One of these interesting situations happened in the ninth inning of today's game. The Pirates were down by one run and Neil Walker led off the inning with a single. The Pirates needed just one run to stay in the game, so that's what they should have been aiming for.
According to math, the chances of scoring one run with no outs and a man on first are about 43.5% and you can expect .435 runs that inning. From there, the Pirates had a decision about what to tell the next batter to do. The two options are bunting the runner to second or swinging to try and do more than that and avoid recording an out. Let's say that Gaby Sanchez bunted Walker over successfully. That would change the situation to having a man on second base with one out. The chances of scoring a run in that situation is 41.4% and the expected number of runs for the inning is 0.69. So by bunting the runner over, the Pirates increased their expected runs for the inning, but actually decreased their chances of scoring Walker's run by 2.1%.
If you were 100% playing to tie the game there it's a bad decision to bunt. However, the Pirates actually increase their chances of winning the game without going to extra innings for a third straight game by bunting the runner over. However, successfully executing a sacrifice bunt is not a 100% guarantee, which Gaby Sanchez so kindly showed us. Sanchez popped the bunt up, didn't move Walker over and recorded an out, lowering the Pirates chances of scoring to 27.6% and lowering their run expectancy to .52 runs.
There is an argument both ways in this situation. For me, I'd like to see the team take the best odds at scoring at least one run, because that prolongs the game. However, the team did play a taxing 16 inning game last night and they were short on bullpen arms. All of this on the day before the St. Louis Cardinals come into town for a weekend series, I can understand why the Pirates would give up a chance to tie for a heightened chance to win the game right there.
That said, Clint Hurdle seems to choose to bunt every single time this situation arises late in games, which probably isn't the best for the team's mathematical chances of winning games.
The full chart is below. The first column is the number of outs there are in the inning, the second column is where the runners are located on base, the third column is how many runs the team is expected to score that inning in that situation, and the last column is the chances of scoring one or more runs. Anytime you question a bunt call, reference this table and let math do your thinking for you (click the image to expand it).
