Batting Game Shares

November 14, 2003

Thanks to comments from Tango, Patriot, Charlie Saeger and others, I’ve developed a methodology for determining Game Shares and assigning them to batters.  As explained in the previous article, I feel that these are important to add vital context to the Win Shares totals.  Without them, player Win Shares can be misleading.

Here’s what I did, and here’s why I decided to focus on Game Shares instead of Loss Shares.

My approach, following Tango's suggestion, was pretty straightforward. I took each team's average runs scored, adjusted for home park, and subtracted them from 148% of the league average. Then I took each team's average runs allowed, adjusted for home park, and subtracted 48% of the league-average runs allowed from them. I used the ratio of these two figures to assign the team's losses to offense and defense.

In other words, I used the inverse of the regular Win Shares methodology to assign losses. You might call these Marginal UnRuns.

Why do this? Because a team's Win Share is a Loss Share for a team's opponent. And vice versa. How many losses did an offense incur? The same number that their opponents' defense won. I just flipped the formulas.

Let me know if that doesn't make sense to you.

The only difference is that I used a 148% threshold to calculate the offensive Loss Shares, while the opponents' defense uses the 152% threshold for its defensive Win Shares. This is the natural bias that James called for in Win Shares, and I'm not going to monkey with it right now.

The exact same inverse logic applies to defense (pitching and fielding) and it applies as well to individual players. So that's how we assign Loss Shares to individual players.

I've doublechecked all the math. It adds up to total team Wins and Losses. I believe strongly that this approach works.

Two more steps: I added the Win Shares and Loss Shares to calculate "Game Shares." These are the number of games, either wins or losses, that the player essentially contributed (times three). Then I calculated Win Shares Above Average like this: Win Shares minus 50% of Game Shares.

Voila! You now have Win Shares in complete context. So let's look at the Mets' leaders in Win Shares Above Average (WSAA):

Player Team WinShares Game Shares WSAA
C Floyd NYM 16.2 15.8 8.3
J Burnitz NYM 9.8 10.2 4.7
J Phillips NYM 13.2 17.1 4.6
M Piazza NYM 9.4 10.3 4.2
J Reyes NYM 9.9 11.3 4.2
T Wigginton NYM 12.9 24.6 0.6
J Roach NYM 0.3 0.0 0.3
R Alomar NYM 6.0 11.5 0.3
See how this changes the order of things? Phillips is now four WSAA ahead of Wigginton which, quite frankly, is where he should be. From a batting point of view, Wigginton is average; Phillips is above average. Check out how the relative order of virtually every batter changes when using WSAA instead of WS.

There is a lot to comment upon here. I plan to calculate batting WSAA for all NL and AL players over the weekend and throw in a lot of observations. But there is one thing I want to comment on right now. You may have noticed it. Cliff Floyd has more Win Shares than Game Shares.

This is the problem with the threshold approach. Some players go over the threshold. In other words, they have negative Loss Shares. If you think Floyd is funky, wait until you see Pujols and Bonds.

This is why I don't just subtract Loss Shares from Win Shares to calculate WSAA. It's also why an "Offensive Winning Percentage" approach doesn't work. Game Shares and WSAA is the approach that does work. The math makes sense, and every "sanity check" I've tried holds up. For instance, Game Shares correlate very highly with number of outs made by batter (correlation coefficient of .99).

I believe WSAA is the correct approach.

 
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