I know nothing about baseball, but wouldn’t this give even more of an advantage to the team batting first?
I would expect the opposite (NB: I am not suggesting a weakness in Felix’s analytical abilities, only that British people don’t usually “get” baseball). The team batting second in the inning always has more information than the team batting first, because the home team (which bats second) knows what the visitors scored in their half of the inning.
The closer you are to “runs,” the more valuable is this differential in information. To see this, take those cases where the first-batting team fails to score in the top of the tenth inning. The home team can then play for “only one run.” If no one is on base, the strategies for “only one run” and “a bunch of runs” aren’t that different. You’d like to start with some extra base hits, home runs, etc., in either case. But with a man already on second (or on third, to see the point more clearly), you can consider some alternate strategies, such as just poking the ball to the opposite field. You don’t need to swing for a home run so much, or try to stretch a single into a double, and so on. You can play more conservatively in the offense, because you know that a single run suffices to win the game.
For the team that bats first, playing for “only one run” isn’t the sure-fire clincher, and so this helps the team that bats second in the inning, the home team.
Or so it seems to me.