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Calculating Win Shares

I. Introduction

Stealing a page from baseball's Bill James, I decided to attempt to calculate college basketball Win Shares. This article will describe how I came up with the Win Shares system for college basketball (please see this article for the pro version of the system). If you believe that any attempt to attribute team success to individual players is an abomination, then read no further, as this article will be of no interest to you.

II. What is a Win Share?

Bill James developed his system such that one win is equivalent to three Win Shares. My system deviates from James's system in three key ways:

  1. In James's system, one win is equivalent to three Win Shares. In my system, one win is equivalent to one Win Share.
  2. James made team Win Shares directly proportional to team wins. In his system, a baseball team that wins 80 games will have exactly 240 Win Shares, a baseball team that wins 90 games will have exactly 270 Win Shares, etc. In my system, a basketball team that wins 25 games will have about 25 Win Shares, give or take.
  3. James did not allow for the possibility of negative Win Shares. In his system, the fewest number of Win Shares a player can have is zero. In my system, a player can have negative Win Shares. I justify this by thinking about it in the following way: a player with negative Win Shares was so poor that he essentially took away wins that his teammates had generated.

III. Crediting Offensive Win Shares to Players

Because the number of statistics we have available to us in our college basketball database is limited (no offensive rebounds, no turnovers, etc.), we will not use methods based on Dean Oliver's work (as the pro version does), although the basic framework will remain the same. Here is the process for crediting Offensive Win Shares (using Shane Battier of the 2000-01 Duke Blue Devils as an example):

  1. Calculate the player's modified points. The formula is: 
      2.0 * (field goals) * (1 - ((team assists) / (team field goals)))
+ 1.5 * (field goals) * ((team assists) / (team field goals))
+ 1.0 * (three-point field goals)
+ 1.0 * (free throws)
+ 0.5 * (assists)
    Plugging Battier's statistics into the formula above we get 741.71 modified points.
  2. Calculate the player's modified shot attempts. The formula is: 
      1.000 * (field goals) * (1 - ((team assists) / (team field goals)))
+ 0.500 * (field goals) * ((team assists) / (team field goals))
+ 1.000 * ((field goal attempts) - (field goals))
+ 0.475 * (free throw attempts)
+ 0.500 * (assists)
    Plugging Battier's statistics into the formula above we get 587.44 modified shot attempts.
  3. Calculate Division I points per shot attempt. Division I points per shot attempt is equal to (division points) / (division field goal attempts + 0.475 * (division free throw attempts)). For 2000-01 this is 1.0534.
  4. Calculate marginal offense for each player. Marginal offense is equal to (modified points) - 0.875 * (division points per shot attempt) * (modified shot attempts). For Battier this is 741.71 - 0.875 * 1.0534 * 587.44 = 200.25. Note that this formula may produce a negative result for some players.
  5. Calculate marginal points per win. Marginal points per win reduces to 0.25 * (school points per game + opponent points per game). For 2001-01 Duke this is 40.31.
  6. Credit Offensive Win Shares to the players. Offensive Win Shares are credited using the following formula: (marginal offense) / (marginal points per win). Battier gets credit for 200.25 / 40.31 = 5.0 Offensive Win Shares.

IV. Crediting Defensive Win Shares to Players

Here is the process for crediting Defensive Win Shares (once again using Battier in 2000-01 as an example):

  1. Calculate school marginal defense. School marginal defense is equal to 1.125 * (division points per shot attempt) * (school field goal attempts + 0.475 * (school free throw attempts)) - (opponent points). For 2000-01 Duke we get 812.28.
  2. Calculate the player's share of the team's marginal defense. The player's share of the team's marginal defense is equal to 0.40 * ((total rebounds) / (school total rebounds)) + 0.25 * (steals / (school steals)) + 0.25 * (blocks / (school blocks)) + 0.10 * (assists / (school assists)). How did I get those weights? Of the statstics we have available, pro Defensive Win Shares are most dependent on defensive rebounds, steals, blocks, and assists, so I regressed pro DWS on those stats and then found the relative importance of each regressor (approximately 40% for defensive rebounds, 25% for steals, 25% for blocks, and 10% for assists). Getting back to our example, Battier's share on 2000-01 Duke is equal to 0.2540
  3. Calculate marginal defense for each player. Marginal defense is equal to (school marginal defense) * (player share). For Battier this is 812.28 * 0.2540 = 206.32. Note that this formula may produce a negative result for some players.
  4. Calculate marginal points per win. Marginal points per win reduces to 0.25 * (school points per game + opponent points per game). For 2000-01 Duke this is 40.31.
  5. Credit defensive Win Shares to the players. Defensive Win Shares are credited using the following formula: (marginal defense) / (marginal points per win). Battier gets credit for 206.32 / 40.31 = 5.1 Defensive Win Shares.

V. Putting It All Together

The final step of the process is to add Offensive Win Shares to Defensive Win Shares. In our example, Shane Battier's total in 2000-01 is 5.0 + 5.1 = 10.1 Win Shares.

VI. Does This Work?

Because this metric is designed to estimate a player's contribution in terms of wins, it makes sense to see if the sum of player Win Shares for a particular school closely matches the school's win total. For 2000-01 Duke the sum of player Win Shares is 39.2, while the school's win total is 35, an error of 35 - 39.2 = -4.2 wins. This error is actually larger than the "typical" error; looking at all Division I schools since the 1998-99 season (the last season we have complete player statistics), the average absolute error is 2.3 wins and the root mean squared error is 3.0 wins.

VII. Feedback

If you have any comments or questions about the Win Shares methodology, please send me some feedback.

Revision History

Version 1.0