Get to Know: WPA/LI

by
March 19, 2008

WPA/LI (context neutral wins / game state linear weights): How many wins a player contributes to his team with the Leverage Index aspect removed, invented by Tom Tango.

Calculating WPA/LI: WPA is divided by LI for each individual play attributed to a specific player and then the WPA/LI for the individual plays is then added up to create WPA/LI for an entire season. This is considerably different then taking a player’s WPA and dividing it by pLI.

Why you should care: Unlike standard linear weights, WPA/LI does take into account the situation. So at times when a walk would be just as valuable as a home run, WPA/LI accurately weights the walk and the home run, where linear weights would still give .13 wins to the home run and the walk .03 wins.

Links and Resources:

Unleveraging Win Probability
The Book Wiki: Linear Weights





 

David Appelman is the creator of FanGraphs.

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niko
14 years ago

David,
I am extremely confused by this description. If WPA were “context neutral” than what would be the point or “removing” the LI aspect? Furthermore, aren’t we technically introducing a LI aspect by including it in the definition/equation? If I understand the stat correctly, it measures contextual (as opposed to wOBA’s inherent) value per opportunity to contribute, and a number closer to zero is worse. It’s be really helpful to include some “baselines”. Also, I understand that mathematically WPA/LI is different than WPA/pLI, but I have been unable to grasp the statistical significance of that fact. Thanks.

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fang2415
13 years ago
Reply to  niko

There are two things about this article which also confused me mightily for a while.

One is the heading “WPA/LI (context neutral wins / game state linear weights)”. I first read this as “WPA/LI is the same as context-neutral wins divided by game-state linear weights”. I believe the intended meaning is “WPA/LI may be called ‘context-neutral wins’ or it may be called ‘game-state linear weights'”.

Second, it took me a long time to realize that the “Why you should care” section explains the distinction between WPA/LI and linear weights, *not* between WPA/LI and WPA (which is probably what most readers are looking for).

WPA/LI is “context-neutral” compared to WPA, because WPA/LI does not, for example, consider most offensive events in the ninth inning to be worth more than most offensive events in the first. So if WPA can be called “wins”, WPA/LI can be called “context-neutral wins”.

But compared to something like wOBA, which uses a fixed set of linear weights for all situations, WPA/LI could be said to be “situational”. wOBA will always consider a HR to be worth 1.70 and a walk to be worth .62, no matter when they happen. WPA/LI, on the other hand, will recognize that with the bases loaded in a tie game in the bottom of the ninth, a walk is just as good as a home run. So WPA/LI can be called “game-state linear weights”, because it recognizes that the same event may be more or less important, and thus weighted differently, depending on the game state.

Complicating things even further is the fact that the “Quick Glossary” link on the stats pages define WPA/LI as “Situational wins”. That strikes me as even more baffling than any of the other supposedly intuitive definitions listed here, especially when it’s listed next to WPA, an even-more-situational measure of wins.

I may still be missing something here, but that’s the best sense I can make of it. I love this site, but sometimes they and the whole sabermetric community seriously need to work on tightening up their language.

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fang2415
13 years ago
Reply to  niko

Also, the importance of WPA/pLI vs WPA/LI isn’t really well explained here or on the Get to know Clutch page (where it really matters because Clutch = WPA/pLI – WPA/LI).

The way I see it, the trick is that WPA/pLI means “sum(WPA)/LI per event” while WPA/LI means “sum(WPA for one event divided by the LI for that event)”. Both are measures of win contributions per unit of leverage, but because WPA/pLI first sums total wins and then divides by total leverage, all wins get divided by the same number. So in WPA/pLI, that bases-loaded walk (or home run) that happened with two outs in the ninth inning ends up counting more than a bases-loaded walk in the first.

WPA/LI, on the other hand, first divides each event’s wins by that event’s leverage, and then totals up the sums; so high-leverage win contributions get divided by high numbers and low-leverage contributions get divided by low numbers. Now the walk-RBIs count the same whether they happened in the ninth inning or in the first. (I think? — anyway, they should be a lot closer in value than in WPA/pLI.)

By subtracting one number from the other, we get some sort of an idea of how much better (or worse) a player did in the high-leverage situations than in the low-leverage ones, which is what Fangraphs reports as Clutch.

Again, I’m not 100% on all the details, but that’s how it makes sense to me.

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