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?