Simple Models of Player Performance

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In this forum I have mentioned a few times different measures of performance we introduce in The Wages of Wins. It occurred to me that perhaps the stories I tell here would be easier to follow if I proved a few more details on the measures we introduced.

Now detailing how we measure Wins Produced for NBA players, or Net Points and Wins for quarterbacks in the NFL, is a bit difficult given the limited space on a blog. And that is one reason we wrote the book. I can say that these measures are quite accurate, and as we note in the excerpt to Chapter Six, if you sum the Wins Produced created by the player’s on an NBA team you will get a number quite close to a team’s actual wins.

So if you wish to understand Wins Produced or Net Points you will have to buy the book. We did create two simple measures – QB Score in football and Win Score for basketball players – that I think can be explained.

Before I explain each, it is important to note why it was necessary to create new metrics of player performance. Sports provide very detailed measures of worker productivity. And these measures can be used to estimate the productivity of different workers or players. To do this, though, you have to link what the player has done – in other words, his statistics – to what the player was trying to accomplish – in other words, win games.

Measures like the NBA Efficiency metric, or the NFL’s quarterback rating measure, do not connect the player’s statistics to win. With a bit of work, though, we were able to take this step and hence we can measure how many wins a player produces in the NBA, or how many net points and wins a quarterback creates in football. Once we did this, though, we thought it might be useful to create very simple measures that everyone could calculate.

Let’s begin with football. We were able to estimate the relative value of a Yard Gained – which includes rushing and passing yards – Plays – which includes passing attempts, sacks, and rushing attempts – and Turnovers – which includes interceptions and fumbles. Our research indicates that one play – in terms of wins and points – is worth about three times the value of a single yard. A turnover is worth about 50 yards. Now these values – 3 and 50 – are not exact. But it is close enough to give you a quick estimate of a quarterback’s effectiveness. Given this, QB Score – which is both less complex and more accurate than the NFLs’ quarterback rating system — is calculated as follows:

Yards – 3 X Plays – 50 X Turnovers

Now let’s turn to basketball. Again the methodology is the same. Determine the relative value of each statistic. Our research indicates that the relative value of a point, rebound, steal, turnover, and field goal attempt – in absolute terms – is equal. Assists, blocked shots, free throw attempts, and personal fouls – again in absolute terms – are each worth less than a point, a rebound, etc… To keep it simple, one can argue that each of these latter stats is worth ½ a point, rebound, etc… Now the ½ value is not exact, but using ½ keeps it simple and we find one gains very little using the exact relative value. In other words, player rankings do not change very much when you use the exact values.

So given this argument, one can measure performance with this simple calculation, which we call Win Score.

Points + Rebounds + Steals + ½Assists + ½Blocked Shots – Field Goal Attempts – Turnovers – ½Free Throw Attempts – ½Personal Fouls

IT IS IMPORTANT TO NOTE THAT THIS IS NOT THE SAME AS WINS PRODUCED. Sorry to interrupt this post with a bit of shouting, but I noticed people were heading for this post and not always understanding what was being said.  For a brief discussion of the difference between Win Score and Wins Produced – and there is a difference — please go here.  Or for a good discussion of what our methods mean for analysis of player performance in the NBA, click on Malcolm Gladwell’s comments here and here.  And for a discussion I offered summarizing what we are saying about the NBA please click here and here.

And now back to the rest of the original post… 

To get at Wins Produced you have to use the exact values, and make a few adjustments – such as adjusting for position played – which we note in the book. Still, Win Score is sufficient to give you a quick snapshot of a player’s performance. And it is especially useful if you wish to know if a player is playing better or worse than he did before.

Hopefully being able to see these metrics will help people understand the stories we tell. Again, further details are offered in the book. I should emphasize that these details do not include any math – in fact we avoided using math in our book. Instead, in what we hope is simple language, we explained how we calculate Wins Produced and Net Points. And from these explanations, we also derive Win Score and QB Score.

– DJ

199 thoughts on “Simple Models of Player Performance”

  1. I can’t comment on your NBA metrics, since I don’t follow basketball. But your QB metric is honestly worthless. A player-rating is meant to measure the value of a player in a way that is at least nominally independent from the performance of the team as a whole. Your measure doesn’t even attempt to seperate the QB from the rest of the team – you don’t even seperate passing yards (which the QB has SOME responsibility for, though much still depends on his recievers, his O-line, and the defense) from rushing yards, which have almost nothing to do with the QB. And it isn’t exactly the QB’s fault when his running back fumbles.

    For real football metrics, go to footballoutsiders.com. Their stats are great at seperating out the value an individual player creates, and at creating team ratings that accurately _predict_ performance, instead of just reflecting stats back. Their off-season prediction models predicted the resurgence of Tampa Bay last season and the emergence of San Diego the season before. In other words, their site is more than just a gimmick by an economist who hasn’t bothered to do any background research.

  2. Pio,
    Let me try and provide more details regarding QB Score. When we calculate this metric we only consider the stats credited to the quarterback. So we only consider the quarterback’s passing yards, interceptions, fumbles, rushing yards,etc…

    What you note about differentiating the quarterback from his teammates we also state in the book. Quarterbacks do not play by themselves. They need receivers to catch, lineman to block, etc… Given how dependent quarterbacks are on their teammates it is not surprising that the performance of quarterbacks, measured via whatever statistics people generally use, tends to be very inconsistent.

    Finally, I like footballoutsiders.com as well.

  3. Please stop the absurd practive of adjusting your NBA statistics for position. Positions in the NBA are becoming so arbitrary that to try to base a statistical analysis on what letter(s) sits beside a players name on the roster is as ludicrous as adjusting for jersey number.

    What position does Jason Terry play? Iverson? Duncan? Antoine Walker? Tracy McGrady? LeBron?

    Your system is flawed at best. It may be the most accurate algorithm yet to measure a player’s value, but that’s not saying much. Hey, I have the most accurate estimate yet of how big the universe is. And?

  4. Hi … after reading some of your blog, I’m looking forward to reading the book. My question is how you account for the endogeneity of a player’s “Win Score” with respect to his composition of teammates? That is, presumably a player’s skills will be complements for some of his teammates’ skills (Kidd’s passing and Vince Carter’s leaping, e.g.), and substitutes for others. And if a player’s Win Score depends on his teammates, then is it reasonable to compare Win Scores across teams?

    Mark Foley

  5. I love this idea, and I think it can come down to specific formula. But there is more to consider, including player smarts and reputation as I don’t believe the relative value of a point – in absolute terms – is equal.

    As a former basketball player, one of my strengths was to get the other team’s “best player” to foul me. I was even skilled enough to sacrifice a lay-up to draw a foul and then hit two foul shots. By the fourth quarter, the team’s star would either be on the bench or super-cautious defensively, given us a tremendous late game advantage. I feel like this contribution lead to a weaken defense and would have given me more Win Score than your formula would give me, since there are minute factors like this that could come in play even in the NBA.

    Also being a “smart player” comes into play when fouling a player. I would like to think there are players, like myself, that make “smart fouls” that save 2 points more than it gives 2 points to the other team. (i.e. stopping a fast break at half-court.) This could sway the Win Score too.

    Not to mention reputation too. For instance, Shaq, and (I’m guessing) teams probably shoot more inaccurate outside shots when he’s in the game which would give his team an advantage, because they are less likely to drive the lane. This also would decrease Shaq’s opportunities at blocked shots that could raise his Win Score number too. I’m sure for a player like Allen Iverson, an opposing coach would put his best defensive player in the game to cover him (sacrificing the regular starter who’s more offensively skilled.) The affects of this would be tremendous as well.

  6. I think your WinScore value is a less accurate form of Tendex or PER ratings commonly used by NBA analysts. Its difficult to know the real win or possesion value of a rebound, steal, block, turnover, etc., and we all know that scoring is only the half of the game, you need to defend the opponent´s score too, but I don´t agree with the fractions assigned to these stats.
    Neither 82games.com have solved that basketball code, that´s why everybody likes to go empiric and just copy winners teams patterns.

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  10. For basketball, I would propose an even simpler method (not that many 1/2s):

    Points + Rebounds + Steals + Assists + Blocked Shots – Field Goal Missed – Turnovers – Free Throw Missed – ½Personal Fouls

  11. Sagaliba,
    You have proposed Robert Bellotti’s Points Created model. This model, very similar to NBA Efficiency, also overvalues inefficient scorers.

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  27. my opinion the guy who completed 6 more passes is better because that is 6 more opportunities to move the chains and 6 more opportunities for his guys to get some yards after catch and 6 more times the ball went to his guy as oppoesed to not

    good post and I like the idea for a new rating system

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  43. I have always thought such formulas overestimate the FT shooting accuracy. Here is why :

    Simple example:
    - player A makes a FG, his WinScore is “1″
    - playerB makes a FG, draws a foul but misses the extra free throw, his winscore is “0.5″
    However, player B did score 2 points using only one possession as did player A. So his rating should not be worse than A’s, if not better.

    So if you are a woeful FT shooter (Shaq’s name comes to mind), being unstoppable, drawing fouls and getting to the charity stripe will count against your winscore if you can’t shoot at least 50% from the line.

    Then of course, not all free throws come after a FG, but those should be treated separately (bonus when converting them, no malus when not)

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  126. Wins = c + j*PTS/PE – k*DPTS/PA + e

    differentiating with respect to PTS we get Marginal value of PTS = j/PE. j is the coefficient; what value of PE is used?
    I see PE = FGA+0.47*FTA + TO – REBO. This can be calculated for each game. But if I am looking at seasons 2000/01 to 2007/08 what value of PE should I substitute in j/PE? Is it the (total PE for every game under consideration)/number of games under consideration?

    Thanks

    E

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