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Friday, May 30, 2008
Linear Win Shares
We either love Pete Palmer’s Linear Weights, or we hate them. Or maybe we know we should love them, but something just… you know, bothers us.
What really bothers us is the single number issue. If you are going to represent something as a single number, we want zero to mean something, since even a below average player should count for something. So, here then, is a way to turn Linear Weights into two numbers.
The first thing we need to do is figure out the plate appearances of our player. But, we need a bit more context. We also need to know the plate appearances of all his teammates. So, we really need is the player’s percentage of his team’s plate appearances. Simple enough.
Then, we need to know how many games his team played, and multiply his PA percentage by his team’s games played. That effectively gives you the number of game slices he’s using up.
We also need to divide by 2, so that the offense gets half the game slices and the defense gets the other half.
So, a player that has 620 PA, while his whole team has 6200 PA earns 10% of the offensive game slices. If his team played 160 games, then he gets 10% of 80 games, or 8 game slices.
With me so far? Now, if a guy is average, then he gets 4 win slices and 4 loss slices. If he’s +1 win above average, then he gets 5 win slices and 3 loss slices. If he’s -2 wins relative to average, then he’s 2-6.
If he’s an average player, but was riding the bench, he might be 1-1. So, that leaves it up to you to figure out if you want the 2-6 guy, or the 1-1 guy. That’s not part of this discussion, but I just wanted to show you how much more a two-number system adds over a 1 number system.
Let’s go through a few examples. Derek Jeter (through 2007) has 106 game slices. According to Palmer’s Batting Wins (via Baseball-Reference.com), Jeter is +23.6 wins. So, since 53-53 would be average, then Jeter checks in at 76.6-29.4. (Feel free to round the number.)
Bill James recently has shown the Win Shares and Loss Shares numbers of a few players. One of my chief complaints of Win Shares was the lack of Loss Shares. Bill has addressed that. For Derek Jeter, he has his offensive WS/LS as 219-86. How does that compare to win sliced numbers of 76.6-29.4? In order to get the scale right, we multiply Palmer’s numbers by 3. So, 76.6 times 3 is 230, and 29.4 times 3 is 89. That gives us 230-89 for Jeter.
That’s pretty close, isn’t it?
Palmer James Player
230-89 219-86 Jeter
Let’s compare how my game slices (times 3) to James win shares plus loss shares (i.e., game shares), for the players that James has listed:
Slices Shares Player
481 468 Yount
424 417 Ozzie
415 421 Vizquel
363 356 Trammell
353 333 Larkin
319 305 Jeter
270 245 Abreu
257 261 Bell, G
Pretty close right? Using the PA approach of the player, we get 481 game slices (times 3) for Yount. His win shares + loss shares is 469. Basically, pretty solid (though the miss on Abreu sticks out).
Using our approach to convert Palmer’s single number into a two-number system (and then multiplying by 3 to get it onto James’ scale), we get:
Palmer James Player
305-177 293-175 Yount
171-252 203-214 Ozzie
148-268 180-241 Vizquel
218-145 214-142 Trammell
234-119 223-110 Larkin
230-89 219-86 Jeter
234-36 197-48 Abreu
153-104 146-115 Bell, G
Yount is “nailed ‘em”, as his Linear Weights is +21 wins, and Win Shares (after dividing by 3) is +20 wins above average. The game slice is 481 for Yount and 468 game shares.
Ozzie is a big miss. For whatever reason, Palmer has Ozzie as -14 wins as a hitter, and James has him as -2 wins.
Vizquel shows a similar gap.
Trammell is a “nailed ‘em”, as is Jeter.
Abreu is +33 wins for Palmer, and only +25 wins for James. Seeing that there’s a 25 game shares/slices gap for Abreu, and +8 wins of gap here, I’m tempted to think that this is a data issue.
George Bell is pretty close.
So, what does all this give us? Well, it leads us to believe that there’s not much separating Linear Weights and Win Shares. That you can make an easy conversion from one to the other. That any problems one might have with Linear Weights is easily “corrected” by introducing a second dimension, and that second dimension is very easy to calculate.
I suspect that the differences we see with Ozzie and Vizquel may be park related. But, we’ll only know that once we know how Win Shares are derived. The Abreu difference must be data related, and I’d discard that as a data point right now.
In the end, it seems to me that Bill and Pete were actually always talking about the same thing the whole time. They were just speaking a different language.