One issue with analysis like this is micro optimizations have more information than simplified abstractions. Consider, in the bottom of the 9th 1 or 2 runs may have identical value. So, reducing the total expected value of runs to increase your odds of a single run may be a very good trade off.
And that's assuming you want to optimize total wins. Increasing your odds of winning the playoffs may reduce your odds of getting into them by having more higher paid people, but a lower average player. Further, maximizing making money over time is yet another option, which may promote showmanship over success.
"But there are situations where the approximation isn’t very good, such as when it’s the 9th inning and the game is tied. In that case, a decision that increases the probability of scoring 1 run but decreases the probability of scoring multiple runs is actually the right choice."
I understood that the "full" model includes these considerations.
I was bringing up that edge case specifically because 'winning' is the obvious optimization, but not necessarily the correct one.
Bottom of the 9th bases are loaded and the guy at bat hit's a home run, that's the kind of thing that sticks with people and makes more money in the long run than a bunt that get 1 run.
And that's assuming you want to optimize total wins. Increasing your odds of winning the playoffs may reduce your odds of getting into them by having more higher paid people, but a lower average player. Further, maximizing making money over time is yet another option, which may promote showmanship over success.