Mathemadage: Outs At Third Base

It’s time for another installment of Mathemadage, where I investigate time-honored baseball sayings using whatever data I can get my hands on and explore whether there’s any validity to them. If you’re new to my writing, I would describe my method as a semi-rigorous blend of math and intuition, with a rigorous amount of skepticism applied on top. If you’re not new to my writing, hi, hello! Welcome back. Today, we’re investigating a saying that was both my top candidate for this article and the one that came up most frequently in the comments of my last one. Yes, it’s time to talk about outs at third base. Oh, and if you’re looking for Five Things, it will return next Friday – Pete Alonso’s return to Citi Field was my favorite thing this week, and Jay Jaffe already covered it.

“Don’t make the first or third out at third base” was one of the rules that got hammered into me most frequently as a kid. It’s so ingrained that the last time I played rec league softball, I bonded with teammates over how we reflexively repeated it every time we coached third base. (I’m a big nerd, OK? I’ll take whatever bonding I can get.)

The logic behind this one makes good sense, too. With no one out, two productive outs could drive you home from second – why risk erasing yourself heading to third? With two outs, most plays that score you from third would score you from second as well – why risk erasing yourself again? But with one out, getting to third base is a big deal, because then a sacrifice fly or well-placed groundout can bring you home. From that angle, the logic is incontrovertible.

But is that how it works in real life in the major leagues? Well, the run expectancy math is a good place to start. I first took data from a broad chunk of the past, generically “the good old days” – 1974 to 2000, DH games only so that I could line it up with modern years. If you’re not familiar with this data, it’s a simple idea that works well at an aggregate level. How valuable is it to have a runner on third with one out? We simply look at how many runs scored in all major league games after that exact situation occurred, and take an average. Do that for all possible combinations of baserunners and outs (and exclude the ninth inning and extras, where there’s no guarantee of a full three outs and score considerations change strategy), and you get what’s called a run expectancy matrix.

For example, in that 1974-2000 era, teams scored 1.369 runs per inning when they placed a runner on third with no one out. After placing a runner on third with one out, they scored 0.96 runs per inning – and 0.383 after a runner on third with two outs. And once we have run expectancy for every possible situation, we can work out the run expectancy change for going from one situation to the next. For example, the difference between being on second with one out and being on third with one out is an increase from 0.696 to 0.960 runs scored per inning on average, or 0.264 runs. The difference between a runner on second and one out and two outs with the bases empty – getting caught going for third – is -0.594 runs.

By comparing the change in run expectancy after a success and after a failure, we get breakeven success rates. Think of a bet where you either make $10 or pay $5. If you’re right a third of the time, you break even. Any more, and you’re profitable; any less, and you’re losing money. You can use the same idea to think about breakeven success rates for base advancement. If you successfully advance, you get “paid” the increase in run expectancy. Get caught? You “lose” the decrease. By using that math, I calculated the breakeven success rate for every base that a runner could try to take. For the purposes of our study, we’re assuming that the trail runner(s) successfully advance, so the breakeven rate only accounts for the lead runner. The conventional wisdom is real:

I think it’s just common sense that advancing from third to home with no outs is the spot with the highest breakeven. But after that, we see that making the third out at third base is quite bad, and that making the first out at third base is quite bad as well. Thus, both require high breakevens. In comparison, going from second to third with one out, or going from first to second with two outs, are comparatively better bets; the breakeven success rate is meaningfully lower.

OK, so that’s where the wisdom comes from. But if you’re like me, you’ve probably wondered whether this still holds in an era of more strikeouts and more homers. Maybe getting to third with no one out is more important now that batters are a little less likely to cash in a runner from third with one out. Maybe advancing is just worse overall now. I came into this study skeptical that the rule would still be true in such a different run environment. So I ran the numbers for what I consider the modern era, 2016-2026:

There’s always going to be some noise when you construct the numbers this way, but these are basically the same. Sure, some breakeven rates have moved by a percentage point here and there, but that’s one advancement per 100 attempts, not a meaningful difference. This felt intuitively fishy to me. But when I dove into the numbers, the reasoning made a weird kind of sense. Yes, the rewards of advancing a base are lower now because of all the strikeouts. But on the other hand, the cost of failure is lower. It’s easier to score without runners on base because home runs are everywhere now. Run scoring is almost exactly the same – but run scoring with runners on base is down, while run scoring with the bases empty is up.

We can say one thing with certainty before going any further: The conventional wisdom here is still true, at least in a broad sense. It’s more costly to make the first or third out at third base than it is to make the second out there. It’s not so much that you can’t do it – but you need to succeed more often to make up for the increased cost of failure.

Baserunners haven’t always followed this rule in practice. An easy way of thinking about it is to look at how often runners are successful when they try to steal third, broken out by how many outs there were at the time. Baserunners from 1974-2000 were successful on no-out steals of third 64.2% of the time. With one out, they were successful 70.2% of the time. With two outs, they were successful 72.4% of the time. But that doesn’t line up all that well with the breakevens we calculated up above:

Runners certainly weren’t internalizing this rule in the past. Their success rates were almost identical regardless of how many outs there were – they were stealing far too much with zero and two outs. That behavior has changed a little bit in the modern era:

The change in success rate on two-out steals is noticeable. I’m frankly shocked by the atrocious success numbers on two-out steals of third in the past. Where were all the cranks yelling about the lack of good fundamental baseball back then? But probably we just didn’t think to measure this result at a granular enough level to notice. In any case, as the color coding indicates, runners still attempt to steal third too often with zero and two outs, while they’re doing a good job of going in one-out spots.

I also tried to measure the rate at which batters successfully stretched doubles into triples. I’m not particularly confident in those numbers, though. The correct “chance of successful advancement” when you’re trying to stretch a double into a triple is pretty hard to tease out, because not every successful triple was a “Should I stretch this into a triple?” decision, but they’re all recorded the same. This felt like a dead end, though I can at least say that runners are making about as many outs stretching doubles into triples as before, and at small enough rates that I don’t at all feel confident splitting by how many outs there were at the time.

There’s one last way to look at how runners think about making an out at third: baserunner behavior on singles. I looked at how frequently runners on first took two bases on singles, split by era and number of outs. This has the same potential shortcoming as looking at triples, but there are more data points here at least. Attempt rate – how often runners try to take two bases from first on a single – doesn’t vary much between zero and one out, though baserunners attempt more often with two outs since they don’t have to be afraid of getting doubled off. That effect holds consistently across eras, though baserunners are more conservative across the board now, attempting to take two bases less often. They’re also successful almost every time; observed success rates for every combination of era and outs hover between 96% and 98%. The numbers don’t really tell us anything about whether batters are thinking, “Don’t make the first or third out at third,” though, so I think the steals numbers are the best way of investigating runner behavior.

I did think of one other check to run. So far, I’d been working in the world of run expectancy: looking at how many runs score, on average, after each situation. But there’s a different way of considering things: How likely is a team to score, period? Instead of working out how many runs scored on average after each state, I just worked out whether a run scored. Take a look at our breakeven percentages for advancing from second to third with zero, one, and two outs now:

That’s pretty much the same shape as the run expectancy breakevens. In other words, the advice is basically true. Making the first or third out at third base is worse than making the second out there. That hasn’t changed over time even as the run-scoring environment has changed, because the run-scoring environment has changed in two ways with offsetting effects. Baserunners are getting better at responding to incentives correctly – they’re making the third out at third base far less frequently than they did back in the olden days.

Oh, and one last note: Maybe we need a slightly more complicated saying. It’s more like, “Definitely don’t make the third out at this base, and try not to make the first out there if you can help it. Honestly, don’t make any outs on any bases if you can, but don’t be too conservative either. Not advancing can be bad, too.” But uh, yeah, that’s a much more complicated rule. Not quite so pithy. So for our purposes, “Don’t make the first or third out at third base,” is close enough.