Talkin’ Softball (Baserunning Aggression)

I have a secret to tell you. Most writers don’t read the comments on their articles. I know, I know, but your well-thought-out rejoinders and witty jokes! It’s mostly a bandwidth issue: there are just so many words. But we pop in from time to time, and boy am I glad that I did this Monday, because I got a softball question to answer (get it?):

Yes! Forget CBA negotiations and lockouts and missed spring training. Forget major league baseball, too. Heck – for this article, forget baseball! Today, like the 1992 Springfield champions, we’re talking rec league softball.

The question is an apt one, and far more useful for the average slow-pitch softball player than an examination of backup sliders or novel sinkers or whatever the heck it is I’m normally writing about. It’s a simple question: how aggressive should you be on the basepaths in a world where almost no one makes outs? For the rest of this article, I’ll be applying the same math that we use for steals in the majors (that golden 75% success rate target) to decide whether to go for an extra base on a single. It could also apply to a steal, if that’s something your league does; I haven’t played in a few years, but the basepaths weren’t exactly lively when I did. For today’s article, though, we’re not going to consider the etiquette or technique, merely how to make your opportunities mathematically advantageous.

I polled an illustrious group of slow-pitch softball experts (read: some people I know who play) to come up with a rough batting line. Opinions on the exact line varied, but I’m going to stick with one that’s close to the league that Pascal specified: an on-base percentage between .500 and .600. The overall league slash line I’m going to work with is .526/.550/.947. I’m also going to assume that every batter has the same line, and every pitcher allows the same line: we’re not going to be filling out lineup cards for your local beer league team today.

Here are the individual outcomes that lead to that slash line:

Some leagues have home run caps, but that’s mathematically tricky, so I just kept the home run rate reasonably low and assumed no caps. I plugged these into a simulator to figure out how many runs this team would score per seven innings. It’s a 16.5-run average, so it’s fair to say that our team is an offensive powerhouse. Next, we need to work out how trying to advance from first to second on a single changes the percentages.

In a setting that resembles major league baseball, we could do this with a run expectancy table. Something like this would tell you that in a run environment that resembles the majors from 2010-15, a successful steal of second with no one out adds 0.241 runs to your expected scoring. Getting caught attempting to steal second with no one out costs you 0.605 runs. Put those together, and you get a breakeven rate of 71.5% – 71.5% of the time, the baserunner will add 0.241 runs and 28.5% of the time they’ll cost their team 0.605 runs. Those two values sum to zero.

I don’t have a run expectancy matrix for the slow-pitch league I made up. There’s no data for it, because it doesn’t exist, and no one keeps slow-pitch softball game logs anyway. Instead, I took advantage of the simulator I mentioned before and started creating my own run expectancy matrix – at least the parts I care about.

First, we need to consider the different ways that an attempt to stretch an extra base (or to steal a base) can end. It can end with a runner on second and no out recorded (I’m only considering plays at second for this article). It can end with the runner being thrown out. Finally, it can end with an error – for the purposes of this article, we’re going to call it a one-base error, but depending on the fielding, that might be underselling it.

Next, we need to use the simulator to find out how many runs will score on average in each of these base/out states. Luckily, that’s easy to do – and easy to do for you at home, if you can use Python. Here’s the code I used to do it. This simulator is very simplistic. You give it a percentage chance of each outcome occurring and an initial base/out state. It rolls a die (generates a random number between 0 and 1, to be precise) and uses that to determine what happens. Each outcome moves the runners, outs, and runs around based on some rules I set out – half of singles are two-base advancements, half of groundouts with runners on first lead to double plays (which might be aggressive), and so on. When the play is over, it starts the process again with another random number.

From there, the simulator keeps count of how many runs score before the inning ends. When the random outcomes add up to three outs, that’s the inning. The simulator notes how many runs scored, resets the bases, and does it again. And again. And again. The code I provided runs one million innings, but nothing’s stopping you from adding a zero and having it run 10 million innings, or whatever your heart desires. After all of those innings are done, the program just takes an average – and now we have a run expectancy for an initial base/out state in our high-offense world.

With a runner on first and no one out, an average of 3.003 runs score per inning. With a runner on second and no one out, that number climbs to 3.331 runs – that extra base is worth 0.328 runs. With one out and no one on base (if the runner gets caught), the run expectancy drops precipitously, to 1.406 runs. Getting thrown out costs you a massive 1.597 runs. Finally, an extra base isn’t worth that much. With a runner on third and nobody out, run expectancy is 3.355 runs – getting to third on an errant throw is worth 0.352 runs relative to parking yourself at first.

If we set the chances of a throwing error at 10%, we can run a quick breakeven for attempting to take second base with no one out. If you advance successfully 72.8% of the time and also pick up an extra base on an error a further 10% of the time, the weighted change in run expectancy sums up to zero. That doesn’t tell the whole story, because you can’t know if a throwing error is coming when you take off. Of the plays that are contested, that’s equivalent to an 80.9% safe rate (72.8 out of 90). In other words, if you don’t want to give up expected runs when you round first and head for second, you should expect to beat a good throw at least 80.9% of the time.

You’re allowed to get aggressive on the basepaths even when there are outs. I also ran the run expectancies for a runner who reaches first with one and two outs:

One out is a slightly worse time to go for it: you need 73.7% successful advancements to add to your 10% of errors, or a breakeven 81.9% safe rate. It’s the same with two outs. All three rates are roughly the same, though: if you’re looking to push the envelope in your slow-pitch game and think that the fielding team will throw the ball away 10% of the time, you need to beat a good throw more than 80% of the time.

Thanks to our run expectancy grid, we aren’t limited to a static 10% error rate. It’s just an equation, and by plugging in a variety of error rates, you can find the breakeven rate (like before, the rate at which you think you beat a good throw that carries no change in run expectancy) for various chances of a throwing error:

I highlighted the best time to go for it for each error rate (in terms of the lowest required breakeven). The higher the error rate, the less sure you need to be you’ll succeed – that’s true regardless of the number of outs. But in a high error rate world, one out is the best time to stretch your singles, because an error gives your team a runner on third with less than two outs, and in a world with no strikeouts, that’s worth quite a bit.

Running wild when you’re the only one on base sounds boring. What if you tried this tactic when there was a runner on third? In this case, I assumed that the runner would come home on an error and stay put otherwise, regardless of the result at second base. Here’s that same breakeven success rate grid, calculated with runners on first and third:

With no outs, the breakevens go up slightly. Why mess with the chance for a big inning? With one out, though, it’s go time: you might “drive in a run” by forcing an errant throw, but there’s still hope to score even if you get thrown out. With two outs, it’s back to being a so-so proposition, because league-wide batting average is so high that the run on third is reasonably likely to score if you don’t risk a third out on the basepaths. Unless, of course, the error rate is extremely high — if that’s the case, you might want to be aggressive to give the runner on third some free scoring opportunities.

So, FanGraphs member Pascal, I hope I answered your question. What are the breakevens for taking an extra base or stealing? They’re similar to the major league baseball rule, but slightly more stringent. If we’re being honest, I doubt you can round first and tell me the difference between a 75% likelihood of reaching second safely and an 80% chance. Run when you feel like it! It’s rec league softball, after all. Do what’s fun, and the results will follow. Oh, and hit some bombs – that’s always a good way to score, no matter what run environment you’re in.

Thanks to Tess Taruskin for her research assistance and softball fact-checking.