SkyKing162's Baseblog

A fan of the Yankees, Red Sox, and large sample sizes.

Win Shares + Loss Shares = Game Shares

This was originally a post at RotoJunkie. It's been modified to seem more like an article for my blog. If you want to comment, head on over to the Sabrmetrics forum. Enjoy...

As a burgeoning Sabrmetrics groupie a few years ago when Win Shares hit the market, I ate it up. I thought it was the coolest ranking method. Well, almost the coolest. You see, there were things that just bugged me about Bill James' Win Shares system, mostly the (many parts) where James made decisions more subjectively than objectively. For example, those weird 40/30/20/10 weighted scales for valuing individual defense, the 52/48 argument (I think pitchers are undervalued, so I'll give 'em more points), and the fact that a team's Win Shares are directly proportional to wins, when there is a lot of variability in wins given a certain ability level. But it wasn't until I really started doing lots of my own baseball analysis that something else started to bug me. I couldn't explain it until I read a pdf document put together by TangoTiger and Rob Wood from Baseball Primer. Plain and simple...

Win Shares just aren't a complete, useful metric without their counterpart, Loss Shares.

Take two pitchers, Bob and Nolan. They don't seem like pitchers of equal ability, except that Bill James (via Win Shares) says they are. So, are they? Oh, you want some stats...ok, here you go:

Bob: 200 IP, 3.00 ERA, 0 BB, 0 SO, 0 HR (yes, every batter puts the ball in play - I love extreme examples)
The common assumption in the post-DIPS world is to say that half the credit for the results of balls in play go to the fielders and half to the pitchers, so I'll stick with that. Thus, since all of the batters Bob faced put the ball in play, Bob gets half the credit (half of all is half) for runs saved during his time on the mound: (6.75 ERA - 3.00 ERA)/9*200*.5 = 41.7 runs prevented, where 6.75 is the replacement level ERA of 1.5 times league average ERA.

Nolan: 200 IP, 4.00 ERA, with peripheral stats such that Nolan garners 75% of the credit for runs prevented (this doesn't mean half the batters he faces put the ball in play - it only means that half the runs scored are a result of balls put in play and the other half are a result of balls not put in play)
Nolan's credit = (6.75 - 4.00)/9*200*.75 = 45ish runs prevented.

Let's assume that both Bob and Nolan pitch in front of fielding teams with the same ability. Win Shares says Nolan deserves more credit, because he prevented more runs, even though he pitched the same number of innings with an ERA a full run higher than Bob. Seriously, would you want Nolan as your pitcher, or Bob? Do you want 200 IP with a 4.00 ERA or a 3.00 ERA? Seems like there's something fishy going on...

The idea behind Win Shares is that it assigns credit (Win Shares) on the basis of responsibility. Nolan's responsible for preventing more runs than Bob, thus he receives more Win Shares. But he's also responsible for allowing more runs than Bob, which Win Shares ignores. What's need is Loss Shares. Bill James even alludes to the fact that he thought about Loss Shares, but left them out because he couldn't figure out how to calculate them. But they're critical if you want to look at the whole picture. In order to compare Bob and Nolan, we also need to know how many extra runs more than Bob Nolan was responsible for allowing, in addition to the number of extra runs Nolan was responsible for preventing.

I don't claim to have come up with a way to calculate Loss Shares (although I believe Tango and Rob did in their pdf file), but let's do a little calculation that's on the right track.

Let's define "runs allowed^" as runs allowed above the "ideal pitcher" (the positive version of the replacement pitcher). Where the replacement pitcher has an ERA of 1.5*lgERA, the ideal pitcher has an ERA of .5*lgERA = 2.25 in our example. (Yes, pitchers often have better ERAs than this ideal ERA, but the point will still get across - plus, pitchers can, and do, have ERAs worse than replacement level.)

Bob gets charged with allowing^ (3.00-2.25)*200/9*.5 = 8.3 runs worse than ideal.
Nolan gets charged with allowing^ (4.00-2.25)*200/9*.75 = 28.5 runs worse than ideal.

Hmmm, Bob's responsible for allowing way fewer runs below ideal than Nolan. Let's combine runs prevented and runs allowed^:

Bob NET = 41.7 - 8.3 = 33.4
Nolan NET = 45 - 28.5 = 17.5

Thus, while Win Shares gives equal credit to Bob and Nolan, "NET Shares" would say Bob's performace was about twice as valuable as Nolan's. Why? Because while Nolan prevents more runs, he's also given more responsibility (aka opportunity) to prevent runs. And with more opportunity, Nolan's also allowing more runs, so much more that his advantage in Win Shares gets negated. It's like saying the Braves are better than the Tigers because they won 94 games to the Tigers' 68, without knowing how many games both teams played. If both played 162 games, the Braves are better, but if the Braves played 200 games and the Tigers played 100, the Tigers aren't more impressive? The same idea holds for Win Shares. Nolan uses a bigger chunk of the defensive opportunities (Game Shares) than Bob and thus should be held accountable for it. So in addition to Win Shares, we need Loss Shares. Together the two imply an all-encompassing stat - Game Shares. Because Nolan's more responsible than Bob for runs while he pitches, Nolan has more Game Shares.

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