A few days ago I introduced PAWS, or Position Adjusted Win Score. This is not actually a new metric, just a new name for Win Score adjusted for position played. At the time, I also noted PAWSPERM, or PAWS per minute. As noted on Friday, PAWS-PERM also spells PAW-SPERM, hence the obvious need for a new name.

After soliciting suggestions I have settled on PAWSmin – a candidate not actually suggested by anyone.

Now that we have a name (which I don’t think spells anything stupid or offensive), let me spend a few moments discussing the story this metric tells us about the value of box score statistics in the NBA.

**A Start – the Win Score formula**

The story begins with Win Score, the simple metric we introduced in The Wages of Wins.

**Win Score = PTS + REB + STL + ½*BLK + ½*AST**

**– FGA – ½*FTA – TO – ½*PF**

The analysis reported in The Wages of Wins indicates that points, rebounds, steals, field goal attempts, and turnovers have basically the same impact – in absolute terms – on team wins. Blocked shots, assists, free throw attempts, and personal fouls have less of an impact. The impact of these latter four statistics is set at ½, a simplification that we note does not alter the accuracy of our analysis. To illustrate, there is a 0.99 correlation between Win Score per minute (with the simplified values) and the per 48 minute evaluation of a player (with the statistics weighted exactly in terms of the value each stat has in terms of wins).

**Calculating PAWS**

Position matters in evaluating basketball players. Centers and point guards do not do the same things on a basketball court. Consequently, if you wish to compare players you must adjust for position played. The per-minute position averages for Win Score (from the years 1993-94 to 2004-05) are as follows:

- Centers: 0.225
- Power Forwards: 0.215
- Small Forwards: 0.152
- Shooting Guards: 0.128
- Point Guards: 0.132

To calculate PAWS, you subtract from a player’s Win Score the Win Score an average player at his position would have produced in these minutes. For example, after 56 games Chris Paul has a 274 Win Score. An average point guard would have a 188.9 Win Score in the 1,430 minutes Paul played. So Paul’s PAWS (which is hard to say) – calculated by subtracting 188.9 from 274 – is 85.1.

**Calculating PAWSmin**

Although totals can tell us something, per-minute values are perhaps more important. Per-minute PAWS, or PAWSmin, is calculated by subtracting the average per-minute Win Score at a player’s position from a player’s per-minute Win Score. For example, Chris Paul has a per-minute mark of 0.192. Since he is a point guard, we subtract 0.132 to arrive at Paul’s PAWSmin of 0.059.

**The importance of the team adjustment**

PAWSmin requires a bit of effort, but not quite the effort needed to calculate Wins Produced and Wins Produced per 48 minutes [WP48]. To calculate Wins Produced we need to note the following:

- A player’s statistics, valued in terms of the impact these statistics have on wins
- The average performance at a player’s position
- The value of team statistics, an adjustment that allows us to account for the quality of a team’s defense and the pace the team plays.

We find that Wins Produced explains about 95% of a team’s wins, or in other words, sums quite closely to the actual number of wins a team achieves. This is not surprising since Wins Produced is derived from a team’s offensive and defensive efficiency, two metrics that – not surprisingly — also explain about 95% of team wins.

The accuracy of Wins Produced has led a few to suspect that it’s all in the team adjustment. In reality, though, the team adjustment has virtually no impact on the evaluation of players offered by Wins Produced and WP48.

To illustrate this point, consider that correlation between WP48 and PAWSmin. Remember, WP48 has a team adjustment. PAWSmin does not. If the team adjustment was driving the story, the evaluation with the team adjustment would be very different from the evaluation of players without any adjustment. But when we look WP48 and PAWSmin we find that these two metrics have a 0.994 correlation. In other words, these metrics are virtually identical.

Furthermore, you can actually use PAWSmin to project WP48. For those interested, the equation is as follows:

WP48 = 0.104 + 1.621*PAWSmin

With this equation you can project WP48 and Wins Produced, and never touch a team adjustment. This equation explains 99% of WP48, so obviously it tells us once again that PAWSmin and WP48 are telling us the same thing.

This analysis clearly tells us that the team adjustment is not why Wins Produced is so accurate. Wins Produced is accurate because the box score statistics tracked for players have been accurately connected and valued in terms of wins.

**The Lessons Learned**

So what have we learned from our analysis of WP48 and PAWSmin? A few bullet points will hopefully drive the lessons home.

- Wins Produced – which is based on the box score statistics tracked by the NBA – explains 95% of team wins.
- This accuracy is driven by correctly evaluating each statistic in terms of their impact on team wins.
- Since PAWSmin – which does not have a team adjustment – has a 0.994 correlation with WP48, it is clear the team adjustment is not what drives this story.

**The value of box score statistics**

All of this leads me to what may seem – in some circles – to a bold statement. I think the box score statistics tracked for players in the NBA are more valuable than the box score statistics tracked for baseball players (which I don’t think anyone has suggested we abandon). As we note in The Wages of Wins, basketball players are more consistent than baseball or football players across time. To illustrate, there is about a 0.6 correlation between a baseball player’s OPS in the current season and what the player did last season. For basketball players, though, Win Score per minute has a 0.8 correlation from season-to-season. In other words, the box score statistics in the NBA have greater predictive power than the box score statistics tracked in baseball.

And ultimately this is a big part of how we evaluate models. In judging the value of a model we consider

- whether the model explains what it purports to explain.
- the ability of the model to predict the future.
- whether the model is simple enough for decision-makers to utilize.

Explanatory and predictive power would seem obvious, although often people develop models and then fail to tell us whether or not the model can actually explain or predict anything. The last point is also very important. You cannot help decision-makers if you are the only one who can actually explain and utilize your model. If that is the case, then decision-makers have to trust that you did the analysis correctly. This is a leap of faith people making million-dollar decisions may not wish to make.

In the end, other people have to be able to utilize your work. So simplicity is as important as accuracy in evaluating a model. As I noted a few days ago, other people are starting to use Win Score, a trend that highlights the simplicity of this approach. Hopefully this is a trend that will continue. Certainly I don’t want to be the only one analyzing basketball with Win Score, PAWS, and PAWSmin.

– DJ

*Basketball Stories*

RJ

February 25, 2007

Position adjusted rankings are a step up to me from not and mitigate to a large extent the concern others express about treatment of defensive rebounds.

I also wonder if instead of a position average for absolutely everybody it might be worth considering a different cutoff – top 60 or 75 by position or a set minimum on minutes played (maybe 400 for the season)?

The number of players by position will vary, with some positions being much larger distributions with larger tails of benchwarmers whoi i am not sure should be affecting the position average. Just throwing it out there for your consideration.

Maybe a side by side of PER and PAWSmin and perhaps other methods could be done to analyze the top candidates for all-nba teams.

Westy

February 26, 2007

I know it is probably a lost cause, but I am still struggling to understand the need for the original Win Score formula to be so simple. If we’re dealing in statistics here anyway, why not go ahead and use the correct weights for each stat so the statistics are weighted exactly in terms of the value each stat has? Why use the simpler formula?

In addition, no explanation I have seen yet has been satisfactory as to why a FGA is just as damaging as a TO. 100% of TO’s go to the other team. Only about three-fourths of FGA (I don’t know the actual number, but will use that as a proxy) do. So shouldn’t FGA’s be weighted likewise (FGA*.75)?

I feel like you’re very close to having something valuable here, but the holes are big enough that it’s obvious where it’s still lacking.

Having played basketball for years, I have a hard time accepting that centers are almost twice as valuable as shooting guards. The difficulty in even creating a shot with good defense is high. This is why we see most SG’s taking last second shots. The required athleticism is high. Just going up and down the floor in games, I know that the best player is usually also the one who is best at creating his own shot. At lower levels that could be the center or the SG, but the higher you go, the more it’s someone who can handle the ball well as well as shoot well inside and out. I am prepared to find out that rebounds are somewhat more valuable than we realized, but common sense tells me many of those are gotten due to floor positioning and that we’re discounting the value of creating shots.

Without the position adjustment, the statistics alone would point towards fielding a team of all centers. We know that wouldn’t work as a team could combat their weakness. Basketball teams are built to not only optimize strengths, but limit liabilities. Positions are exposed to different difficult situations and thus the optimum player abilities for the positions on the floor has evolved to what it is. Therefore, a statistic (the basic Win Score formula) that inherently values certain positions over others seems faulty. In essence, the position adjustments required seem to be correcting for overweighting statistics that are largely based on floor positioning.

dberri

February 27, 2007

Westy,

As I note in the comment, the player evaluation with the simple formula, adjusted for position played, is virtually the same as the complex formula. Since simpler is easier to understand, why not use the simple formula? Of course, if you don’t want to, go ahead and just use Wins Produced.

Not sure how to make you see the value of a FGA, but I will repeat what I think I have said before. If a player misses a field goal, and there is no offensive rebound, the possession ends with no points. If a player commits a turnover, the possession ends with no points. So a field goal attempt and a turnover have the same value. This should make sense intuitively. It is also what the regression indicates.

I would add that you have not convinced me that there are any obvious holes. I think you need to explain what critieria we should use to create and evaluate a model. I have laid out my criteria.

About creating shots…. there is only value in creating shots if they go in. If they don’t go in, where is the value in this? Again, you need to show me how incorporating this factor improves our explanatory and predictive power. The “this just makes sense to me” argument is not very convincing.

And finally, about position adjustments… In baseball you also need a position adjustment. The amount of offense you expect from a first baseman is different from what you expect from a second baseman. Players have to be compared to the alternative. That is just the nature of evaluating performance. Not sure how to make that clearer.

Hope all this helps.

Huey

February 28, 2007

“If a player misses a field goal, and there is no offensive rebound, the possession ends with no points. If a player commits a turnover, the possession ends with no points.”

I think what Westy is trying to say is that a missed field goal appears only to be equivalent to a turnover if there is no offensive rebound. That’s why he mentioned that 3/4ths of all missed shots go to the other team, and why he was arguing for a a weighting of .75 instead of 1.00. I think Hollinger was arguing with you along similar lines.

TK

March 1, 2007

I think DB just answered this on a different thread, but you’re conflating FGAs with what happens after the shot. Let’s break down the outcomes.

If the attempt is good, the player accumulates the 2 (or 3) points for the made bucket and ends up +1 or +2. (And the Win Score reflects a positive possession.)

If they miss and rebound their own miss (like someone suggested Shaq does all the time) they end up even (-1 on the FGA and +1 on the board). (Thus, the Win Scores stays the same, reflecting that nothing has changed to help or hurt the team, which still has the ball.)

If they miss and someone else on the team picks up a rebound, then they end up -1 while the teammate ends up +1. (Thus, the Win Scores go down and up for the two players, but overall the team is even, reflecting a neutral possession.)

And if they miss and the other team rebounds, the player ends up -1, which reflects that they’ve hurt the team. And it’s THIS result that’s the same as a turnover, which has the same effect.

(And all of this is just on the intuitive level — completely beside the point that the regression suggests these weights in the first place.)

TK

dberri

March 1, 2007

TK,

You said it better than I said it. That is exactly right.

bballer

March 2, 2007

I agree with Westy in that the formula does not need to be so simple. Guards get punished for being the offense and big men who grab boards get inflated win scores. This is especially the case when there’s a big man who can’t score on a team with aggressive guards. A good example would be the championship Detroit Pistons with Billups/Hamilton and Ben Wallace. Doesn’t the fact that Wallace could never be relied on to create a shot put more pressure on the guards to create scoring opportunities? With the NBA’s 24-second shot clock this is especially the case as situations where opportunities must be created arise numerous times in every game. If you factor in that Hamilton will need to have a good defensive player on him and Wallace’s defender is pretty much free to provide help on defense it is even more true. Why should shooters like Hamilton and aggressive scorers like Iverson be punished for creating opportunities that their teammates would never be able to create?

dberri

March 2, 2007

bballer,

Everyone is compared relative to his position, so no one is getting punished for playing guard or rewarded for being a big man.

Your re-iteration of the argument that there is value in creating shots seems to fly in the face of the empirical evidence we have from the Iverson trade. After Iverson left the 76ers managed to find someone else to take shots. In fact, as expected, the team actually improved. Given this evidence, isn’t it time to put to rest the argument that players should be rewarded just for taking a shot?

Westy

March 2, 2007

Hey thanks for the responses, Dave and TK. I understand the rationale somewhat more clearly.

I guess my thought is that this weighting as described may evaluate the team well, but incorrectly values the players involved. Could slightly different weightings for FGA and offensive and defensive rebounds predict wins just as well? The way it’s set up above is that the player who shoots (and I think there’s inherent value in creating a shot as there wouldn’t be made shots without a created shot) is punished for a miss rebounded by one of his teammates. There wouldn’t have even been the chance for the offensive board without the shot. I agree that the end result of a missed shot rebounded by the opposition and a turnover is the same. But for an individual player, a created shot (a FGA) has to be more valuable than turning it over. The way it’s set up now, just coming across the halfcourt line and handing it to the other team is treated the same as running through an offensive sequence, working to get, and getting a shot that happens to miss.

In regard to the comparison with baseball, there isn’t a position adjustment for batting average in baseball because every player is doing the same thing– hitting a baseball safely a certain % of the time. Certain positions tend to be weaker at that statistic as you note, but probably are better in others (slugging).

In WinScore, however, supposedly every statistic important to winning is included. If that were the case in baseball, all the other intangibles including fielding would be included in a combined formula that weighed the contributions of each separate position and produced one final ‘value’ measure.

Thus in WinScore, if every necessary statistic is used, why are centers almost twice as valuable as SG’s? Somehow it seems the importance of ballhandling, outside shooting, and perimeter defense are being shortchanged.

The Franchise

March 6, 2007

Westy-

A created shot, though, is only valuable if it is likely to go in–to generate points. If it generates points, then the player gets credit for those points, which is a greater amount than the shot costs the player. If they’re taking good shots, they’ll be fine. If they’re putting up bad shots, then there’s a problem.

“Creating shots” only has value if other players are less capable of doing so, which does not actually seem to be the case.

Greg

March 13, 2008

Hey Dr. Berri. I’ve been reading the journal, and I really like the work you’ve done. I haven’t read the book, so I apologize if I’m asking questions you’ve already answered. Here goes:

The Win Score metric makes a basic assumption that all rebounds are equal. To state the case in terms of possession (since that is what the metric is built for) offensive rebounds are not the same as defensive rebounds. Defensive rebounds often come down in an area where they can be retrieved by several different members of the defensive team. With the shooting teams’ perimeter players backpedaling to the opposite end of the floor, a missed field goal presents a sizable disadvantage for the offensive team (5 on 3). Thus, a rebound is significantly more likely to be recovered by the defense than by the offense. The statistics bear this out; all players on all teams throughout all eras collect many more defensive rebounds than offensive rebounds. This would indicate that it is harder to grab offensive rebounds than it is to grab defensive rebounds. Additionally, defensive are far more likely to be gathered by players who are not beneath the basket, but partially as a result of the work done by the players under the basket (e.g., when a big guy taps a rebound out and it is “collected” by a guard, when a rebound bounces long, hits the ground, and is recovered by a guard, or when a rebound bounces over the frontcourt players’ heads’ and a little guy catches it). Essentially, this tells us that “rebound scavengers”, little guys who gather up rebounds without boxing out, can be overrated. I know this is kind of like stepping on sacred ground here, but Jason Kidd is a great example of this. Throughout his years in New Jersey, Kidd has played with weak centers, and typically smallish PFs. Now, if Jason Kidd averages more rebounds pg than Nene (or K-Mart, depending), thiscould be because Jason Kidd,a guard, is better at rebounding (a skill that involves taking a ball from amongst a group of big men) than the Nuggets’ PF. However it also could be because the Nuggets also employ Marcus Camby, and Jason typically plays with Jason McCullough, Jarrod Collins, and Mikki Moore. Since we might take it as obvious that big men are better than little men at wrestling the ball away from other big men, perhaps the second option is more likely.

Blah, I’m getting kind of long-winded here. I had some other questions, but I think I’ll wait ’til later on them. Thanks!

Greg

March 13, 2008

Just kidding! One other thing. This might help to explain the most confusing thing about your player ratings: namely that Jason Kidd, a very low-percentage shooter, always rates very highly. Possibly he is overrated in Win Score because he gets sole credit for a great number of rebounds that indicate little skill on his part. Perhaps this could be rectified by valuing off rebounds slightly more than def rebounds. Okay, now I’m finished.

Jason

September 22, 2008

Hi DB – I was trying to figure out PAWS for the Bulls in 1988 (wanted to answer my own question about why Chicago slipped backwards in 1989 despite the improvements of Pippen and Jordan’s continued excellence), but I hit an immediate snag. How do you determine who was a PG v. an SG? I don’t think it can be done retroactively, can it?

MJ led his team in assists in 89, and Hodges and Paxson certainly don’t read as PGs with their high rate of fire from 3 and low assists. But MJ also led in points and fgas and was by far the largest guard AND defended primarily at the SG. Would the system work if we break it down simply by G, F, and C rather than using all 3 positions?

Patrick Marshall

December 30, 2008

How is the formula WP48 = 0.104 + 1.621*PAWSmin adjusted for the College game? I would like to have some accurate win scores for college players as well and wondered if the static numbers in the equation were different then for the 40 minute college game.

Also are the position averages different?