If you read this site, you’re probably familiar with the rule of thumb that says stolen bases are only beneficial if they are swiped with roughly a 75% success rate. This number stems from looking at a run expectancy chart and comparing the difference in expected runs after a successful stolen base and the difference in expected runs after a failed attempt. At some success rate, the entire benefit a team received from stolen bases is cancelled out by the combined detriment of all of the failed attempts – this is the break-even point. Of course the break-even point is not the same for every situation. Previous studies have shown this required success rate drops as the game moves into the later innings and increases the further a team is down by – but what do these break-even points look like based on the number of outs in the inning?
Stealing second base:
The chart below plots the expected run difference versus stolen base success rate based on the 2009 to 2011 run expectancy charts. This plot was included primarily as a sanity check, but you can see that regardless of the number of outs in the inning, the break-even point, which is the crossing of the x-axis, falls between the 70% to 75% success rates we’d expect to see.
Stealing third base:
This event was the primary reason for this post. Commonly accepted baseball principle is to not make the first or third out at third base. The rationale for this is qualitative in nature. With zero outs in the inning, there will be plenty of opportunities to drive in a runner from second, so there is no need to risk losing the baserunner. Of course with two outs in the inning, making the third out at third removes any chance of that baserunner actually scoring. Therefore, situations with one out are left as the circumstance where a baserunner might as well take a risk. The plot below clearly agrees with the accepted convention as we see success rates of 78%, 69% and 88% for zero outs, one out, and two outs, respectively, for break-even points.
What some dub as the most exciting play in baseball sees an even bigger split based on the number of outs in the inning. With zero outs in the inning, an 87% success rate is required. With one out, a 70% success rate is required. Finally, with two outs only a 34% success rate is required. The qualitative explanation for why a runner shouldn’t make the first or third out at third base can be applied here, with the difference that if the runner is successful, a run does actually score. This causes the required success rate for stealing home with two outs to drop significantly. Does anyone else think Jacoby Ellsbury, Brett Gardner or Michael Bourn can steal home at a greater than 34% clip?
Double steal of second and third:
Assuming the catcher is attempting to throw the lead runner out, we again see splits in the break-even points for double steals – 64%, 60% and 76% success rates for zero outs, one out, and two outs, respectively. The required success rates for a double steal with less than two outs is lower than “normal” because outside of stealing home, the change in run expectancy we see from a first-and-second situation to a second-and-third situation is the largest increase of any movement on the run expectancy chart when considering the possible outcomes from conventional stolen bases. In other words, a double steal is more valuable than a single steal, which makes plenty of sense. In addition, the increased benefit of a double steal beyond a single steal is proportionally stronger than the more severe penalty of failed attempt.
In no way am I suggesting that the accepted rule of thumb is wrong. In fact it represents most situations quite well. Just remember that there is quantitative evidence that backs up the adage of not making the first or third out at third base – and that if Coco Crisp gets thrown out trying to steal home with two outs in an inning, it was probably a worthwhile attempt.