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I hope the model is realistic enough to have players play slightly better at home than away overall, given neutral parks.
But even if not, there's a small strategic advantage to being the home team and knowing how many runs you need each inning when you bat if the game is close at the end, for use of one-run strategies, including who you need to send home in a tough situation to tie it
Another of the strategic advantages of being the home team, if you don't have the DH, is if you pinch hit for the pitcher in a given inning, you get one more inning pitched from that pitcher than the away team doing the same.
With traditional closer usage, the closer will generally come in for the home team in the 9th inning rather than waiting for a lead, which may never come, to protect.
So the home field advantage comes from the combo of matching the team to the park, players playing slightly better at home if the park is neutral toward them, and the strategic advantage. We don't know if the second is in the game though it probably is; but the first is there if you pick players well for your park, and the third is always there.
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