## Third base coaches, get your windmill arm ready

May 30, 2007 9 Comments

A request came through on the SABR Statistical Analysis distribution list requesting some information about how often runners attempt to take “extra” bases on base hits. That is, how often do runners attempt to go from first to third on a single, first to home on a double, or second to home on a single (and how often do they succeed). I took a look at the last seven years (2000-2006) and found a few interesting patterns in the data.

I broke down each of the potential events by their occurences with either two outs or less than two outs. Not surprisingly, runners tried for “extra” bases more often when two men were out, as they were able to run on contact. And, by and large, they were successful. In all cases, success rates were above 90%, no matter which “extra” base was attempted and no matter how many were out. There was a curious hiccup though that caught my eye. With two outs, and a runner attempting to score, either from first on a double or from second on a single, rates of attempting to take the extra base go up, but success rates go down by a percentage point or two. Third-base coaches take a few more chances with two outs, but is that the right thing to do?

The question of whether or not teams have optimized their “regular” stolen base attempts is been one that’s been studied. The general agreement is that a manager should expect about a 70% success rate for a steal attempt to make sense and wouldn’t you know it, teams generally have about a 70% success rate in stolen bases. The standard practice is to use the run expectancy matrix. Let’s assume that there are no outs and a runner on first, and the manager is considering whether or not to send him. Right now, his team has a run expectancy (using 2006 figures) of .927 runs. If he breaks for second, he might be safe, in which case, the team will have a runner on second and no one out, for a run expectancy of 1.154 or he might be out (no runners, 1 out) for a run expectancy of .298.

Let’s find the percentage of times that this runner must be safe (we’ll call it p, with 1-p representing the percentage of times he will be caught stealing) for this strategy to break even, that is to where the runs expected in the current situaiton (runner on 1st, no outs), is equal to the run expectancies of the possible outcomes (either SB or CS). The algebraic formula is:

Current run expectancy = probability of being safe * RE of situation after being safe + (1-p) * RE of situation after being caught stealing

Plugging in the numbers:

.927 = (p) * 1.154 + (1 – p) * .298

.927 = 1.154(p) – .298(p) + .298

.629 = .856(p)

(p) = 73.5%

With one out, the break-even point is 73.5%. So a manager should have 73.5% confidence that his runner will steal safely in this situation for the steal sign to make sense..

But, what’s the break-even point for trying to “steal” home from first on a double? We can calculate this one with the same logic. We assume that any runners who had been on second or third have already scored, and the third-base coach is now faced with the decision of a certainty of second and third vs. attempting to push the runner with either a run scoring (and a runner still at second) or the runner being thrown out (and a runner still at second, unless the runner was nailed at home for the third out.) Let’s take a look at the data for no one out. With no one out and runners at 2nd and 3rd, a team can expect to score 1.965 runs. If the runner is safe, there’s a run in on the play, plus a runner at second with no one out, for a total run expectancy of 2.154 runs (1.154 for the runner on second and one for the runner that scores on the play). If the runner is out, there’s a runner on second with one out, for a run expectancy of .736 runs. If you plug all of those numbers in, the break even point is 86.7%. With one out, the break even point is 79.4%. With two outs, the break even point actually drops to 43.1%!

That covers first to home on a double, but what about other “stolen” base situations. For second to home on single (assuming no other runners), with zero, one, and two outs, the break even points are 91.7%, 70.3%, and 39.8%. The message here is that given the chance of “stealing” a run, it’s better to take it, especially with two outs. In order for a runner to score from third with two outs, the next batter will have to do something other than make an out. Even the best players manage that a little bit north of 40% of the time.

For first to third on a single, the break-even values are 91.2% with no one out, 76.9% with one, and surprisingly, back to 91.6% with two outs. Score one for conventional wisdom. You really don’t want to make the first or third out of an inning at third base.

But, for the last seven years, success rates have been in the low-to-mid 90s. It looks like third base coaches aren’t really optimizing their use of the old windmill arm. Why not? Well, if a third base coach sends the runner and he makes it, the runner gets the credit (or the fielder made a bad throw or the catcher didn’t block the plate or it was just “expected” and nobody notices.) If he gets nailed at the plate, the third base coach gets blamed, probably even more so if it’s the last out in an inning (or worse, the game). It looks like third base coaches are concerned more about their own backsides than the well-being of their teams!