Baserunning 101

A question arose as to what constitutes a reasonable stolen base percentage, that is how many times must a Nyjer Morgan successfully steal a base before he makes up for getting caught stealing a base.  I'd like to demonstrate one way to answer that question and give some rules of thumb on the subject.  I call it "Baserunning 101", but I also want to give a feel for the mathematics required to do the calculations.  Trust me, the math is not too difficult.


The important thing to understand is what one is attempting to accomplish by stealing a base.  It's not always the same thing -- it depends on the situation.  In some instances it's a matter of simply trying to avoid a double play; in some cases it's a matter of trying to score an important single run (for example, a late-inning tying or go-ahead run); and in some instances the team is hoping to maximize the number of runs they (expect to) score.  Note that maximizing expected runs is often accomplished differently than maximizing the chances of scoring.  If at the beginning of any one inning  I could improve my chances of scoring to nearly 100%, but at the expense of never being able to score more than 1 run, I would jump at that chance, because it's not likely a team that scores 9 runs every game is going to lose very often.  In general though, a team should want to maximize the number of runs they expect to score.  For the rest of this discussion, I will assume that this is indeed the goal of a team.

Through the miracle of computers (and a lot of manual labor!) various people have developed "run expectancy matrices."  These are tables of data listing the average number of runs scored by (Major League) teams given different game situations.  Here is one comprised of data from all the games in the 1999-2002 time span, thanks to TangoTiger.  (The values in the matrices change as time goes on, but not dramatically so).  




































The row along the top indicates the number of outs.  We will go ahead and assume that the numbers here apply to any Nationals game situation (not a valid assumption, but close enough to continue).  Thus, when Nyjer leads off an inning with a walk, the expected number of runs the Nats score rises from .555 to .953 (again, yes, this is making the assumption that the Nats score an average of .555 runs per inning, or nearly 5 per game -- lately it's not anywhere near that, but stay with me!)

The question is what percentage of time does Nyjer need to be successful in his steals for him to attempt to steal.  Let's pretend that Nyjer never gets picked off first before he even has a chance to try.  

Set p to be the probability of a successful steal.  If Nyjer attempts to steal, then with likelihood p, the expected runs rises from .953 to 1.189 (0 out, runner on second), but if he fails, which happens with probability 1-p, the expected runs drops to .297 (1 out, nobody on base).  Thus, the expected runs if he attempts a steal is the sum of these two quantities, i.e.

Expected Runs With Steal Attempt = p*1.189 + (1-p)*.297.

The break-even point is the value of p in which the expected runs is not changed by the steal attempt, i.e. when

p*1.189 + (1-p)*.297 = .953.

It's not too hard, if you recall your sixth grade algebra, to find that the break-even point is approximately .735.  Thus, if Nyjer cannot successfully steal at least 73.5% of the times he tries to steal second with nobody out, then he should not try to steal.

It's fairly easy to build a formula for break-even points:

B.E.P. = (RE w/o steal - RE failed steal ) / (RE successful steal - RE failed steal).

So, for example, if Nyjer is alone on second with 1 out, should he attempt to steal third?  The relevant numbers are

RE w/o steal = .725

RE failed steal = .117

RE successful steal = .983

In this case, the BEP comes out to 70.2%.  Not a whole lot of difference.  As a matter of fact, 70 - 75 % turns out to be a pretty good rule of thumb in most cases.  But note that a stolen base percentage anywhere close to these values will affect the expected runs scored only very slightly, not more than a few runs difference for an entire season.  If, on the other hand, your stolen base percentage is closer to 50%, then you are really beginning to cost your team runs.

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