Through all the craziness of the AL MVP debates in the past week, I’ve heard one claim argued over and over without much rebuttal. It is this: Miguel Cabrera has been a monster in September, and because games mean more in September, Miguel Cabrera’s performance during September should be given extra weight.
Now this makes sense intuitively, for the same reason that WPA (Win Probability Added) makes sense intuitively. A win or a loss in September is going to alter a team’s chances of making the playoffs much more than a win or loss in April would. If we had a game-wide equivalent to WPA, games in September would have a higher leverage index than games in April, just like plays in the 9th inning have more significance than plays in the 1st inning.
But wait a second. That’s not entirely true. In blowout games, plate appearances that occur in early innings when the score is close have a higher leverage index than plate appearances in late innings when one team is behind by a lot. For example, the leverage index of the first play of the game is 0.9, which is slightly less important than average. But the leverage index when the away team is down by 4 runs in the top of the ninth is 0.4 (and would be much lower with an 8-run defecit).
Similarly, the games that the Astros play this month mean nothing. They are mathematically eliminated from the playoffs, so a win and a loss have the same effect on their chances of making the playoffs: 0%. However, in the first game of the season, though the result didn’t mean much, it meant something. So for the Astros, a player that performed well in April and was average the rest of the time is more valuable than a player that performed well only in September and was average the rest of the time.
There’s a problem with that logic, though. If the Astros won an extra game in April, it would have the exact same effect as if they won an extra game in September instead. If they won the game in April, they might have the illusion of having a better chance, but assuming the rest of the results stayed the same, it wouldn’t mean any more than a September win would.
The same is true for a single game. Imagine a game in which the home team wins 1-0, the one run being a solo homer. For the purposes of WPA, a homer hit in the first inning would have much less value than a walk-off homer hit in the bottom of the 9th. The 9th inning home run increased the team’s chances of winning by close to 50%, while the first inning home run probably only increased it about 10% (just estimating here, though the exact values are out there somewhere).
But did the 9th inning home run really matter more than the 1st inning home run? Either way, the home run made the difference in the game. There may have been more pressure on the batter in the 9th, and more celebration afterwards, but a solo homer would have been equally important as far as the end result is concerned.
The reason WPA doesn’t give as much credit to the 1st inning homer is uncertainty. In the first inning, we don’t know if the game will end 12-2 or 1-0, so we just take the aggregrate of those scenarios and calculate the importance of that home run accordingly. But in the 9th, there’s much less uncertainty about how the game will end, and no uncertainty about how a home run will affect the result. Yet looking back on the game afterwards, we can see that a first inning home run would have had the same effect on the game as a walk-off.
With this in mind, doesn’t it seem unfair to reward the player who hit the walk-off more than the player who hit the first inning home run. They both contributed equal value to the team, and should be rewarded accordingly. Similarly, while these September games feel more important because there is less uncertainty, why should we weigh September performance more than April performance?
Yes, Miguel Cabrera has come through in a big way in September, but if we switched his September and May, the Tigers would be in the EXACT same position as they are now. The narrative would be different – people would be saying that Cabrera is choking when the needs him most – but the end result would be the same. So instead of looking at month by month numbers or WPA (though Trout is winning in WPA), we should look at overall numbers. Yes, the clutch factor should be taken into consideration, but don’t use WPA as the be-all and end-all of clutch hitting (and please, I beg you, don’t use RBI either).
The Fundamentals 
“But did the 9th inning home run really matter more than the 1st inning home run?”
Of course it did. If the home run occurred in the first inning the entire rest of the game would be different. The sequence of batters in the remaining eight innings would be different, the pitch selection to each batter would be different so the result of each plate appearance would be different so the outcome and result of the game would be different. You can’t pull something out of a sequence of events and then claim that all of the other following events would have been unchanged. That is not how the anything in the world works. And that applies to wins in April vs. wins in September.
That’s a very good point, Alan. But I think, if anything, if reinforces my point. The first inning home run probably influences the game positively for the batter’s team, right? The pitcher may have more confidence, the manager will put in better relievers if they’re ahead, etc.
I wasn’t trying to say, necessarily, that the home runs are exactly equivalent, but that the change in the team’s probability of winning does not make the 9th inning home run more important. In a 6-5 win, each of those 6 runs was equally important to winning the game, whether they came in the 1st inning or the 9th inning.