Win Shares

Win Shares is a statistic developed by Bill James that attempts to apportion credit for all of a team's victories to individual players. It differs from many sabermetric methods in that it considers the team as a whole, rather than placing the individual's statistics in an average context. Win Shares are first distributed between the team's offense and defense. The defensive credit is broken down first between pitchers and fielders, then between fielding positions, and finally to individual fielders. The unit for Win Shares is thirds of team wins; a team that wins 100 games will have 300 Win Shares credited to its players.

The guiding principle behind Win Shares is the comparison of units and players to "marginal" performance. A summary of how Win Shares are created can be found at Baseball Graphs. Baseball Graphs also posts an annual update of all historic Win Shares data, available at this link

Dividing Credit Between Offense and Defense

The first step in figuring Win Shares is to determine what percentage of wins go to the offense and defense of the team. The initial step is to determine how many runs an average team would score in the team's park in the same number of innings:

ExpR = Lg(R/IP)*PF(R)*IB
where PF(R) is the park factor in terms of runs, and IB is an estimate of team innings batted, figured as IP - Home Wins + Road Losses. ExpRA = Lg(R/IP)*PF(R)*IP

Next, marginal runs are calculated. A marginal offense is one that scores runs at 52% of the league average; a marginal defense is one that allows runs at 152% of the league average:

TmMR = R - ExpR*.52 TmMRA = 1.52*ExpRA - RA

The percentage of team marginal runs contributed by the offense is the percentage of team wins that the offense will be credited for, and likewise for the defense:

TmOWS = TmMR/(TmMR + TmMRA)*W*3 TmDWS = TmMRA/(TmMR + TmMRA)*W*3

Dividing Defensive Win Shares Between Pitching and Fielding

To distribute team DWS between the pitchers and the fielders, James uses seven criteria: Defensive Efficiency Record, strikeouts, walks, home runs, errors and passed balls, double plays, and winning percentage. Each of the seven factors is converted to a number of "claim points", which are used to determine the breakdown. For an average team, 67.5% of the shares are allocated to pitchers.

Distributing Offensive Win Shares to Individuals

Once team OWS are known, it is relatively straightforward to find individual OWS. First, the individual marginal runs are figured:

MR = RC - Lg(R/Out)*Outs*PF(R)*.52

where RC is the player's Runs Created and Outs = AB - H + CS + SH + SF + GIDP

Any sub-zero MR figures are zeroed out, and the positive MR are summed. The percentage of team OWS for each player is proportional to the percentage of MR they contributed:

OWS = MR/sum(individual positive MR)*TmOWS