Wednesday, June 25, 2008

Optimal Baserunning
I've seen a few stories lately on how the Red Sox are stealing a lot of bases at a high success rate this season. So far, led by Ellsbury, they're stealing at a pretty amazing 84% rate. Considering the breakeven point for hurting your team in the runs department is around 65% (this is the percent the defense is trying to keep the running team below), that looks pretty good. But I was wondering what is an optimal number for a team success rate? I can't seem to find this information anywhere, so I'm going to make it up. Let's assume there is a flat distribution of stolen base opportunities, ie the same amount of situations where a baserunner will be safe 0% of the time, 25% of the time, 50%, 100% and all points in between. The distribution is probably normal around the break even point in real life but flat is much easier to work with. Runners on base should be trying to go any time a steal gives their team an edge so they should be running in all situations where the anticipated success rate is >=65%. If the distribution of opportunities is flat, then a team which runs the bases perfectly will on average steal successfully (.35/2)+.65=83% of the time.

I can't say whether the goal this season was to steal around 85% or whether it's just because the Red Sox suddenly have some guys who can run but are still relatively conservative (compared to other teams), but to me it looks like right now the Red Sox are taking the optimal advantage of the opposing teams' defenses. In a league where most other teams are stealing at the equilibrium rate where the net value added is 0 (in other words trying to steal as often below the breakeven point as above it), the Red Sox result looks like a pretty huge edge. It will be interesting to see if A. other teams start copying their optimally conservative/aggressive approach and/or B. if opposing defenses ever adjust to the fact that the Red Sox have been robbing them blind.


Blogger Pete said...

I'm going to assume your equation for ideal baserunning success assuming a flat distribution is correct, because I'm too lazy to figure it out myself. But as you say, a flat distribution is pretty unlikely - how many times are you going to have a 100% (or for that matter, 0%) chance of success on a steal attempt? That alone suggests that a flat distribution isn't realistic, but even without that, it's probably much more like a normal distribution, as you suggest. However, that should mean that teams that run the bases perfectly will end up with a lower overall success rate, because so many more of their chances are centered closer to the mean. Again I'm too lazy to do the math, but it's going to come out lower than 83%. That has to mean that the Red Sox have been fairly lucky to a certain degree, right? You can't run the bases better than perfectly. Either that or they're really good at identifying those running situations that are well beyond break-even - for example, they only run when their chance of success is greater than 75% rather than the 65% break-even point you mention. This seems to suggest that either the baserunning success rate of the Sox is a product of small sample size and luck, or that they would be well-served to run more than they are now.

10:01 AM  
Blogger John said...

you are right, i agree with the reasoning, they probably had been partly or mostly lucky. i actually originally intended to talk about why the red sox should run more given their gaudy success rate, but then i got convinced that their results were already optimal.

so i think for an individual runner at 1st, the distribution of his situations is probably something like normal, or gamma, but i couldn't really envision a general form for the entire team of individuals. i was thinking for the red sox it might be more normal since ellsbury was attempting about half their steals and his situations are probably centered around 85%+ while the rest of the team is lower.

since then though they've been less lucky and it looks like teams are paying much more attention. come to think of it, if the defense is smart and thus the two sides are in equilibrium, then every baserunner's situation curve should be centered at the breakeven point, since teams would pay lots of attention to fast guys and hardly defend slow guys at all. i think we talked once in game theory about how stolen bases are neutral ev in equilibrium.

3:53 AM  

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