.580

.540

.500

So, the chance of a home-sweep for each is .58^2, .54^2, .50^2. The average of that is .541^2. Suppose that you had 5 teams, with these win%: .620, .580, .540, .500, .460. Now, the average following the same logic is: .543^2.

Granted, it will not be a uniform distribution. But the distribution would certainly be wider than what I'm suggesting here.

My point is that you can't just take the average. I can take a league mean of .540 and I just showed how the home-split is akin to having a league mean of .543.

Regardless, you can look at the overall year-to-year home win%, and see big jumps/drops in win% every year. The difference here is well within the noise levels.

]]>However, the higher statistics for the consecutive-day games give a much smaller uncertainty (roughly .0025). Using them it looks like the win probabilities may not be the same from the first game to the next. If they were, the win probability inferred form the WW probability plus the loss probability inferred from the LL probability should add up to 100%. They actually add up to 100.84% with an uncertainty of around .35% -- not an overwhelming effect, but suggestive that something more complicated is going on.

Assuming that the winner of the first game increases their chance of winning the next game by x, and that the home team has a win probability of w in the first game, I estimate w = .539 +/- .009 and x = .008 +/- .002 from the consecutive-game data given. The fact that x is four standard deviations from zero seems to indicate that the probability of winning a game increases by almost 1% if you've won the previous game (within a particular series), whether you're the home or visiting team.

This analysis is crude, and win probabilities obviously change from game to game due to different pitching matchups, but it is interesting.

]]>I think another possibility is that the home team is always a bit more comfortable--better clubhouse, slept in their own beds the night before etc. For one game, this might not make a difference but when the visiting team is working on hour 7 or 8 of game day, it might matter. If this were true, then we might also expect double-header splits to show the home team winning the latter game a bit more often than the opposite case. It might also be true that day/night double headers behave more like games on consecutive days whereas double-headers played truly back-to-back (single gate) would show the favor to the home team.

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