Could the home field advantage in baseball be due to the "principle of last action?"

Question

It has been observed that in baseball, a home team has a statistical 54-46 advantage, all other things being equal. There have been various theories to account for this, including the impact of fan support, and possible "home team" bias by umpires.

But there may be a more tangible home team advantage called the "principle of last action." This advantage derives from the fact that the home team bats and score last in every inning, and in the game itself.

In poker, there is a large advantage to being last, and seeing what other people have done. For instance, if you are "last" with a mediocre hand, and have observed other people betting timidly (or not at all), you might bet to steal the pot. If others have "raised" each others' bets, you might "fold" and let the stronger hands fight it out. If you were first to go with the same, mediocre hand, you would have to bet (or not) without knowing what others wanted to do.

Beginning in the ninth, and all the extra innings, if the home team ever takes the lead, the visiting team will not have a "return" opportunity in a subsequent inning. The home team can win in a one-run "walk-off," while the visiting team will have to score as many runs as they can in the top of the ninth, and hope that they are "enough."

Say the game is tied at the end of the eigth inning, and the visiting team scores x runs in the TOP of the ninth. The home team knows that it needs to score exactly X runs to tie, and x+1 runs to win. It can manage it "bench" in the bottom of the ninth for maximum effect. On the other hand, if the visiting team has a one run lead in the top of the ninth, it must wonder, is that enough? Can we save the bench for tomorrow, or do we need to "pile on," now? Likewise, the visiting team has to make a decision in the bottom of the ninth whether to use as many pitchers as it takes to stop the tying run, or save relievers for an extra inning game.

Other sports such as football and basketball don't have such a clear separation of offensive and defensive "rounds." (In those sports, unlike baseball, it is possible for a defender to "run back" the ball for a touchdown or basket.) Could this separation of offense and defense be what lends a home field advantage in baseball?

Answer 1

Yes. Homefield advantage does play a role late in close games. Though my brief analysis indicates that it doesn't account for all of the record disparity.

Fangraphs has a great model that predicts, based on game state, how likely a given team is to win at any given moment in the game based on historical data.

Let's look at a recent 0-0 game that went all the way into the bottom of the 10th and was won in a walkoff. Cubs vs Pirates, opening day.

We can see in this game, that starting in the first inning, the home team had about a 4 percentage point better odds in the middle of the inning then they did at the beginning of it. This increased as the game continued until the 9th and 10th innings where the odds are 11.4 percentage points higher. However, it's worth noting that at the top of each inning the odds are 50-50. When both teams have equal numbers of at-bats remaining, the odds are about the same when the score is tied at 0.

Let's look at one more situation. Let's look at a one run lead going into the 9th inning. We'll need to examine two games for this one. In the first game, the home team is up one to begin the 9th. We'll use this Orioles vs Redsox game also from opening day. The odds of the Orioles winning was 83.3. Contrast this to the odds of the Away team winning a 1 run game in the 9th. For that we'll use this Braves vs Nationals game. Looking at the odds going into the top of the 9th, we see that the Braves had a 84.9% chance of winning it, but after going hitless in their final at-bat, their odds of winning were only 81.6%.

The contrast to note here is the 1.7 percentage point difference going into the last at-bat for the losing team. When the home team has another at-bat it makes a difference nearly 2% of the time.

Obviously these two examples don't account for the full home field advantage, but the fangraphs data does show a clear edge for the home team historically due to last action.