When you think of stolen-base prowess, whom do you think of?

Rickey Henderson, of course. The Man of Steal has 1,406 steals, most all-time by a long-shot. Perhaps you remember Lou Brock, who’s second on the list with 938 steals. Ty Cobb and Vince Coleman also come to mind. Maybe you prefer Tim Raines, whose 84.6% success rate edges Rickey’s 80.7% success rate by a decent amount. You may even think of Honus Wagner, whose 97.9% success rate is tops all-time for players with at least 700 attempts.

These guys are good choices, but you should strongly consider Cleveland Indians rookie Bradley Zimmer — he of the 18 steals in 19 career attempts — in your thoughts. The art of the stolen base may be lost, but Zimmer and a couple other young players are keeping the flame alive. They run less often than those considered historically great, but they run much more efficiently.

How can I make this claim? Bradley Zimmer’s attempted only 19 steals in his career. How can we compare his success rate with those of Raines and Henderson, who attempted 954 and 1,741 respectively?

The answer is: we construct a model and use empirical Bayesian analysis to estimate not only the probability of the true-talent success rates of these guys, but also see how likely it is that Zimmer has the higher rate.

## Bradley Zimmer vs. Raines vs. Henderson

Stolen-base success rates have fluctuated throughout the decades, as the following figure shows:

A 72% success rate in the 1980’s, when Henderson and Raines did most of their thievery, is rarer than in the 2010’s for Zimmer. So when building a model, we need to consider the year. To do this I built a beta-binomial regression model that estimates true-talent success rates for each season, taking the year into account modeled as a spline with 5 degrees of freedom, used it as my Bayesian prior for each player-season, and then added the results over each players’ careers.

When combined with each player’s on-field results, we get the following distributions for Zimmer and the guys everyone always thinks of:

The peaks of each curve are the estimates of true-talent stolen-base success rate for each player. They are:

- Zimmer: 82.1%
- Raines: 78%
- Henderson: 77%

Zimmer’s graph is much wider and shorter than the other guys’. This is because we have much less information about his success rate. To feel confident in saying Zimmer is better than Raines or Henderson, we must do a couple A/B tests.

First, Henderson and Raines need to vie for the right to challenge Zimmer. Which of the two is more successful at stealing bases? The answer is Raines. I simulated 1,000,000 seasons of basestealing for each player. In about 75% of these seasons, Raines has the higher success rate. The following graph shows a density plot of their joint probabilities.

About 3/4 of the cloud is in Raines’ favor. So Raines is 75% likely to be a better base-stealer than Henderson. How likely is it that Zimmer’s a better basestealer than Raines?

The answer, again, is about 75%:

The weirdly shaped density cloud reflects the disparity in sample sizes between the two men. But the conclusion is the same: about 75% of the cloud falls on Zimmer’s side of the graph, indicating the likelihood he’s more successful at stealing bases than Raines was.

## Bradley Zimmer vs. Everyone

I’ve shown that Zimmer is likely better than Raines and Henderson at stealing bases. But that’s not all. Zimmer may be better than *everyone in the last 107 years*.* *The following graph of estimated success rates for all players since 1910, along with 95% credible intervals, supports this claim:

Zimmer and fellow rookie Lane Adams, who is 10-for-10 in his career, lead the pack. The wide bars of their graphs reflect the lack of information we have about these guys. Meanwhile, the bars for guys like Coleman, Raines, and Henderson are much shorter. We have far more information about these guys’ rates, so we can pinpoint their true-talent success rate with more certainty.

This list isn’t static. Zimmer will continue stealing bases, and in 2018 he may fail more often than he did in 2017, which would change the ordering of this graph. Ditto with the other active players on this list: Billy Hamilton, Byron Buxton, and Trea Turner chief among them.

But for now, when you think “best basestealing talents”, you should think about Bradley Zimmer.

(Photo by Erik Drost)

P.S. Many thanks to David Robinson and his e-book *Introduction to Empirical Bayes* for inspiring the techniques used in this article.