Rodman and Lee slightly lower, but might it be more accurate?
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Jon Posner // November 9, 2007 at 9:21 am
I understand Jason, I understand that you don’t believe anything that isn’t proven in statistics, but come on… have you ever played basketball? I mean, it is just simple knowledge that it is harder to score the ball than rebound the ball. That really isn’t going out on a limb here at all. And if I wanted to prove that statistic I suggest looking at the top scorer and top rebounder and see how many players are within 25% of the leader. My guess is you will have a lot more rebounders than scorers that are within 25%. This is because scoring is harder, and the ones who master scoring are truly above everybody else. Rebounding, on the other hand, really isn’t that hard of a skill to attain, and thus, it is easier to get within the top 25%
Owen // November 9, 2007 at 9:33 am
Westy – Mild complexity? This would add enormous complexity. I can go the Knicks box score and calculate WS for every player in about three minutes. I can’t do that with your system.
As i pointed out, Berri has said that changing the value of all rebounds to .7, i.e. the “Kaufman inspired formula,” wouldn’t change the ratings of players (.99 cor). It seems like if this is the case, what you think DB should do, for fairly arbitrary reasons it seems to me, would be an incredible amount of chewing for not a lot of meat.
And actually, given the a player like Kobe is a much better rebounder than other guards, it might actually hurt his rating. Really, the only player this adjustment would help would be scorers who don’t rebound well.
At the end of the day, I am sort of puzzled that you want to go to such great and arbitrary lengths to show that David Lee and Ben Wallace are not as valuable as the data indicates according to DB. David Lee had a better plus minu than Kobe last year, by a good margin. And I think it’s pretty clear, even after four games, what the difference between last year’s Ben Wallace and this year’s version means to the Bulls.
Jon – “it is just simple knowledge that it is harder to score the ball than rebound the ball.”
Alright. I very much doubt you are correct. But do a study and demonstrate it empirically. You can post it at APBRmetrics and get feedback, then post a link here so we can look at it.
Jon Posner // November 9, 2007 at 9:46 am
I don’t think you understand what I mean by “harder”. I mean in terms of literal skill it takes to score a basket, or get a rebound. If anybody here on these comments have played basketball before, they will attest that the skill it takes to score a basket is greater than the skill it takes to rebound a ball. And I have never done a study and don’t know how to, I just read all the studies that you guys do.
And Owen, then you state, “Mild complexity? This would add enormous complexity. I can go the Knicks box score and calculate WS for every player in about three minutes. I can’t do that with your system.” So what ??!! You should not favor a basketball statistic because it is quick and easy to calculate. You should favor it because it is more accurate. Whether or not it is more accurate, I don’t know. (Personally I agree with him and think that is a good adjustment, but then again I am not a statistician and don’t know much about statistics) So if this could potentially bring more accurate results, then you should be in favor of it. That is the goal, correct?
And it is not arbitrary reasoning. His statement is that the rebounder should not get full credit for his rebound. His teammates have an effect on him getting that rebound and thus deserve credit for it. Do you disagree with that?
Jon Posner // November 9, 2007 at 9:54 am
and how would changing a rebound to .7 not effect the ratings??? maybe somebody could link to where berri said this so I could read it or jason or maybe even berri himself could explain how a change in his formula would result in the same outcome
Guy // November 9, 2007 at 10:14 am
“As i pointed out, Berri has said that changing the value of all rebounds to .7, i.e. the “Kaufman inspired formula,” wouldn’t change the ratings of players (.99 cor).”
That doesn’t show rebounds aren’t important, but just the opposite: because the WS rating is so dominated by rebounds to the exclusion of scoring, changing the rebound coefficient doesn’t make much difference. Relying on WS ratings at NBA Babble, and looking at players with more than 1000 minutes, I get these correlations for Win Score:
Rebounds .90
Points .63
FG% .51
Jason // November 9, 2007 at 10:22 am
Jon, when you make a statistical argument, you might want to actually check things before just spouting out nonsense. For minimum games/minutes played to qualify for the scoring rebounding title last year: The top per minute scorer last year was K. Bryant (37.1/48). 75% of this is 27.825. 18 players scored within 25% of his total. The top per minute rebounder was Mutumbo (18.1/48). 75% of this is 13.576/48. 20 players were better than that.
Hmmm, so “many more players” were within 25% of the rebounding leader than were within 25% of the scoring leader means 2 more players. 2=many? Really?
No, there’s not really any more evidence for your statement that “rebounding is easier” based on your statistical conjecture than there was based on your blanket statement from personal experience. Yawn. Please do try to think about what you post before posting, Jon.
You did say one thing that was true though. You are not a statistician and you do not understand statistics. It is peculiar then that you spend time criticizing a statistical model.
Jon Posner // November 9, 2007 at 10:48 am
If you look at my post, I said I would guess there would be many more. I did not know what the outcome would be. You did the work and proved me wrong. (2 is not enough).
Owen // November 9, 2007 at 12:09 pm
Guy – What happens if you do it for PawsMin?
Regardless, WP is not simply a measure of how well a player rebounds, which I think is what you seem to be suggesting.
Jon Posner // November 9, 2007 at 12:22 pm
My question for Jason, Owen, or anyone who wants to answer. Do you believe players effect other players ratings? Is there a test that could be done that could prove this one way or another?
My belief is that Kobe Bryant raises the WP of his teammates. Maybe not all of them, but in general, because of Kobe Bryant, other Lakers WP is higher. I don’t have statistics to prove it, and am asking someone if they can prove or disprove it. Maybe the WP of Lakers with Kobe on the court vs. Kobe off the court? Is that possible to calculate?
Guy posted this article earlier- http://www.82games.com/pelton13.htm
This is basically what I am saying, but not in terms of Wins Produced.
My biggest problem with WP is that what a player brings to the table for a team is not only shown in his statistics. It is shown in the statistics of others. Basketball is a TEAM game.
Joey C. // November 9, 2007 at 12:29 pm
Jon, I like plus/minus but what if Kobe’s backup really stinks. Kobe’s plus/minus would be inflated. Useful info to have if you’re Phil Jackson and know that Kobe should get the bulk of the minutes because of how the team suffers when he’s off the court. However, it’s tricky to gauge how useful that information is for another GM considering trading for Kobe. Is plus/minus or wins produced more transferable? Statistically testable but I’m not sure. Either way, no one is saying you have to look at these measures in isolation. Both might capture somethign the other doesn’t so to evaluate a player you’d want to look at each measure in the context of the other.
Joey C. // November 9, 2007 at 12:32 pm
Did the 76ers team shooting % go down after AI left last year?
If Iverson’s low shooting % was explained by his “selflessly” taking the bulk of the shots b/c his teammates would do even worse, than the team shooting % should have gone down after AI left. If dberri is right, the team shooting % should have gone up. Which was it?
Owen // November 9, 2007 at 12:43 pm
Jon – This is a question that is addressed at great length in the book, The Wages of Wins, and in many posts on this blog. DB’s answer has always been yes, players affect other players. The law of diminishing returns applies in basketball for instance. Putting Rodman on a team will reduce his teammates rebounds somewhat.
However, he thinks this effect is fairly small, and that people may exaggerate interaction effects beyond what the data suggests is realistic. Basically, most of the value in a player is in his own abilities, not in those of his teammates. The major test of this is that when players switch teams or teammates, their statistics don’t change very much. Obviously, there are exceptions, but as a general rule it works very well. If Tyson Chandler and Eddy Curry were to switch teams, their rebounding numbers are not going to change much. Players are what they are, for the most part.
Basketball is a team game. That is what I love about it. However, right now, in the NBA, there are massive incentives for players to score more and shoot more. In my mind, this makes the NBA today much less of a team game than it used to be.
Another way of saying that would be, if players in the NBA were compensated according to Wins Produced, it would be a much more team oriented game. That actually, ultimately is what is most exciting about WP for me. If it catches on, it might make the NBA much better to watch, That’s my opinion only of course.
You do seem curious about basketball and statistics. I would definitely recommend getting the book. It might be very interesting for you. Berri and his co-authors make their case much better there than we can in a comment thread.
Joey C. // November 9, 2007 at 12:45 pm
I second Owen’s book recommendation. Wages of Wins was eye-opening for me and changed the way I watch basketball.
dustin // November 9, 2007 at 12:50 pm
Dberre was right about their wins. Why does it matter if he is right about their shooting %.
Oren // November 9, 2007 at 12:54 pm
Joey C,
I’m not sure that’s necessarily the case. Don’t forget that the 76ers received Andre Miller instead of Allen Iverson.
Perhaps Andre Miller simply does a better job passing the ball then Allen Iverson did. And that makes the Philly players more effective.
Now the interesting thing about AI is that while it seems he’s taking fewer shots as a Nugget, it doesn’t seem to me like his shooting percentage is improving(it’s a bit worse but he’s taking more threes so it evens out), nor are his assist numbers improving.
Joey C. // November 9, 2007 at 1:01 pm
dustin wrote Dberre was right about their wins. Why does it matter if he is right about their shooting %
Dberre was right about their wins. That’s one data point. Given randomness, confidence intervals surrounding predictions, etc. it’s not like you can take one data point and then generalize that the theory is confirmed. If the wins changed for the reasons Dberre said the wins would change, it would be even stronger proof. Still just one data point but more difficult to make that prediction accurately and capture the specific elements.
Joey C. // November 9, 2007 at 1:03 pm
Dustin, to take an extreme example, what if Dberre had been right about their wins but only because the coach changed the minutes of bench players and with those increased minutes they did better than the starters had been doing. (This isn’t what happened but just makes the point that the specifics of the forecast can be relevant to evaluating it.)
Kurt Gehlen // November 9, 2007 at 1:03 pm
Much of Jon’s complaint seems to center around the fact that it seems easier to learn to rebound/block shots than to shoot/score. I tend to agree, but whether a skill is learned or inherent is irrelevant. Defense and rebounding may be largely a function of inherent characteristics, i.e. height, strength, leaping ability as opposed to how many hours you spend in the gym, but this doesn’t matter. To use his example, Desagana Diop is 7′ tall, something Kobe can never hope to be.
Jon Posner // November 9, 2007 at 1:05 pm
Owen, I plan on getting the book, but just wondering before I read, does he prove that players do not have much of an effect on each other, or does he just believe it?
Joey C. // November 9, 2007 at 1:06 pm
Jon, he offers some statistical support. He doesn’t just arbitrarily believe it. Trust me, the book is worth reading. That doesn’t mean I agree with everything in it. But it is very, very interesting and thought-provoking.
Joey C. // November 9, 2007 at 1:09 pm
Oren, you wrote to me Perhaps Andre Miller simply does a better job passing the ball then Allen Iverson did. And that makes the Philly players more effective.
I agree. However, if you look at a broad data sample instead of just this one switch than I think my hypothesis could be tested the way I toulined. On average, the incoming player wouldn’t necessarily be a better passer. That kind of stuff would even out across a sample of all players traded, switching teams thru free agency, etc.
dberri // November 9, 2007 at 2:07 pm
Okay, we are at 95 comments. 96 counting my comment. All we need is four more and we will hit triple digits on this post.
By the way, I am going to recommend The Wages of Wins. In the editing process, both for the hard cover and paper back, I read it many, many times. I can’t say it was still great after I read it more than a dozen times. But it was still pretty good after three or four reads. Certainly it is worth reading just once.
Pete // November 9, 2007 at 3:14 pm
Joey C.,
Wouldnt’ the simpler and more elegant test just to be to take Iverson’s performance each season at Philly and check for a correlation between shot attempts and shooting percentage. (There might be tricky selection bias issues– i.e. he shoots more on days when he’s shooting better — but there would be ways to plausibly control for this I think.)
Pete // November 9, 2007 at 3:17 pm
For the Iverson test I just proposed, I implied but should have written explicitly that we would look at shot attempts and shooting % game by game. And look at it each season to control roughly for a consistent supporting cast.
dberri // November 9, 2007 at 3:41 pm
Pete,
This post might answer your question. Marty wrote this in June of 2006. Basically he looked at the link between shot attempts and shooting efficiency. He failed to find much of a relationship.
http://dberri.wordpress.com/2006/06/11/the-law-of-diminishing-returns-in-the-nba/
Pete // November 9, 2007 at 3:58 pm
Dr. Berri, thank you for the link.
It has a very good empirical answer to my question (“Wouldnt’ the simpler and more elegant test just to be to take Iverson’s performance each season at Philly and check for a correlation between shot attempts and shooting percentage”):
“Iverson took at least five shots in 663 games. Just like Kobe, we find a significant and POSITIVE relationship between shot attempts and field goal percentage. Again, the more he shoots, the better he shoots. And when we look at games where he took at least twenty shots we again find no significant relationship at all. What does all this tell us? The story that shot attempts and shooting efficiency have a negative relationship is not in the data.”
dberri // November 9, 2007 at 4:32 pm
Pete,
Glad I could help. By the way, your comment was #100.
Jon Posner // November 9, 2007 at 5:31 pm
i disagree with this test. of course, if you were to look at iverson and bryant they would shoot better the more they shot. that is because there is no limit to how much they can shoot, and when they are “feeling” it, they would shoot more. but say for example, Iverson was told by George Karl, you are only taking 10 shots a game. After that, you are getting pulled. And Iverson did this repeatedly not by choice, but because the coach was dictating him so. I have a hard time believing that if that were the case, Iverson would shoot the same percentage he shoots now. That is where diminishing returns works. As a lead player on his team who handles the ball and is the leading shooter, that is how Iverson shoots. If Iverson were strictly say a spot up shooter, his shooting % would almost certainly go up. Don’t know if I am exlpaining myself well, but I hope I am getting my point across.
So if my assumptions were correct (we will never find out because Iverson will always be a dominant, ball-handling guard), Iverson would be a more efficient shooter when he takes less shots.
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Joey C. // November 9, 2007 at 5:51 pm
Jon,
The way I would control for this is to look at cumulative shot attempts for the game after each quarter. For example, if Iverson attempted 4 shots in Q1 and 15 shots in the game this would be recorded. Let’s pretend this happened in game 1. In game 2 Iverson attempts 15 shots in the first half. He does this because as you would say he is “feeling” it. He wins up attempting 32 shots for the game. The shooting percentage for all of game 1 could be compared with the first half shooting percentage in game 2. If your hypothesis is correct, the shooting percentage in game 2 should be higher. If the study Pete mentions on disproved diminishing returns is correct in the assumptions underlying the conclusion, then the shooting % in H1 game 1 and full game 2 would be about the same.
Joey C. // November 9, 2007 at 5:55 pm
In the example I just gave, if the shooting % in H1 game 1 and full game 2 would be about the same, then this would be very strong evidence against the notion that shooting percent materially drops as more shots are taken. As it is, I found this study– http://dberri.wordpress.com/2006/06/11/the-law-of-diminishing-returns-in-the-nba/ — to be reasonably convincing. (I say only “reasonably convincing” b/c of the possibility that a player attempts more shots in a game against weaker competition. The way the study is conducted implicitly overlooks this.)
Kent // November 9, 2007 at 6:30 pm
Joey C., interesting proposed methodology. Are statistics broken down by quarter (per game) available anywhere on-line?
Guy // November 9, 2007 at 7:42 pm
Kent/Joey/Pete/Jon: The argument for high-volume shooters is NOT that their efficiency falls when they shoot more. As Kevin Pelton wrote about Marty’s post: “this result is neither surprising nor inconsistent with a theory that players lose efficiency when they take on more possessions. When a player has a favorable matchup or simply a hot-shooting night, his teammates are likely to get him the ball, giving him more shots. He’ll also likely play more minutes, meaning more shots if you don’t adjust for shots per minute played.” http://www.82games.com/pelton24.htm
Indeed, this would be a bizarre argument to make in defense of players like Bryant, since the obvious implication would be they should shoot less!
The actual argument is that if these players cut back on their shooting, the players who take the shots in their stead will not be more productive. The notion is that many of the low-volume shooters look good now because they get to “pick their shots” and because the shooting star draws the best defenders and double-teams. But these same low-volume players would be much less efficient if forced to take more shots. Now, I don’t know if this is true. To answer this question you have to study what happens to the supporting cast when star shooters aren’t in the lineup (since they likely won’t agree to cut their shot attempts in half for our experimental purposes). Pelton’s article on Kobe shows it was true of one team in one season, but that doesn’t prove much by itself. Looking at more players and seasons would provide the answer.
However, Marty’s study isn’t even responsive to the argument, much less convincing.
dberri // November 9, 2007 at 8:54 pm
Guy,
Marty was addressing this proposition: Allen Iverson shoots poorly because he shoots so much. The proposition tells us that there should be a negative relationship between shot attempts and shooting efficiency. Marty studied the data and failed to find that relationship. So he was exactly responsive to the argument.
Okay, enough on that. I have a question for you.
You have posted many comments here, as well as at Sabernomics and at The Sports Economist. In general you have commented on someone else’s research. All of these comments lead me to wonder — is there a Guy Washington blog out there someplace? Or some place you are publishing your own studies? And what specifically have you studied? Okay, that was three questions.
RJ // November 9, 2007 at 8:54 pm
If Ray Allen continues to take far less shots this season in Boston than his Sonics past he might be an interesting case for the efficiency/usage discussion. In the initial games his FG%s are way up while taking a third less shots.
Joey C // November 9, 2007 at 9:41 pm
Guy writes “To answer this question you have to study what happens to the supporting cast when star shooters aren’t in the lineup.”
Isn’t that what plus/minus is doing among other things?
Also, I think it was worthy of study and interesting that shooting percentage does not drop with shot attempts.
What you suggest is interesting too (that players w/ low shooting % might still be helping team if other players would have even lower shooting %), but I think a non sequitur to the discussion we were having.
How about this, though? If Iverson’s shooting % is lower than his teammates, then he isn’t helping the team with the incremental shots he is takign? And, yes, maybe he’s drawing a double team. This is why looking at a variety of statistical measures is good. If you look at both plus/minus and wins produced together you’ll have a good picture. I would not want to look at just the former, though. Plus/minus captures some of the player interactions and intangibles. However, as already argued on this thread, your plus/minus would be inflated if your backup is terrible.
Joey C // November 9, 2007 at 9:46 pm
No single statistical measure will capture all interactions. Some people keep flocking to these comment threads and saying over and over again that wins produced doesn’t capture “boxing out,” etc. I don’t really think any statistical measure does. Nor do I think it’s debunking these statistical measures to point out that they aren’t perfect represenations of reality. No model is. A model, though, can distill a lot of information. There’s lots of studies of how statistical algorithims are much better for predictive purposes than human judgment. And no one is saying you have to use any of these statistical measures in isolation. As I wrote before I like plus/minus but wouldn’t want to to use it in isolation. The same thing for wins produced. IMHO wins produced is the best measure for aggregating conventional box score statistics.
Joey C // November 9, 2007 at 10:06 pm
RJ, I’m not sure I’d use Ray Allen as a case study. Switching teams introduces a bunch of factors that change. You are trying to gauge the effect just of amount of shots + shooting % so you want to isolate just that variable.
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Pete // November 9, 2007 at 11:47 pm
Guy:
You say “Indeed, this would be a bizarre argument to make in defense of players like Bryant, since the obvious implication would be they should shoot less!”
This is a tricky one b/c if a player shoots a lot and has a low shooting percentage you’re saying he’s valuable if the surrounding teammates would have even lower shooting percent. That means that player is very valuable to that team. However, how good is that player? His value would be less to other better teams. Wins produced actually captures the drop-off in shooting whereas plus/minus and looking at points scored in isolation (the Rosenbaum approach) would not.
Pete // November 9, 2007 at 11:49 pm
(Of course Guy might reply to me that a player on a bad team could benefit with a higher rebound total and wins produced will get “fooled” by that. )
Kent // November 10, 2007 at 12:40 am
Pete,
With regards to your last point, there aren’t a finite number of rebounds to be obtained. (Technically there are but since the opposing teams is getting so many rebounds, the rebounds of a given team can expand quite a bit.) There are, however, a finite number of shots that can be taken. So it’s no the same thing. In other words I’d be more comfortable thinking that a player’s hi rebound total from one team could transfer to another (thereby increasing the new team’s total rebounds) than I would be assuming that a player’s hi inefficient shot attempts for one team would lead to more points scored by a team he switches to.
Pete // November 10, 2007 at 9:34 am
Kent, Good point. Thanks much for the feedback.
RJ // November 10, 2007 at 10:22 am
Of course changing teams affects things and this one case especially with that wouldn’t carry an argument but it will be interesting to see what happens with Allen. It is rare that a 20+ shot guy reduces shots dramatically in one year while presumably healthy- if that happens. But it is real early and Ray might go back more to old habits. What happens with Pierce will be checked as well.
Harold Almonte // November 10, 2007 at 11:02 am
Every basketball statistical action must have a credit, if you succesfully accomplish it, and a cost if you fail and it costs a lost of possession (I’m not sure when a teammate takes the OR, The fail shooter must be full punished). In this area scorers are the most suffered, because are the only one who are individually punished. Defense, more than fouls, are punished collectively.
In another blog somebody said that in basketball the risks are not distributed the same among all the players, and you will see that generally SGs have the lower +/- on their teams, or lower than the common sense says to you, but this is difficult to take out with a formula without making a lot of factors (more than just position factor) which define and fairly weight the different skills and responsibilities on the floor, and it must start with a better analysis of “scoring and defensive usage” distribution, and the individual cost of that away from the collective, or TEAM win. A better balance between individual punishment and team punishment.
Kent // November 10, 2007 at 11:17 am
RJ, I wonder what the record is for largest improvement of a team from one season to the next. I would think the Celtics could be strong contenders to break that record. (They switched a lot of the roster so it’s not even a meaningful record but still interesting trivia.)
Kent // November 10, 2007 at 11:18 am
Harold A, are you saying that some of the coefficients in wins produced should maybe be transferred from the individual to the team?
Harold Almonte // November 10, 2007 at 11:27 am
What it’s knowed is some players are obligued to take the most risky actions and the relative negative stats, making their teammates statistically better, relative to that action. Ballhandling and boxing out are just two of them.
Kent // November 10, 2007 at 11:50 am
Harold A., Interesting. Plus/minus would presumably capture ballhandling and boxing out, right?
Of course plus/minus then introduces a lot of other noise.
But what if plus/minus was used in conjunction with wins produced? Implicitly are you saying that very good plus/minus and medicore wins produced means box score statistics aren’t fully capturing how good the player is?
If so, I think I agree. Looking at the 2 measures together seems like it could be very powerful for predictive purposes.
Kent // November 10, 2007 at 11:51 am
Harold A., Interesting. Plus/minus would presumably capture ballhandling and boxing out, right?
Of course plus/minus then introduces a lot of other noise.
But what if plus/minus was used in conjunction with wins produced? Implicitly are you saying that very good plus/minus and medicore wins produced means box score statistics aren’t fully capturing how good the player is?
If so, I think I agree. Looking at the 2 measures together seems like it could be very powerful for predictive purposes.
Kent // November 10, 2007 at 11:53 am
It’s just that plus/minus seems to measure how a good a player is for one particular team. I’m not sure how well it would translate to a different team.
Harold Almonte // November 10, 2007 at 12:09 pm
It’s just probably that plus-minus is biased depending on wether you play in a very good (a lot of +), or very bad team ( a lot of -), and your play time ( a lot at the + side, or the – side). Or maybe adjusts doesn’t adjust enough.
But the team win regression of stats is okay, but I think an individual/collective regression of each possible stat (boxscored or not) must be made first. And I’m trying to say rebound is not an act of one.
Harold Almonte // November 10, 2007 at 12:34 pm
Neither it’s scoring (assisted or supposedly not assisted), nor failing without failing assistance, nor stealing a previously lost or deflected ball, nor is succesful (more than virtual) a block in terms of possession until a teammate grabs the ball, nor defending better because you got let to switch to a better matchup, etc.
Harold Almonte // November 10, 2007 at 12:39 pm
How much percentage of individual and how much of teammates and context have each stat.
Kent // November 10, 2007 at 12:52 pm
Harold A, Understood. But wins produced is still unbiased if there aren’t players that consistently benefit disproportionately from their surrounding teammates. In other words, 10% of steals might be the consequence of a ball deflected by a teammate. But if that 10% is randomly distributed then wins produced is probably fine in not attributing that to teammates. Maybe players with a lot of steals are still overvalued, but if this team element is also randomly dispersed across the other s tatistics, then similarly it wouldn’t introduce bias. It’s really a matter of how good of a model approximation is to make these assumptions. So you’re arguing for alterations in the wins produced weightings to reflect team performance? Seems reasonable.
Kent // November 10, 2007 at 12:54 pm
BTW, this blog post from Mark Cuban implies that the Dallas Mavericks — at least internally — track deflections– http://www.blogmaverick.com/2005/11/02/i-love-this-game/
Guy // November 10, 2007 at 1:18 pm
Kent:
Here’s one effort to adjust plus-minus in order to control for quality of team-mates and other factors: http://82games.com/ilardi1.htm
**
“What you suggest is interesting too (that players w/ low shooting % might still be helping team if other players would have even lower shooting %), but I think a non sequitur to the discussion we were having.”
Joey (if you’re still out there): it was a non sequitor to the discussion, but not to the underlying issue. The issue raised by Pelton and others is whether a different (lower) break-even efficiency standard should be expected of high-volume shooters. They are saying, in essence, that it’s harder – and thus more valuable – to shoot 50% when taking 30 shots a game than 10 shots a game. The corollary is that if high-volume star shooters took fewer shots, the players who took those shots would be less efficient then they are now. (Whether they are less efficient than the star shooter depends of course on the specific players in question.)
It does not follow from this that players who take fewer shots will have higher efficiency, because they tend to be less talented shooters; it also doesn’t follow that star shooters will shoot better in games they take few shots, because of the factors causing them to take fewer shots (superior defense, injury, etc.). I’m sure someone, on some blog, has made these claims (as can be said of all claims), but it is not the argument made by serious analysts like Pelton and Rosenbaum. And again, I don’t know if the argument is right or not. But looking at the correlation of shots and FG% doesn’t give us the answer.
Harold Almonte // November 10, 2007 at 1:19 pm
I think before you build a formula, the “possession logic” used is too cloudy to weight stats, because you are not completely sure how much of the possession belongs to the usager from the rest of the lineup, and the treatment to continuation plays is the most arbitrary and where this logic has some struggles.
Then the usage weight of every stat needs a lot of analysis before a team win regression, and before take conclusions from this big ststistical make up, and before compare skills and to say this skill deserves more money.
What is the true logic? Some metricians say, if you use any linear, no matter the logic used to distribute weight, and apply a team win regression and a team adjust, you will be as team win predictable as the best. No matter if the credits distribution is a disorder, the team regression and the adjust force an order, but individuals pay.
Mark // November 10, 2007 at 1:27 pm
I remember hearing how Horry lead the Lakers in deflections during the championship years, so I know the Lakers track deflections. I suspect most teams do.
There are plenty of statistics that don’t make the box score. Some might not even make sense outside of the couching staff, like failed defensive rotations, box-out percentage or who knows what.
Joey C. // November 10, 2007 at 1:50 pm
“They are saying, in essence, that it’s harder – and thus more valuable – to shoot 50% when taking 30 shots a game than 10 shots a game. The corollary is that if high-volume star shooters took fewer shots, the players who took those shots would be less efficient then they are now.”
Guy, Couldn’t this be controlled for by comparing the shooting % of the player w/ a lot of shot attempts with the shooting % of his surrounding teammates? If the teammates have much higher shooting percentages, then it’s likely the “star” player is shooting too much and his incremental baskets achieved inefficiently aren’t helping the team. What do you think?
Joey C. // November 10, 2007 at 1:53 pm
“Some metricians say, if you use any linear, no matter the logic used to distribute weight, and apply a team win regression and a team adjust, you will be as team win predictable as the best. ”
Harold A., thats’ true in sample. It’s a tautology I think. But is it true out of sample? I bet wins produced is more predictive than Rosenbaum residuals are.
Harold Almonte // November 10, 2007 at 2:21 pm
JoeyC. – The scoring probability of a shot depends on the opponent defense and how much easiness they give up. The scorers who got to be in the “easiness moment” more time, shoot more, but a lot of the time the “easiness” the team get and can create is a long distance, or contested, or double teamed shot. You know the risks and who pays by a probably colective decision.
I think plus/minus is already a team adjust, and I don’t know if a team win regression can be applied to this metric. And if you want to consider individual skills outside the lineup and the back-up, probably an individual adjust would nedd to be made, I don’t know if thats possible. It’s like comparing oranges and apples.
Pete // November 10, 2007 at 2:33 pm
Mark,
I think in the NFL they now track “hurries” and not just “sacks.” Maybe deflections:hurries what steals:sacks.
Pete // November 10, 2007 at 2:34 pm
Guy,
Maybe these shooters you are deifying are just ball hogs and not taking excessive shots “for the good of the team.”
Pete // November 10, 2007 at 2:35 pm
Harold A., I guess it’s kind of like in the NFL where Randy Moss is getting double covered and Walker is getting extra catches as a result. Maybe there needs to be something like plus/minus applied to the NFL to control for this. (in addition to conventional reception stats)
Harold Almonte // November 10, 2007 at 3:00 pm
Pete.-But although plus/minus could measure what somebody smartly called “residuals”, I don’t know how much you can correctly control an individual performance rating with that. What some people do is a compound of a linear and plus/minus (and sometimes player off. or deff. efficiency, maybe as residual and contextual as +/-) with their arbitrary weight of each one. How do you know what is the less arbitrary weight?
Harold Almonte // November 10, 2007 at 3:41 pm
Ratings have decided to take it easy with scoring and are trying everybody accept that efficiency and points per shot is the only thing you must watch and be resigned to the boxscore easy way.
It’s obvious there’s a conflict against playing experience and common sense who knows that there are a lot of things (difficult to account or not) that must be factorized and can put a scoring rating head down, like usage responsibilities factor, assisted factor bydificulty of shot creation and ballhandling skills, by how assisted is your team, how assistant is your point guard, and even for you not being the point guard, etc. All of that can be some way measured, and those are the real kind of controls that linear ratings need.
Joey C. // November 10, 2007 at 4:06 pm
Harold A., what about simplicity and transparency? No model will capture every element of the real world. A good model could still serve as a filter.
Joey C. // November 10, 2007 at 4:08 pm
Mark,
Did Horry lead the Lakers in steals or just deflections? Bill Simmons says Horry belongs in the hall of fame because he is clutch. Same thing with Curt Schilling (of the RedSox).
Harold Almonte // November 10, 2007 at 4:28 pm
What a transparency if you don’t know what is more “inky”, what is boxscored tracked from what is not, what is each player’s possession credit from the team possession? Do you think the only thing that didn’t have simplicity and needed to be adjusted was off the ball and help defense? I think they are not filtering enough and are making up with statistical magic.
Harold Almonte // November 10, 2007 at 5:16 pm
Another thing, according to 4 factors ( that means also team win regression I think), good rebounding (off. plus deff.) is as correlated to wins than good scoring (about a 20% each one I think). Of course they are as much correlated to loose if you perform bad. Probably this can be extrapolated to individuals, but both skills are not treated the same, you rest points to bad scoring and you can be negative (looser) when you are under the league average. Boxscore an ratings don’t let rebounders be negative, you can be good or bad, but zero is your is your floor. Isn’t this strange?
Pete // November 10, 2007 at 5:25 pm
Harold A., what are these correlations of?
I guess the first correlation is team point differentials and team rebound differentials, right? What about the second one? Is it correlation of point differential against points scored? Is the former correlation higher because it captures some defense and points scored only captures offense? Thanks.
Harold Almonte // November 10, 2007 at 5:44 pm
4 factors is really 8 factors, and correlations of 4 splitted in 8 has been measured by several metricians with similar results: scoring (20%), scoring defense (20%), offensive ballhandling-TO (12%), stealing (12%), OR (10%), DR (10%), FT (7.5%), FT defense-Fouls (7.5%). That’s average of course.
But that’s not important. The different levels of negativity or punishment of skills is where the unfairness is.
Kent // November 10, 2007 at 6:02 pm
Joey C:
You wrote: “I like plus/minus but what if Kobe’s backup really stinks. Kobe’s plus/minus would be inflated. Useful info to have if you’re Phil Jackson and know that Kobe should get the bulk of the minutes because of how the team suffers when he’s off the court. However, it’s tricky to gauge how useful that information is for another GM considering trading for Kobe.”
IIRC adjusted plus/minus accounts for this. Your criticism is valid for the regular plus/minus measure. But adjusted is supposed to control for this.
Kent // November 10, 2007 at 6:04 pm
Harold A, those correlations are interesting . ARe they supposed to be like regressing runs against OBP and OPS like is done in baseball?
Pete // November 10, 2007 at 6:38 pm
Post #150. Luol Deng and Ben Gordon are truly controversial figures!
Harold Almonte // November 10, 2007 at 6:39 pm
Probably. At the offensive end of course. You are regressing a rate, not a single stat like hits, strike outs, etc., but are runs and points equal to team wins? I don’t know. Some ratings weight stats not necassarily to win-points. Are win predictable? not much. Are skill predictable? maybe.
The problem with basketball is that its boxscore doesn’t let you rate stats and every skill against the own performer ability, the opponent and his teammates. League efficiency average, giving up to opponent, and diminishing return just punish some of them.
Guy // November 10, 2007 at 7:03 pm
“Guy, Couldn’t this be controlled for by comparing the shooting % of the player w/ a lot of shot attempts with the shooting % of his surrounding teammates? If the teammates have much higher shooting percentages, then it’s likely the “star” player is shooting too much and his incremental baskets achieved inefficiently aren’t helping the team. What do you think?”
Joey: You’ve identified a central question in evaluating any performance: What is the alternative? Should a 45% shooter take 30 shots a game? 15? None? You can’t possibly answer the question unless you know, or at least estimate, what will happen if he doesn’t take the shots. For a weak team, it may make sense for even a pretty inefficient shooter to take a lot of shots, while on a strong team it would be a mistake for that player to consume many opportunities.
But to value and compare players across the NBA, you have to measure against a consistent benchmark, a level of shooting efficiency that generally has zero value. (In baseball analysis this is referred to as “replacement level,” generally about 70-75% as productive as an average player.) In Wins Produced, the zero value level for shooting is basically 50% efficiency. A player at that efficiency level has no value as a shooter (though of course he may contribute via rebounds, steals, etc.). For example, Kobe Bryant shot 50% on 1,359 2pt. attempts last year. According to Wins Produced, Bryant would have been just as valuable if he had shot only 59 times at the same efficiency, and let his teammates take the other 1,300 shots. (Actually, he would be slightly MORE valuable in that scenario, since he shot 49.7%, but let’s call it a wash.) At 49% efficiency, Kevin Garnett would have been more valuable if he had never taken a 2-point shot.
Clearly, these are radical claims and many fans and analysts disagree. At the same time, a metric like PER has a zero value (or “break-even”) efficiency rate of around 30%, which seems too low. What is the right rate? I don’t know, but the choices certainly aren’t limited to 50% or 30% — the right answer likely lies somewhere in between.
The additional question raised by Pelton’s analysis is whether the break-even point should vary based on the number of shots taken. There’s a good parallel in baseball: pitchers appearing in a relief role can throw harder than starters, and enjoy an advantage of about 1.00 in ERA just because of their role. Many relievers post ERAs under 3.00, but almost no starters. So you have to evaluate relievers against a higher standard. Perhaps analysts will eventually adopt a similar approach for shooting in basketball.
Joey C. // November 10, 2007 at 7:51 pm
Guy,
Great explanation. Thanks v much. I understand better now.
“In Wins Produced, the zero value level for shooting is basically 50% efficiency. A player at that efficiency level has no value as a shooter (though of course he may contribute via rebounds, steals, etc.). For example, Kobe Bryant shot 50% on 1,359 2pt. attempts last year. According to Wins Produced, Bryant would have been just as valuable if he had shot only 59 times at the same efficiency, and let his teammates take the other 1,300 shots … . At the same time, a metric like PER has a zero value (or “break-even”) efficiency rate of around 30%, which seems too low.”
Kent // November 10, 2007 at 8:22 pm
Harold A. asks “are runs and points equal to team wins?”
Yes, they are. Please see Pythagorean win expectation– http://en.wikipedia.org/wiki/Pythagorean_expectation
Owen // November 10, 2007 at 8:59 pm
Guy – Not sure I agree with that explanation.
Not a sabermetrician, or an economist, but my understanding of replacement level is that it is floor, a minimum, This differs from WP, which is built around an average level of efficiency. You wouldn’t bring a player in from the NBDL and expect him to shoot at average efficiency and volume, would you? It’s a different thing it seems to me. Also, I sort of have to wonder why you arbitrarily choose to focus on 2 pt fgs, it seems a bit confusing. A player’s shooting efficiency, especially a player like Kobe, is not simply a function of his 2 pt fg%. You need to think about ts%, about scoring efficiency as a whole, no? You have to look at his three pointers and his ft’s especially. There is a tremendous amount of value in being able to draw foul shots and sink them, since its much easier to score from the foul line. IMO, ft’s probably should be viewed as an adjunct of that 2pt shooting.
Also, it seem very untrue, in my understanding, that it doesn’t matter whether he shoots 59 shots or 1359. WP doesn’t simply measure scoring efficiency. There is a reason why DB posts points per 48 in his player profiles. If you don’t take shots at an average level, and you shoot at an average rate, this would actually depress your WP greatly. In the scenario you describe, Kobe would be scoring about .5 points per game. It would be very hard for him to produce wins from his scoring off of less than a point per game, correct?
Your analysis also doesn’t take into account the position adjustment. It seems you are saying that Kobe is compared to the league average, but my understanding is that he actually would be compared to the average for his position.
At the end of the day, you are correct I think in your estimation that scoring is not the largest value in WP. You can see that in the book where they post the chart of Kobe and Shaq. that the “gaining and maintaining possession,” a composite of rebounds, turnovers, and steals, accounts for a larger share of WP. Kobe’s numbers were 3.8 WP from scoring, and 10.1 from G&M. I can’t say I understand it perfectly actually. It may be much harder to generate that kind of excess value when you score, making his scorer more valuable than it looks. I don’t know.
But the logic that scoring is relatively fungible, if that’s the right word, seems sound to me. Scoring is something everyone can do in the NBA. Why should there be a big bonus for taking a large percentage of your teams shots, when other players can take them also? Also, small differences in turnovers and offensive rebounding can allow players to make up fairly big differences in scoring efficiency. If I capture 1.5 more rebounds than average, and commit one less turnover per 40 than average, while taking the same number of shots, my team will score 2.5 more points on average. If I shoot at 50% rate, taking 20 shots per 40, my team will score 42.5 points. So my offensive impact would be the same as a 55% shooter who rebounds and turnsover at an average rate.
That at least is how I figure it…
Joey C. // November 10, 2007 at 9:42 pm
Oren, thanks for the explanation. I almost let Guy trick me!
Guy // November 10, 2007 at 10:09 pm
Owen:
I thought focusing on 2PA made it easier, but perhaps it had the opposite effect. And you make a valid point that drawing fouls and going to the line is a function of attempting shots. So let’s do this: create a “new Kobe” who takes only half as many shots, scores half as many points, goes to the foul line half as often, commits half as many turnovers, and otherwise performs the same. My estimate is that his PAWS48 declines just 7%. If he reduces his shooting by 100%(!), his PAWS48 drops 14%. (And that assumes he doesn’t increase his rebounds or assists despite not taking a single shot!)
So even taking those factors into account, I see Win Score as telling us that 1) only 14% of Kobe’s value comes from his shooting, and 2) if he stopped shooting entirely, it would cost the Lakers about 2 wins.
Guy // November 10, 2007 at 10:30 pm
Joey: No “tricks,” I promise…..
Owen, you ask “Why should there be a big bonus for taking a large percentage of your teams shots, when other players can take them also?” Well, that’s the question we’ve been debating. It depends on a) how many other players shoot as/more efficiently, and b) whether those players could maintain that efficiency if forced to take more shots (and with the star shooter now drawing less focus from the defense). Perhaps the Lakers really would win just as much if Kobe took 10 shots a game, and he’s massively overpaid. I guess it’s just a big misunderstanding……
Joey C. // November 10, 2007 at 10:51 pm
Guy says “If he reduces his shooting by 100%(!), his PAWS48 drops 14%.”
This assumes that his teammates can pick up the slack, i.e. replicate his other shots with the same percentage. I’d be careful with this anlysis, though. What if you assumed every single player on the team didn’t attempt a shot you’d still expect the team to have wins according to wins produced. You might be making a good point that points are undervalued in the wins produced schematic. But I think what you’re doing is a little gratuitous by carrying everything to the extreme like this.
What if a baseball team wins their first game 161-0 and then loses the next 161 games by 1 run? win expectation would be way off b/c it says the team should have a .500 record. Have I just disproved notion of win expectation? (No)
Joey C. // November 10, 2007 at 10:59 pm
Actually, the 7% drop in value if Bryant’s shot attempts decline by 50% is a good hypothetical. I went overboard in calling your example gratuitous. My apologies.
Kent // November 10, 2007 at 11:14 pm
Guy wrote: “you ask “Why should there be a big bonus for taking a large percentage of your teams shots, when other players can take them also?” Well, that’s the question we’ve been debating. It depends on a) how many other players shoot as/more efficiently, and b) whether those players could maintain that efficiency if forced to take more shots (and with the star shooter now drawing less focus from the defense). Perhaps the Lakers really would win just as much if Kobe took 10 shots a game, and he’s massively overpaid.”
I think that’s a really good succinct summary of the big debate going on with wins produced (and with Hollinger’s PER). To that I’ll just add that the other debate is whether interactions are being reflected sufficiently and then whether plus/minus can help there as a supplement.
Owen // November 10, 2007 at 11:19 pm
Guy – Not sure about your calculations, or your understanding of WP, but I think you are probably right. WP clearly is not driven by scoring as other models seem to be.
And I think that’s correct. A basketball player’s value isn’t determined, largely, by his scoring.
To bring it back to the post that started this thread, with a twist, let’s compare Kobe and Ben Gordon. Look at their stats.
http://www.basketball-reference.com/fc/pcm.cgi?req=1&cum=0&p1=bryanko01&y1=2007&p2=gordobe01&y2=2007
Gordon and Bryant have extremely similar scoring stats. They each notch over 30 points/48. Gordon had a ts% of 57.2. Kobe was .8% percent higher, at 58%.
Everyone agrees Kobe is a much better player than Gordon. Why is that?
Is it Kobe’s 6 extra points per 48 that makes him All World and Gordon a middle of the road guy?
Or is it the fact that Kobe is, per 48.
2.1 rebounds better
1 assist better
.6 steals better
.3 blocks better
.5 turnovers better
1.4 Pf better
When I look at comparison like that, DB’s approach makes a lot of sense. Everything a player does is important. Scoring is just a part of the picture, and maybe not the most important part.
dberri // November 11, 2007 at 12:02 am
I do think these comments work better when I don’t chime in. But I thought I would just throw this out there. Sometime ago I did an examination of Reggie Miller where I noted that he produced 173 wins in his career. Miller was really just a scorer. He didn’t get alot of rebounds, steals, etc… He scored. And he produced wins. Wins Produced doesn’t show that scoring doesn’t matter. It just shows that other things a player does also matter.
Kent // November 11, 2007 at 12:11 am
http://dberri.wordpress.com/2006/07/20/scorers-and-wins-produced-again/
Why was a pure scorer so adept at producing wins? The key is Miller’s shooting efficiency. About ten years ago Rob Neyer – quoting Michael Canter — argued that one good way to assess efficiency from the field is to subtract free throws made from a player’s points total and then divide by field goal attempts [(PTS-FTM)/FGA]. The average player in the NBA scores a bit less than one point per field goal attempt. In every year of Miller’s career he averaged more than one point per shot from the field. Not suprisingly, such efficiency translates into victories.
Pete // November 11, 2007 at 12:40 am
The dberri article Kent posted ends like this:
“I do not think the evidence shows that we undervalue scorers. Then again, if someone produces a model with the statistics valued differently – and that model can be shown to have greater explanatory and predictive power – then I am all in favor of using the new model. But you can’t just say you have a better mousestrap, you have to show me the dead mice ”
It’s funny that a year and a half later we’re having the same debate. There’s even Harold A. in that old comments thread!!!
Kent // November 11, 2007 at 1:02 am
Guy W, When Kobe Bryant gets traded we should try to make predictions using wins produced, plus/minus, hollinger PER, rosenbaum residuals, etc. about how the lakers + the other team will do for the rest of the season.
Joey C. // November 11, 2007 at 1:26 am
Oren says “When I look at comparison like that, DB’s approach makes a lot of sense. Everything a player does is important. Scoring is just a part of the picture, and maybe not the most important part.”
I agree. I like the idea of a weighting scheme to sum the major box score statistics. I don’t think any reasonable person would disagree with that. What some people here are debating is whether the weightings DB uses are optimal. Some people are perfervid about arguing that rebounds are weighted too heavily by DB. I like the design as is.
Joey C. // November 11, 2007 at 1:46 am
Harold A.,
You wrote 4 factors is really 8 factors, and correlations of 4 splitted in 8 has been measured by several metricians with similar results: scoring (20%), scoring defense (20%), offensive ballhandling-TO (12%), stealing (12%), OR (10%), DR (10%), FT (7.5%), FT defense-Fouls (7.5%).
You’re running a correlation of points scored with the difference of points scored and points allowed. Of course the correlation will be high! Something about this just seems really fugazi to me.
Kent // November 11, 2007 at 2:03 am
Joe C, Points scored will correlate with points allowed because it signals something about the pace of the game. IMO, the more useful correlation would have been shooting percentage with wins (or point differences).
Guy // November 11, 2007 at 6:57 am
“Actually, the 7% drop in value if Bryant’s shot attempts decline by 50% is a good hypothetical.”
Joey: I stated that incorrectly. His PAWS48 would decline by 7%, but that’s his value above an average guard. His total value, as measured by WP48, would actuall decline just 4% (less than 1/2 a win). Of course, with Kobe taking half as many shots, it seems likely he will increase his rebounds, have more assists, and/or increase his shooting percentage, so really WP is suggesting the Lakers would likely win more games if Kobe shot much less.
[Owen: feel free to check the calculations: it takes about 3 minutes with Excel).
Owen // November 11, 2007 at 8:49 am
Guy – Look at this comparison of Jordan and Bryant at 28, and Gordon at 23.
http://www.basketball-reference.com/fc/pcm.cgi?req=1&cum=0&p1=bryanko01&y1=2007&p2=jordami01&y2=1992&p3=gordobe01&y3=2007
They all score very similarly. Their ts%’s are within 1% point. Jordan and Bryant’s volumes are identical. Gordon lags, but not by all that much.
Basically, it’s hard to choose between these player looking at just scoring. The difference between them quite clearly is in non-scoring categories. Jordan is as much better than Kobe there as Kobe is better than Gordon.
I don’t particularly want to tinker with Excel. Not that good at it. So let me ask this.
What actually happens if you switch Kobe and Ben Gordon? Are the Lakers going to be hurt because of Gordon’s scoring 31 rather than 37 points per 48. Is it Kobe’s scoring that will be missed? Or is it everything else?
Given a choice between replacing Kobe with a guard who scored as well as he did and as efficiently, like Ben Gordon, or a player who did everything else as well as he did, but scored at an average level, which one would you take?
Joey C. // November 11, 2007 at 12:03 pm
Guy W, I’m tempted to say we could project the implication of Kobe taking less shots by looking at the shooting percentages of his teammates. There must be some optimal threshold. (We’d be making a bunch of assumptions so this wouldn’t hold for Kobe attempting 0 shots but maybe it applies locally for him attempting 1 less shot, etc.)
Of course wasn’t there a study recently by a Villanova stats prof about using last year’s batting average to predict this year and making an estimated adjustment for number of at-bats? In other words if someone hit .450 last year, it means they might not be good b/c clearly they got limited number of at-bats.
similarly, if someone’s shooting % is 0.70 maybe it’s because they only take shots very selectively for a reason and that % would drop precipitously if they shot more.
What do you think?
Joey C. // November 11, 2007 at 12:07 pm
Owen, wouldn’t you not choose Ben Gordon b/c (1) he scores inefficiently and less than the others, and (2) he gets less rebounds and assists. You seem to be focusing on the latter but i think the former applies too.
Kent // November 11, 2007 at 1:04 pm
Guy, your argument of Kobe not shooting strikes me as reductio ad absurdum.
Owen // November 11, 2007 at 1:47 pm
Joey C – In the example I chose, Gordon actually was not much less efficient than Bryant of Jordan, as I noted in my post. They all had ts% btw 57-8, they all scored more than 30 pts per 48. Bryant and Jordan scored 20% more points than Gordon, but also used 20% more possessions to create those points.
If you want to understand the difference between Gordon and Kobe, and Kobe and Jordan, you have to look beyond scoring. When you do though, the story becomes quite clear.
Joey C. // November 11, 2007 at 2:01 pm
Owen, Also Kobe + Jordan won multiple championships each. Gordon has not won a championship. The performance of Kobe + Jordan’s teams have been better than that of Gordon.
Kent // November 11, 2007 at 2:43 pm
Joey C,
Championships won says a lot about the supporting cast, not just the star player. Look at Kevin Garnett stuck playing for the Wolves all these years. Now he hasn’t even lost a game as a Celtic!
Kent // November 11, 2007 at 2:44 pm
BTW, does anyone know why assists only count half as much as points in win scored? What is used to derive that weighting? Thank you.
Owen // November 11, 2007 at 3:31 pm
Joey – I agree with Kent on the supporting cast. But Ben Gordon simply isn’t that good, another reason why he won’t be winning any championships.
Kent – Re assists, your best bet is to read the book for that.
Mark // November 11, 2007 at 3:38 pm
I believe most are going the wrong way when comparing FG% to the number of shots attempted. Groups statistics are good at some things but not others. In this case there are clearly factors pushing for both correlating and inverse correlating statistics.
Reasons for correlations include better shooters should get more playing time and better matchups should get both higher % and higher shot attempts.
Reasons for inverse correlation include improved shot selection and players who tend to get the ball as the shot clock expires.
I’m not sure how the overall statistics work out, but quite honestly I don’t care unless one comes up with a way to isolate the various cases, and I don’t see how you can do that with just a box score.
Jason // November 11, 2007 at 3:41 pm
My understanding is that the value of an assist was determined by regression based on the isolated change in assists vs. winning probability. At the team level, assists *shouldn’t* matter since a point scored without an assist is worth a point scored with an assist and an assist is not necessary for a basket. However, an assist is a proxy for how much a player helps the efficiency of teammates. Someone gathering assists is doing so because teammates are gathering baskets.
The team adjustment in Dave’s model in part makes sure that assists don’t get counted as extra credit at the level of the team but in essence, it redistributes a portion of successful baskets to the player who assisted the basket. Without the teammate adjustment, either there would be no way to credit players who help other players get baskets else some baskets would get extra credit. Since the latter isn’t valid (there are not extra credit points for an assisted basket in the final outcome of a game) the former is necessary.
In win score, the value is half the basket, which is more or less just a convenient rounding of the value in Wins produced relative to the weights of a point in both metrics.
Kent // November 11, 2007 at 3:48 pm
Jason,
Thanks much for that very helpful reply. So the relative weights of the box store statistics are determined by univariate regressions of win probability (or point differentials?) against each stat? For example, regress [team points scored minus team points allowed] against rebounds. Then repeat that regression but use assists instead of rebounds. If rebounds get a sensitivity half as much as assists than rebounds would count double in wins produced. Is that how it works?
Westy // November 11, 2007 at 3:56 pm
Owen,
You note, “If you want to understand the difference between Gordon and Kobe, and Kobe and Jordan, you have to look beyond scoring. ”
Of course! We all agree that rebounds, assists, etc. are important. That’s why it’s obvious Kobe is better than Gordon. But exclusively being a scorer is the job of some players in the NBA. Guys like Korver, Hamilton, etc.
DB cites Reggie Miller as an example of someone who did well in WP mainly by shooting. One example?! Arguably the best shooter of all time is how good you have to be to produce wins well via shooting?
And examples abound of players who seem to only be good at rebounding who are rated highly by WP. Wallace, Chandler, Lee, Rodman, etc. Could it be because rebounds should be individually divied up differently?
dberri // November 11, 2007 at 5:07 pm
About assists..
The value points, field goal attempts, free throw attempts, rebounds, turnovers, and steals are taken from the link between wins and the efficiency metrics (offensive and defensive efficiency). The results of this regression can also be used to determine the value of a personal foul and blocked shot.
Assists, though, come from a model of individual player productivity. This model is detailed in Chapter Seven of the book. From this model it was found that an assists was worth about 2/3 the value of a point. In calculating Win Score, this value is changed to 1/2 for simplicity.
And about scorers… there are other scorers besides Reggie Miller who produced large sums of wins. I will try and write a post on this sometime this week.
Jason // November 11, 2007 at 5:09 pm
There are a few possibilities. One is that rebounding should be divvied up differently. It is possible that the full value of a rebound doesn’t belong to the player credited in the box score sufficiently.
One is that the ability to score in isolation of all other factors is undervalued and there’s a premium on ’shot creation’ not recognized. While the total number of shots cannot gauge this, the return on shooting measured by team fg% might suggest this. If a top scorer’s absence results in a lower rate of return based on points per possession, then that scorer’s contribution was missed.
Another possibility is that rebounds really are that valuable. Anecdotally, how does the record of teams with top notch rebounders compare when the rebounder is not available? One could compare the variance in record for teams when their leading scorer (presuming that said individual isn’t the same player) is out (either by game or by +/- total, though both have limitations and strengths). While not definitive, this test could strongly suggest whether one statistic was overcredited and was easier to replace than another.
Pete // November 11, 2007 at 6:08 pm
This is all very interesting. A question– Why are we restricting everything to linear functions?
Kent // November 11, 2007 at 11:06 pm
Pete,
If you use non-linear weights your susceptibility data mining is kind of high. The number of possible models expands enormously.
Kent // November 11, 2007 at 11:08 pm
“From this model it was found that an assists was worth about 2/3 the value of a point.”
Is this just saying that only 1/3 of points scored on field goals are unassisted?
Kent // November 11, 2007 at 11:09 pm
Jason C. writes “If a top scorer’s absence results in a lower rate of return based on points per possession, then that scorer’s contribution was missed … ”
Plus/minus could do this, right?
dberri // November 12, 2007 at 12:01 am
Kent,
The value of an assist comes from a model of an individual player’s productivity. Basically, a player’s per-minute peformance was regressed on how many assists his teammates accumulated (and a collection of other explanatory factors). From this model the value of assist was determined.
Okapi // November 12, 2007 at 1:13 am
Would this– http://www.wagesofwins.com/CalculatingWinsProduced.html — be the best source if I wanted to learn the mechanics of the calculations? Thanks.
Harold Almonte // November 12, 2007 at 7:43 am
Pete-”It’s funny, half a year and the same debate”.
It’s a bad thing, because the only result is everybody is entrenching in their supposed own trues. The real true is everybody and all inear ratings use the same boxscore and some variations of the same possession logic.
“My true”, from that time has allways been that the original sin is inside the boxscore first, and the possession logic later, that creates those different stats break evens problems from its different punish treatments, and the personal interpretations about continuation plays.
I’ve allways sustained it doesn’t matter who wins the “using the best statistical methods” war, in the end everybody would need to go to basics again, and create a better logic by universal consensus.
Harold Almonte // November 12, 2007 at 8:26 am
And then, the different ideologies (most”team win stats producer” player Vs. most “skilled by certain stats” players) is a secondary thing.
Harold Almonte // November 12, 2007 at 8:36 am
One and half a year and my english is as bad.
dberri // November 12, 2007 at 8:38 am
Okapi,
The article [Berri (2008)] is better, but not out yet. Until then, this will have to do.
Harold,
Yes, you have been leaving the same comments for 18 months. A couple of points… there is no statistical “war.” Dean Oliver, Wayne Winston, and I do not fight about this stuff. We are all professional researchers and I think we get along very well.
Second, I have no idea what you mean by “create a better logic by universal consensus.” Do you want us to move away from empirical analysis and just vote on this stuff?
Kent // November 12, 2007 at 9:06 am
If I’m understanding table 2 of this correctly –
http://www.wagesofwins.com/CalculatingWinsProduced.html — then the coefficient for rebounds and points is the same because of intuitive logic of possessions and not because of a regression. Is this correct?
A rebound creates (or maintains) a possession so has a weighting that equals [coefficient for pts scored ] * [average # of pts scored per possession]. Since average # of pts scored per possession is 1, then the coefficients are roughly equal. Is my interpretation correct?
I want to clarify so that I’m not still asking the same question 18 monts from now!
Kent // November 12, 2007 at 9:08 am
The debate has evolved in 18 months in QB Score at least. The penalty for an interception is -30 yards. It used to be -50 yards.
Kent // November 12, 2007 at 9:12 am
BTW, here is the topic of Malcolm Gladwell’s new book– http://www.kottke.org/07/11/malcolm-gladwells-new-book-on-the-workplace-of-the-future The book will be on “future of the workplace with subtopics of education and genius.” With the exception of the great review of “Wages of Wins,” he seems now to focus on topics that will help his corporate speaking career and politically correct agenda.
dberri // November 12, 2007 at 9:14 am
Kent,
It is from the regression we get the value for a point, rebound, etc… All the values come from a regression. But there is an intuition behind the results as well.
And there really wasn’t a debate on QB Score. I just got a hold of more data. It is odd that the football work has not generated anywhere near the debate as the basketball stuff.
Kent // November 12, 2007 at 9:18 am
dberri,
Thanks for the reply. I love QB Score. It’s a simple measure and addresses the complaints with QB Rating I’ve had. (QB Rating is complicated, ignores rushing, and overemphasizes touchdowns while ignoring fumbles.)
Harold Almonte // November 12, 2007 at 2:03 pm
Berri-I don’t know if it’s something that depends on metricians or it’s above all of you, but the fact is probably won’t never be posible to track and even create a measurable stat for every defensive attempt, in order to regress and have their respective “negative possession credit” like scoring is penalized every attempt, and we’re talking about 50% of the game. Of course fouls is not that stat, there are fouls at both side of the floor. At least your team defense adjust is probably the most advanced try on this area actually.
The different continuation plays logic variations that produce the different offensive break evens (and rebound weights) is another fundamental struggle, and this is BEFORE regressions, and even BEFORE giving a “possessional point value” to plays not status cleared as final isolated plays, shared, or continuations yet. Regressions don’t fix that, and the only old stuff is that the lack of fundamental data carries to the rest of ratings unfairnesses.
If it’s neither a contest, nor probably proffesional zeals, the fact is that to settle with just approximations and not to avoid the polarization of ideas, being as smart to do it, is a wasting of a debate…but, entertained.
Kent // November 12, 2007 at 2:18 pm
Harold A,
you wrote,
“The different continuation plays logic variations that produce the different offensive break evens (and rebound weights) is another fundamental struggle, and this is BEFORE regressions, and even BEFORE giving a “possessional point value” to plays not status cleared as final isolated plays, shared, or continuations yet. “
I’m not sure I’m following your reasoning. Can you please clarify or give an example? Thanks.
Mark // November 12, 2007 at 2:31 pm
I’m not exactly sure what Harrold is talking about, but it has always bugged me that a rebound off a missed free throw is given the same weight as any other rebound. Personally, I think not counting the rebound at all would be a closer approximation to actual value. Wins Produced gets around this slightly by correcting for position, but it is still a fundamental flaw in the base statistics.
Harold Almonte // November 12, 2007 at 2:43 pm
Continuation play, or FGMissed continuation play begins with the pass at the offensive end, followed with the FGMissed (and its defense), and then a rebound (offensive or defensive). The way to judge all this action affects scoring, rebounding, defense, and probably assisting too. Every action can be related or not to the next and the prior, a summatory of isolated possession stats and no continuation plays, or a set of shared and even opposed actions, some of then affected by probabilities.
Pete // November 12, 2007 at 5:22 pm
Harold A, are you saying a per possession approach is artificial because it makes discrete a continuous game? And the predispositioning from the prior play should count as well? If so, how exactly would you quantify this?
Joey C. // November 12, 2007 at 5:50 pm
I think Harold A. is saying some of the rebounding credit should be dispersed across the rest of the team. He’s been saying it for 18 months.
Harold Almonte // November 13, 2007 at 5:46 am
Everybody, including metricians have prefered to quantify this arbitrarilly, the most easy way possible. I suppose there are others not so easy statistical ways for deciphering this basketball enigma. I’ve saying those less easy ways could pay a lot of dividends and earnings to all linear ratings. But, until then, all of them are more a caricature (with personal style) than a picture of basketball players.
Harold Almonte // November 13, 2007 at 6:12 am
It’s like when you increase the pixels in a photo, then you can see it’s not the face on mars, but a detailed mountain.
Joey C. // November 13, 2007 at 8:15 am
Or when you close your eyes and eat ice cream, and then realize it’s a sandwich.
Mike H // November 13, 2007 at 1:08 pm
To paraphrase Harold – “All your evidence is belong to caricature!”
Joey C. // November 14, 2007 at 3:27 am
I like cats.
Amped Freestyle Snowboarding » Comment on Are Luol Deng and Ben Gordon Both Worth $50 Million? by … // November 14, 2007 at 9:49 am
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Ritegran // November 15, 2007 at 6:33 pm
If the report is true (both Deng and B Gordon get similar offer – 50 millions for 5 yr), then this just shows how lack of intelligent Paxson is. As you have pointed out, Deng is much better than BG. Note that Deng always guard his man, while Hinrich is demanded by Skiles to always guard for Gordon (including many elite SGs). If BG needed to guard his man (like the starting SGs on other teams), his offensive efficiency (or WP) would be worse (or much worse) than Deng’s, because he will shoot poorly due to exerting more energy on the defensive end (additionally the opposing star SGs will shoot lights-out over him).
Furthermore, Hinrich only gets 47.5 millions/5 yr, and BG is only half as good as Hinrich. They have similar offensive talent, although BG has better offensive stats; that’s mainly because Hinrich has to exert so much energy on the defensive end to guard Gordon’s man (unless the opposing team has a star PG) so that BG can conserve his energy to shoot the ball. Therefore, BG’s PER or offensive efficiency is inflated, which is obtained at the sacrifice of Hinrich’s offensive game. Defensively, Hinrich is way, way better than BG. If you also consider intangibles that Hinrich brings to the game (eg, he doesn’t need the ball to be effective, is better passer, unselfish, leadership, etc.)…
I like to think how much a smart GM like Buford or Dumars would pay a role player like BG; my guess is 3 to 4 millions/yr. The initial contract of McDyness with the Pistons is ~ 5-6 millions/yr, even though an all-around big like McDyness is hard to find. Bowen’s salary is ~ 4 millions/yr, even though he is the best perimeter defender in the NBA. BG shooting percent does not even rank among top 40 last year (particularly he doesn’t play much defense, so he needs to shoot a high percent to not hurt the team).