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!

### 9 Responses to Third base coaches, get your windmill arm ready

1. Guy says:

PC: I don’t quite follow your last graf. Are you saying that runners are safe at home >90% of the time, even in two-out situations where break-even is around 40%?

2. Pizza Cutter says:

Guy, you got it right. The actual success rates in MLB are around 91-93% with two outs, even though the run expectancy break even is in the 40s.

3. Guy says:

PC: If you haven’t already, you should read Dan Fox’s work on this subject. He did several pieces at THT, the first of which is here: http://www.hardballtimes.com/main/article/circling-the-wagons-running-the-bases-part-i/. He’s done several more at BPro — if you’re a subscriber, search for his articles.
The 90%+ success rate doesn’t have to mean coaches are too conservative (tho it could). Ideally, they will send runners in all p>.40 situations, which will result in an average success rate far above .40. If there are a lot of situations where p>.90, and relative few between .40 and .90, then you’ll get a high average.
For example, on singles to OF w/ runner on 2B, runner is sent home 90% of the time on hits to LF, 97% to CF (!), and 92% to RF. So even if every single runner stopped at 3B were sent, and made out, the overally success rate would be over 80%.
To figure out if coaches are being too conservative, I think you’d have to do some analysis of the runners being held, and where ball was hit, to see if runners are indeed being held in a lot of .40 to .90 situations.

4. tangotiger says:

I agree with Guy. In essence, all those 90%+ “attempts” are noise. You really need to focus on those 20% to 60% plays to see how a coach handles those.
Pizza: can you create a 2000-2006 chart similar to this one that I have for 1978-1990. It will be interesting to see the differences.

5. MGL says:

yes, Tango and I have talked about this before, as when we were working on the baserunning chapter in our book. It is very difficult to say how many runners had x% chance to make it and whether or not coaches were sending too much or not enough. You have to do something like look at pitchers, presumably the slowest runners in the league and see how often they are sent and do or do not score on balls hit to various parts of the OF. Then you can go from there, althought it is still a little tricky. I think it is a good assumption that third base coaches and most players in general are too conservative especially with 2 outs. Although everyone knows to be more conservative with 0 and 1 out and more aggressive with 2 outs, still coaches are not going to want to get too many guys thrown out for the last out. Ditto for the players. For example, lets say that a player goes from 1st to third with 0 or 2 outs optimally and occasionally gets thrown out, which he should (when he has greater than a 90% chance but less than 100%, which should happen occasionally). What is going to happen? That player will be criticized every time he gets thrown out at third (with 0 or one out) even though he is only getting thrown out occasionally when it is correct to make the attempt. Is the same argument I often talk about with game theory. Pitchers must throw “bad” pitches every once in a while to keep the batters honest, but they will get criticized when they do, so they probably don’t do it enough (i.e., they are too predictable). For example, A. Reyes got criticized in public for throwing a first pitch fastball to Nook Logan with a runner on second and two outs. Although this is kind of a silly criticism in general, you CANNOT ever criticize a pitcher for any given pitch unless you know how often he throws that pitch in that same situation. What if Reyes said, “Hey skip, I was only going to throw that fastball 10% of the time, and you happened to notice (and criticize) that 10% pitch!” If Reyes never threw a first pitch fastball to Logan in that situation, Logan would know that (presumably or eventually) and you would HAVE to occasionally throw one to keep him from looking offspeed!

6. MGL says:

And when you (Pizza) say that the BE point in SB% is 70% and that “lo and behold the actual SB% in baseball is 70%,” there should be no “lo and behold” there! If baseball were optimal, then the acutal SB% should be much higher since no one should make at attempt unless their success rate were AT LEAST 70% (assuming that the BE rate is constant accross all game situations).
Also, even though the BE point might be 70%, we MUST include the value of the runner going when the ball is in play. No one has ever quantified this in a study, AFAIK, although someone on our blog estimated the value (based on the extra hits and extra bases minus the occasional LD DP).
Plus, as we all mention from time to time, SB rates include busted hit and runs, so a 70% rate is probably 72% or so for actual SB attempts (and not H&R’s). Plus any analysis of SB has to include pick-offs, balks, and pickoff errors, as these are the direct result of a threat of the stolen base. If there were no stolen bases there would be very few pickoff errors, pickoffs and fewer balks, especially by LHP’s (the balks and pickoffs).

7. Guy says:

“No one has ever quantified this in a study”
Actually, MGL, Pizza Cutter took an important step in addressing that in his post prior to this one, finding that the CS% drops considerably when batter doesn’t swing (non-H&R). In the comments, Beamer reports a similar finding.
Figuring out the cost and benefits of H&R attempts is another question of course, but it sounds like Retrosheet has the necessary data (runner in motion before contact) to do that.

8. Pizza Cutter says:

MGL – Interestingly enough, I did some stuff a little while ago that the speed of the runner is not as important as how far the outfielder has to throw to try to nail him.
http://baseballpsychologist.blogspot.com/2007/03/runner-tagging-from-third-heres-throw.html
http://baseballpsychologist.blogspot.com/2007/03/theres-gonna-be-play-at-plate.html
Tango – I can e-mail that data to you, if you like.