On offense, your most precious possessions are your 27 outs.
The Cardinals went to extra innings on Friday night in what would eventually be a loss after 12 innings. In the 10th, the Braves brought in Livian Hernandez to start the inning. Carlos Beltran led off the inning with a double to right field. Allen Craig was walked to fill first base and set up the double play. After the intentional walk, Yadier Molina came to the plate.
Molina proceeded to sacrifice bunt toward third base. Was this a justifiable call statistically?
The key here is that the Cardinals needed one run to win the game. They were no longer in a scenario where the more runs they scored the better. For the Cardinals, playing at home, they were in a sudden death match. Push a runner across home plate and you win.
That's an important distinction because a sacrifice bunt is normally a pretty quick way to reduce your probability of multiple runs. In order to evaluate this, we'll take a look at something called a Run Expectancy (RE) matrix. There are multiple kinds of RE matrices but the most common one is the matrix that shows how many runs you can expect to score based on where you have baserunners and how many outs there are. These "expected runs" come from historical data. So if you look back at the years 1993-2010 (which are the years for the first table here), and total up how many times there was a man on 1st and 0 outs, then total up how many runs were eventually scored that inning and divide by the number of times that situation occurs, you can develop an RE matrix.
In Friday night's game, the Cardinals had runners on 1st and 2nd with no one out. Historically, we should expect the team to score 1.556 runs in that scenario. After the bunt, the Cardinals had runners on 2nd and 3rd and 1 out. Under that scenario, we'd expect the team to score 1.447 runs. When the Cardinals sacrifice bunt like they did on Friday, they are reducing the number of runs we'd expect them to score. That is why you will often find statistically inclined observers of baseball to abhor the bunt. It's true for every situation (barring a suicide squeeze). Bunts are the true rally killer.
But the Cardinals didn't need a rally on Friday night. They needed to push Carlos Beltran across home plate. Craig was superfluous to the situation from an offensive standpoint and was only problematic in the sense that he facilitated the possibility of a double play. The real question for Friday night was whether the Cardinals were more likely to push Carlos Beltran across home after the bunt.
The answer is yes. If you head back to the RE tables at this link, you'll find the second table shows the probability of scoring a single run under baserunner/outs scenarios. With runners on 1st and 2nd and no outs, the Cardinals had a 64.3% chance of scoring a single run. With runners on 2nd and 3rd and 1 out, the Cardinals had a 69.8% chance to score a run.
With that bunt, the Cardinals increased their likelihood to score a run -- and therefore win the game -- by 5.5%. This conclusion comes with a host of caveats that mostly surround the actual players involved. How good likely is Molina to hit into a double play? How likely is Hernandez to induce a ground ball? How fast is the runner at 1st? How good are the infielders defensively? A 5.5% increased in scoring a run assumes a context neutral (or more precisely the mean scenario of the aggregate data from 1993-2010) environment.
Ultimately, it wouldn't matter for the Cardinals. Livian Hernandez would walk Matt Carpenter after Molina's successful bunt and David Freese, pinch hitting, would ground out into a double play ending the threat. This is a very specific scenario, however, where the bunt was the right call or, at a minimum, a defensible call. It doesn't happen often but the Cardinals took advantage -- intentionally or not -- of a statistical advantage by bunting in the 10th inning.