In the bottom of the 9th inning in a tie game, the leadoff batter for the home team hits a double. According to researcher Tom Tango, teams in this situation have a win probability of 0.807. Because the home team only needs one run to win the game, some managers will choose to have the next player attempt a sacrifice bunt, which allows the runner on second base to reach third base while the hitter is thrown out. If the sacrifice bunt is successful, then the home team has a runner on third base with 1 out and a win probability of 0.830. However, if the sacrifice is unsuccessful and the runner is thrown out at third, there is a runner at first with one out (win probability of 0.637). What is the minimum probability of a successful bunt that would warrant using the bunt?
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