Which of these two baseball scenarios is more advantageous?

Let’s say your team is in a tied game, batting in the bottom of the ninth inning. You just need one run to win the game.

Which of these two scenarios is more likely to result in the winning run scoring:

  1. Bases loaded, no outs
  2. Men on second and third, no outs

I can think of arguments either way. In scenario 1, a walk or hit batsman wins the game. However, with scenario 1, there is a force play at every base, meaning it is easier to throw out the runner on third who is trying to score on a ground ball. I have even seen games where the pitching team was faced with scenario 2, and they decided to walk the next batter intentionally to load the bases. Has anyone done a statistical analysis to show which scenario is better for the team at bat?

Yes. The great Tom Tango did: Run Expectancy Matrix, 1950-2015

With no outs or two outs, you have a higher chance of scoring a run with the bases loaded. But if there’s one out, it’s reversed.

Right, with one out you can have a double play to end the inning, which is the typical situation where they will walk the next batter to load the bases.

They might walk a batter with no outs to hopefully minimize the number of runs, but not in the bottom of the 9th with no outs of a tie game where one run wins it. And of course, they might walk a batter if he’s a much better hitter than the man on deck.