The draw is for idiots

I don’t know the name of this phenomenon, but I imagine everyone has experienced it at one time or another. You hear something enough times and start repeating it without really thinking about it critically. My example: the break-even stolen base rate. I’ve heard this term so many times over the years, often in connection with teams stealing too much or not enough, that I’ve incorporated it into my thought processes as if it were my own.

But then someone asked me why the optimal stolen base success rate was around 70% and I realized I was wrong. It was a moment of lightning inspiration: just listening to the counterargument once is enough to reevaluate your old, uncritically assumed thought. Why Should do teams continue to steal as long as they are successful more than 70% (more or less) of the time? I couldn’t explain it using math.

The other side of the coin, the idea that teams should succeed at a breakeven rate much better than their overall breakeven rate, is incredibly easy to understand. There is a difference between marginal return and total return. Consider a business in which you are making investments. Your first investment amounts to $10. Your next one will earn $8, then $6, and so on. You could continue investing until your business breaks even, until you make a negative $10 investment to offset the first one, more or less ($10 + $8 + $6 + $4 + $2 + $0-$2- $4-$6-$8-$10). But it’s clearly a bad decision. You should stop when your marginal the return stops being positive: when an investment returns you $0, you can simply stop going and pocket $30 ($10 + $8 + $6 + $4 + $2 + $0).

When it comes to stolen bases, not all opportunities are created equal. Statcast logs record steal probabilities that take into account runner’s speed, distance to second, batter’s hand, and all sorts of other variables you’d want to include to get a good estimate of success. In this year’s data set, which does not contain all thefts (double thefts, home invasions, and failed pickoffs are notable exclusions), there were 644 thefts for which Statcast estimated a 5% probability of theft being discovered. or less. That estimate was pretty good! Those base stealers were caught just 1.2% of the time. This is the stolen easy money, the $10 you earn on your first investment.

On the other hand, Statcast classified 184 thefts where the model predicted a theft detection rate of between 31% and 35%. Once again, the model was pretty good: Catchers threw out 38.6% of base stealers. This is the negative $2 investment in this example. Those thefts probably weren’t a good idea.

Now, a stolen base tying run still has meaning. According to our play-by-play database, the average successful stolen base event added 0.169 points to a team’s expected rating. The average caught steal event cost a team 0.394 points. Do the math, and that means a 70% success rate has an expected value of zero. Excluding double thefts from the analysis, this is approximately 71%.

Of course, expected value isn’t the only thing that determines whether it’s a good time to steal. Whoever bats next matters. Game state matters. Whether the pitcher gets spooked by a successful steal probably matters, though certainly not in a way that I would feel comfortable saying we could measure. But in a broad sense, you can think of 70% as a rule of thumb. You should need a good reason to attempt a robbery if you think it will be successful less than 70% of the time, and similarly, you should need a good reason Not steal if you are successful much more than 70% of the time.

What does this mean for the league-wide stolen base success rate? Let’s go back to my marginal return example from earlier. Attempts with a theft detection rate of less than 5%? They are the $10 investment. Thefts with a theft detection rate between 5% and 10%? They are more like investing $8 and so on. I tabulated all of this data (see the appendix below for a quick discussion about it) and used it to estimate what the overall base success rate of stealing would be if players only stole when marginal returns were above zero.

In other words, I took all the stolen base attempts with an estimated steal rate of 30% or less and added them up. This is the majority of thefts recorded in the database, believe it or not. Statcast estimated the chances of 3,410 thefts in 2024. As many as 2,764 of those transported have a 30% or lower chance of theft. These 2,764 opportunities resulted in 2,397 thefts and 367 thefts, a success rate of 86.7%.

In other words, all positive marginal value stolen base opportunities – those where the batter is on the right side of the draw – have an average aggregate success rate of about 87%. If the league falls short of this, there are some nasty steals in the mix. Given that the overall success rate in Statcast’s sample is 80.8% (again, excludes certain types of steals), it’s clear that a certain amount of bad base stealing attempts are destroying the entire sample.

Here’s another way to think about it: Using changes in my average point expectation from above, “good steals” added 260 points of expected scoring to their teams. But when you look at all tracked stolen base attempts overall, you only get 207 total value attempts. In other words, “bad steals” cost teams 53 points.

Interestingly, the “bad thefts” were as bad as the “good thefts” were good. The average good steal added .090 runs per attempt. The average bad steal costs 0.082 executions per attempt. There have been far more good attempts than bad – 81% of thefts tracked by Statcast fell on the right side of the breakeven line – but that bottom 20% is dragging the overall numbers down.

That 70% line is hardly a bright dividing line. There are stolen base attempts with a draw well below 70% and others with a higher draw. It’s just an aggregate number and I don’t pretend to have an opinion on every single theft attempt throughout the year. But as a general rule, it’s fair to say that about a fifth of attempted robberies this year were businesses with negative expectations.

Another complication: It’s not like there’s a flashing red light telling you the odds of successfully stealing a base on every play. Small fractions of a second separate an 80% chance from a 65% chance. The pitcher who throws an upward fastball instead of a downward changeup could easily explain this. If you’re willing to take a few tries with a marginally negative expected value in exchange for being more aggressive overall, that might change the calculation slightly.

Let’s say teams are fine with stolen base attempts that only have a 65% chance of success: a tie plus a margin of error. We add this group to our hypothetical group of stolen base attempts with good decisions and we get an overall success rate of 85.1% and a total of 252 runs added. That seems like a more reasonable estimate to me: I personally would prefer my base runners to be aggressive with the new rules.

You can quibble with many particular hypotheses here. Maybe the break-even rate is a little different from my estimate. Maybe the cost of steals to the player at the plate – throwing pitches to give the runner a chance, getting distracted by a shifting defense, and so on – changes the math. Baseball is much more complex than my little simplification. But one thing’s for sure: If your team can steal bases at a draw rate, they’re stealing too often. Don’t focus on breaking even your overall numbers – focus on marginally stealing breakeven and stop stealing after that.

Appendix: The trend is your friend, except at the end, when it bends

Here’s a graph of Statcast’s estimated percentage of thefts caught versus actual rates, broken down into 5% groups:

Whoa, the right side is pretty weird, huh? The first half of the graph looks almost perfect, then things get weird. Is there something strange with the numbers?

Not exactly! Two things are happening here, each highlighting a limitation of this type of analysis. First, the graph is lying to you. The data follows a trend line until about 50% are caught stealing, at which point things get wild. But that’s not half the sample: it’s 94% of the sample. Almost every theft attempt results in an estimated theft detection rate of less than 50%. Of course it does! This gives an effective theft detection rate of 20%. There is an excessive amount of noise in the right half of the graph: there are one-third as many observations in the entire right half as the leftmost data point. Here it is in table form:

Second, imagine what a play would be like with a 75% chance of getting caught stealing. Maybe it was a failed hit-and-run attempt, or maybe the runner fell. Most likely, though, this is a delayed steal, and trust me when I say that a model that depends primarily on runner position and speed will have problems with delayed steals, particularly when they represent a small portion of the sample.

I observed every stolen base attempt with an estimated probability of being caught stealing greater than 50%. The vast majority of the odd ones — the 85-90% segment contains seven steals and five hits — were delayed attempts that exploited defensive inattention. If the catcher shot all the way to second base at full speed every time, I have no doubt it would be an out almost every time. In my eyes, this is the classic case of a model that is very good in the general case having problems with some trending outliers.