Sports fans tend to put athletes into one of three categories. There are great players, such as Tim Duncan, Kevin Garnett, and Steve Nash. Then there are good players, like Lamar Odom, Corey Maggette, and Ray Allen. And then there are average players.
This latter category appears to contain all players who are not “great” or “good.” In other words, sports fans tend to live in a place adjacent to Garrison Keillor’s Lake Woebegone. In Lake Woebegone, “all the women are strong, all the men are good looking, and all children are above average.” In sports we see a similar story. All players are either average or above average. In essence, no one is ever “bad.”
If we think about it, though, we know someone has to be below average. Performance tends to follow a normal distribution. Most players hover around average. A few players, though, are “great” and these can be found in the right tail of the distribution. And just as we have a few players who are well above average, there also must be a few players who are way below average. Such players reside in the left tail of the distribution. And one of these is the primary subject of today’s post.
The Impact of Willie Green
Last summer the Philadelphia 76ers were pre-occupied with Allen Iverson. Should “the Answer” be traded or not? While Philadelphia postponed their answer to the question of “the Answer, the team did make one move. The 76ers re-signed shooting guard Willie Green to a five year contract. And Green responded to this new contract by posting a career high in points per game. So although the 76ers didn’t do much last summer (they did a great deal during the regular season), the one move the team did make looks like it worked out.
Well, that would be your story if all you looked at was scoring. If you looked at Green’s complete statistical profile it would be hard to find a reason to place him anywhere near Lake Woebegone.
Table One: Evaluating the Performance of Willie Green
Table One reports what Green did in 2006-07 per 48 minutes, as well as was what he has done across his career. And for comparison sake, I also report the average performance of a shooting guard per 48 minutes played.
The aspects of Green’s performance where he is below average are marked in red. And yes, this table just bleeds. Relative to an average shooting guard, Green is below average in his career with respect to shooting efficiency (both from the field and the line), rebounds, steals, blocked shots, assists, turnovers, and personal fouls. The only thing he does at an above average pace is take shots from the field. And this propensity to take shots allows him to score at an above average level.
When we put the whole picture together, we see that Green is not just a bit below average. Last year an average shooting guard would have produced 3.8 wins in Green’s 1,842 minutes. Green, though, posted a (-4.6) Wins Produced. In other words, replacing Green with just an average shooting guard would increase Philadelphia’s wins total by 8.4 wins. Such a change would have put the 76ers in the playoffs last season.
Let me put this performance in some perspective. Andre Iguodala is the leading producer of wins for the 76ers. Iguodala’s WP48 (Wins Produced per 48 minutes) was 0.195 in 2006-07. Such production across 3,062 minutes was worth 12.4 wins to Philadelphia last season. In sum, Iguodala is really good.
However, the combination of Iguodala and Green was only worth 7.8 wins. Replacing both players with average performers would have given the 76ers 10.2 wins, or 2.4 more victories. This means that the distance between Iguodala and the average player is smaller than the distance between Green and an average guard.
Okay, more perspective. Green is 8.4 wins below average. Replacing Kobe Bryant with an average shooting guard would have cost the Lakers in 2006-07 about 8.8 wins. So Green is as far below average as Kobe is above the mean.
The Least Productive
Alright, Green is clearly living in the left tail. But he is not there alone. Here are the ten players produced the lowest quantity of wins (or the most negative totals) in 2006-07.
Table Two: The Ten Least Productive Players in 2006-07
Leading the list is Adam Morrison, who I have discussed previously. As Table Two indicates, if the Charlotte Bobcats had replaced Morrison with an average player the team could have expected to win 11.6 more games. Yes, Morrison had a truly awful rookie season. There is hope (not much, but some) that Morrison can get better. Other names on this list, though, are not likely to improve. Jason Collins, Antoine Walker, and Brian Scalabrine are all veteran players who do not have much hope of turning their games around.
Addition by Subtraction
Okay, there is a reason why we tend to all wish to live in Lake Woebegone. Saying that people are “bad” is not nice.
It’s important to note that when I say Green is a “bad” basketball player, I am not saying he is a “bad” person. Just like many “good” basketball players don’t seem to be particularly “good” people, I am sure there are many “bad” players who are really nice people. For example, John Amaechi came across as a fairly nice person in promoting his book last year. But for his career he produced (-18.9) wins, so he clearly qualifies as a “bad” NBA player.
So why am I picking on Green? Well, I was going to write a post reviewing the 76ers in 2006-07. And my angle was the impact of Green. But it took me so long to flesh out this angle that I decided to focus the entire post on Green and other “bad” players, saving the Philadelphia post for another day.
So although this column sort of wandered off in a different direction, it does make an important point. When we look the Celtics in 2007-08 we note the importance of adding “good” players like Kevin Garnett, Ray Allen, and James Posey. But a team can also see the same impact in the standings if it simply replaced a truly bad performer with someone who was just average. In sum, addition by subtraction is a real phenomenon. It simply requires that one recognizes which players need to be subtracted.
– DJ
Our research on the NBA was summarized HERE.
The equation connecting wins to offensive/defensive efficiency is given HERE
Wins Produced and Win Score are discussed in the following posts
Simple Models of Player Performance
What Wins Produced Says and What It Does Not Say
Wages of Wins Journal 
William
October 8, 2007
As a Bobcats fan, this boosts my spirits. If the Bobcats split Adam Morrison’s minutes between Jason Richardson, Gerald Wallace, and Matt Carroll, we’ll be subtracting 2,000 “very bad” minutes and replacing them with 2,000 “average/good” ones.
Brian
October 8, 2007
One nit-pick: I disagree with the assumption that the distribution of NBA talent is normal.
I would believe, however, that basketball talent is roughly distributed normally throughout the general male population.
NBA talent is selected from the very right tail of the population’s talent distribution. If NBA talent scouts and GMs had perfect knowledge of players’ prospects, the distribution of talent in the NBA would look like the right tail of a normal curve truncated on the left. There would be no tail, just a vertical line.
But since talent scouts/GMs are not perfect, and because players can fundamentally improve and decline, there would indeed be the tiniest of tails on the left of the curve. But the players in that tiny left tail would rarely see playing time, if any.
The on-court performance of players IS normal because their performance is due to the interaction of player vs. player talent, all in the right tail of the talent distribution. The results of game-interaction is normal, but not necessarily the underlying talent distribution. I suppose you could think of it as a corollary of the central limit theorem.
I don’t think this invalidates the main point of your post, though.
Chris S
October 8, 2007
I had basically the same thought as Brian when I first started reading the post. Depending on how efficient NBA GMs & coaches are, one might expect the left tail of the distribution to cut off at some “replacement level” of talent/effectiveness. While on the right-hand side of the curve, there’s perhaps no limit to the talent level.
Of course, even in baseball where statistics can (arguably) easily measure the level of effectiveness of a player, there are still below-replacement-level players in the lineups, so it’s not surprising if in the NBA it is indeed a normal distribution (especially considering the game interaction effect that Brian mentions).
Okapi
October 8, 2007
Bloomberg story last week headlined “Baseball Has Smallest Gap Between 1st, Worst Teams in 107 Years” — http://www.bloomberg.com/apps/news?pid=20601079&refer=home&sid=abEIWvvbO7Ts
Does anyone know if a Noll-Scully calculation for this season supports that notion of parity?
Thank you.
Okapi
October 8, 2007
Performance tends to follow a normal distribution.
Is this true for the dispersion of wins produced?
Art De Vany wrote a paper on statistics like hom runs following a power law distribution– http://www.arthurdevany.com/webstuff/images/DeVanyHomeRunMS.pdf
Guy
October 8, 2007
Okapi:
The Noll-Scully ratio is mathematically incorrect as a measure of league competitiveness, as I wrote in the comments in this post: https://dberri.wordpress.com/2007/05/22/some-nice-things-i%e2%80%99ve-missed-%e2%80%93-nba-playoff-edition/#comments. Noll-Scully tells you that the NFL is highly competitive, when it actually has the lowest level of parity (similar to NBA). Baseball is indeed highly competitive, as much so as MLS.
* *
FYI: HR-hitting ability IS distributed normally in MLB, if measured on a per-AB or per-PA basis. De Vany is mistaken about that (and many of the other claims in that paper).
dberri
October 8, 2007
Guy,
I read your comment on the Noll-Scully and was, to put it politely, unimpressed.
Okapi,
I will try and put up a post on competitive balance in baseball soon.
dberri
October 8, 2007
Forgot to comment on Brian.
Yes, I agree. Should have left out the stuff on the normal distribution. Isn’t really necessary for the point I was making.
Guy
October 8, 2007
Dave: Thanks for remaining ‘polite.’ But I’m not sure what “unimpressed” means in this context. The ratio of observed SD in winning % to random error does not give you the variation in true talent in a league. This isn’t a matter of opinion, it’s a matter of mathematical relationships. NFL teams routinely post win%s over .700 because they really are (0ften) that much better than other teams. Even with a 16-game season, we wouldn’t expect to see nearly as much variation in NFL win% as we observe if the league were as equal as Noll-Scully implies.
Now, maybe by “parity” or “competitiveness” you mean something other than how large the spread is in teams’ actual ability to win games. If so, could you explain? Thanks.
Brian
October 8, 2007
Regarding competitive balance in general, I’d like to add my 2 cents.
Much of the focus of research on this topic regards how far apart the true talent levels or winning % are between the winning and losing teams *in any one year*. But that’s only half the story.
The gap between the top and bottom teams might be relatively small, but I think the really frustrating thing is when we see the same top teams and bottom teams each year.
I think most fans would be ok with occasional dominant and doormat teams, just as long as they aren’t the same teams each year.
Guy
October 8, 2007
Brian: great point.
Dave: Take a look at this article in JQAS: http://www.bepress.com/jqas/vol2/iss4/1/. Eli Ben-Naim et. al. also find that the NFL is the least competitive league, using a different methodology than mine.
Brian
October 8, 2007
All stats and math aside, the competitiveness of a sport or league can be quickly judged by how dependent a “team” is on one person.
Take tennis. Federer dominates the sport. No one beats him, ever. One reason is that the sport is completely dependent on him alone. Golf is the same way. Tiger Woods dominates, but less so than Federer, partially because there are more variables in golf.
Next is basketball, where one or two great players can carry a team. Add a third and you’re going to the championships. Even though there are five players on the court, one or two can take a disproportionate amount of shots, or get more rebounds, etc.
Then there is baseball, where there are 9 batters and fielders all contributing equally. But starting pitchers are more ciritical–they contribute to the outcome of every pitch where the other players only participate in a relative few.
And football is a weird hybrid. On defense, 11 players share roughly equal responsibility and can compensate for other’s weaknesses. But on offense, one player, the QB, touches the ball every play, and his performance makes or breaks his team’s season. RBs also shoulder a disproportionate share of responsibility.
If you look at NFL offensive competitive balance, it’s non-existant. Offenses with reliably good QBs can dominate for years. But even the best defenses have their ups and downs. Offensive performance distribution (in points scored or yds gained) is very wide compared to its defensive counterpart.
Paulo
October 8, 2007
Dave,
I agree on your view that Morrison can still be “saved”, but unfortunately, he doesn’t do anything productive well – he’s not an above average shooter, rebounder, defender, etc.
It’s appalling how some of the people on the rest of the list actually start. I feel bad for Jason Kidd.
William,
You’re gonna love J-Rich. I’ve followed the Warriors since the Antawn Jamison-Hughes-Richardson days, and if there was one of those guys who earned his money, it’s Richardson. He’s definitely a more complete player now, compared to being a spectacular dunker before. Never complains, plays good D (sorry, I grew up watching MJ, Pippen and Payton, so I’m not really sure, but he’s not a liability) and is better than his 16 PPG says. Unfortunately, I don’t see Morrison having a significant drop in his minutes. To make matters worse, MJ doesn’t want anything to do with Isiah Thomas.
Sam Cohen
October 9, 2007
I’ve never been a fan of Willie Green, and I’ve never understood why the Sixers signed him to that contract. I was already feeling depressed over John Hollinger’s prediction for the Sixers (I think it was 21 wins), but now you’ve gone and made it even worse!
dberri
October 9, 2007
Sam,
It took 14 comments before someone noted what I said about Green.
About the Sixers… I think they are better than 21 wins. So don’t be too depressed.
Chirstopher
October 9, 2007
I think I know why the Sixers wanted Green. Look at some games where Iverson was out and Green started in his place. You’ll notice that Green effectively turned into AI in several instances. He scored a lot and shot a lot etc. And 2 is better than 1…
Owen
October 9, 2007
Christopher –
Willie Green – Career TS% = 46.1 %
Allen Iverson- Career TS% = 51.5%
Allen Iverson isn’t all that great on that metric, but Green is absolutely dreadful. Truly horrible.
It would be so interesting if Billy King read this website. It’s amazing to think how much the Sixers might improve simply by replacing Green with something close to average.
I will be very interested in your Sixers post. Reggie Evans was an interesting pick up for them, will be fascinating to see what he can do in the East if given minutes. He is a perfect fit I think.
Westy
October 10, 2007
Dave,
Not sure if this is the right place to post it, but I wanted to point out to you that the Basketball Prospectus site is up and running.
On their first day, they posted this (http://www.basketballprospectus.com/article.php?articleid=9) article.
Any thoughts on how it relates to your research? Why do you not consider offensive usage in your formula? It would seem that a player who offensively is low usage, but defensively rebounds well would then be overrated in your system. And one could then also claim that the fact that defensive rebounds are their to grab are more a result of his teammates’ defense than his own contributions.
dberri
October 10, 2007
Westy,
Marty looked at the link between shot attempts and shooting efficiency and failed to find anything. This result was posted (I think) in June of 2006 (or May). So I am not sure the usage story is supported by the empirical evidence.
That being said, it might be interesting to see someone try and do as you suggest.