Simple Models of Player Performance

Posted on May 21, 2006 by


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