Thursday, February 23, 2023
Improving WAR - Alternative to WPA
On Sept 8, 2019, the Astros beat the Mariners 21 to 1. That 20 run differential was based on the Astros batters getting 22 hits and 7 walks, while the Astros pitchers allowed 1 hit (a HR allowed by Cole).
The issue
In a context-neutral setting, we would have expected a 17 run differential, fairly close to the actual 20 run differential. The context-neutral runs-to-win conversion is roughly 10 runs per win, and so, sabermetrically, the Astros were +2.0 wins above average (WAA) using their actual runs scored and +1.7 WAA if we relied on their wOBA by their batters and pitchers.
Every game however has the winner with +0.5 wins above average (and every loser is -0.5 WAA). In order to properly credit the Astros batters and pitchers with their excess runs, we need to devalue their runs in the context of this game. The typical way is to use Win Probability Added (WPA), which has the nice property of guaranteeing the winner gets +0.5 WAA and the loser gets -0.5 WAA. However, WPA depends on real-time information. This is a fine approach if you are a bettor or a fan, living in the moment. But from the standpoint that a run scored in the first inning is as impactful as the run scored in the last inning, then WPA is not the tool for this job.
I will now introduce the tool for this job.
Pluses and Minuses
We can break up all the performance of the batters and pitchers in terms of good things they did to advance toward a win (the pluses) and the bad things (the minuses). For batters, that means the pluses are the hits and walks, while for pitchers, that means it is the outs. On the minus side, it is the flip side: batters are outs, and pitchers are hits and walks allowed.
For the game in question, the Astros batters generated +18.5 positive runs, while the Astros pitchers generated +6.5 positive runs. In terms of negative runs, Astros batters are at -6.5, while the Astros pitchers are -1.5. Adding it up, and the Astros players are +25 positive runs and -8 negative runs. The context-neutral total is +17 runs above average, which we are trying to translate into +0.5 wins.
The approach
So, how do we get there? We are going to ultimately use a 10 runs per win conversion, so we are trying to get an effective +5 runs above average (to convert to the +0.5 WAA). We treat the -8 negative runs as our baseline for this game. In order to get to +0.5 WAA (or +5 runs above average), we need +13 positive wins. Since we have +25 positive runs, 13/25 factor. In other words, we chop in half all the positive things that the Astros batters and pitchers did, since that is the excess. While it is bad luck that Gerrit Cole paired his 1-hitter to his batters getting 21 runs scored, we still only have +0.5 WAA to hand out. And we get there by diminishing all the good things the Astros players did in this case.
On the flip side are the Mariners. They had +8 positive runs and -25 negative runs. All of the bad stuff they did also gets chopped in half. While it was a terrible performance all-around, there is still only one loss in the game, or -0.5 WAA.
So, why is this approach better than WPA? Well, WPA treats each plate appearance as its unit-of-work. Once the plate appearance is over, the transaction is over, and so, we reassess where we are in the game. In this game, the impact of the last plate appearance is far far lower than the impact of the first plate appearance. As I said, that is fine if you live in the moment. But if you think of the entire game as a single unit-of-work, that the game itself is one transaction, then every plate appearance has to be treated independent of the score in real-time. And instead, it has to be evaluated dependent on the final score. And the approach I have laid out is one way to get there.
Close game
On Apr 20, 2010, the Padres beat the Giants 1-0. Indeed in this game, the Padres only had one hit and three walks, while the Giants scattered six hits and two walks. While in a context-neutral setting, the Giants played better. In reality, it is the Padres that won the game. We want to recognize their performance in the context of this game.
The Padres earned +7 positive runs and -10 negative runs. We want to convert their context neutral -3 runs above average to their game-winning +5 runs above average. Treating their +7 positive runs as the baseline, then we need -2 negative runs to get our overall +5 RAA. And so, their -10 negative runs will count as only -2 negative runs within the context of this game. They did alot of bad stuff, but in context, it did not really hurt them. So, we only count 20% of the negative runs in terms of their win impact.
Alternative
Does all of this make sense? I am not sure. I could have just as well used the -10 negative runs as the baseline, and then count the +7 positive runs as +15, and therefore double all their positive things they did. Or some combination of the two, maybe treat it as an expected +11 positive runs and -6 negative runs. And so, we apply a factor of 11/7 to the +7 positive runs and -6/10 to the -10 negative runs.
In any case, we now have a framework for a game-level WPA-type of approach. And we just have to figure out the details.
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