I don’t know the identify for this phenomenon, however I’m guessing everybody has skilled it sooner or later. You hear one thing sufficient occasions, and also you begin to repeat it with out actually considering critically about it. My instance: the breakeven stolen base fee. I’ve heard that time period so many occasions through the years, usually in reference to whether or not groups had been stealing an excessive amount of or not sufficient, that I included it into my thought processes prefer it was my very own.
However then somebody requested me why the optimum stolen base success fee was round 70%, and I noticed that I’d been unsuitable. It was a bolt-of-inspiration type of second – you solely want to listen to the counter-argument as soon as to re-assess your outdated, uncritically assumed thought. Why ought to groups maintain stealing as long as they’re profitable greater than 70% (ish) of the time? I couldn’t clarify it to myself utilizing math.
The opposite facet of the coin, the notion that groups must be profitable at much better than the breakeven fee within the mixture, is extremely straightforward to know. There’s a distinction between marginal return and whole return. Think about a enterprise the place you’re making investments. Your first funding makes $10. Your subsequent one makes $8, after which $6, and so forth. You may maintain investing till your enterprise breaks even – till you make a unfavorable $10 funding to offset that first one, kind of ($10+$8+$6+$4+$2+$0-$2-$4-$6-$8-$10). However that’s a clearly dangerous determination. It is best to cease when your marginal return stops being optimistic – when an funding returns you $0, you possibly can simply cease going and pocket the $30 ($10+$8+$6+$4+$2+$0).
On the subject of stolen bases, not each alternative is created equal. Statcast information caught stealing possibilities that bear in mind runner pace, distance from second, batter handedness, and all types of different variables you’d need to embrace to get a great estimate of success. On this 12 months’s knowledge set, which doesn’t include each steal (double steals, steals of dwelling, and failed pickoffs are notable exclusions), there have been 644 steals the place Statcast estimated a caught stealing likelihood of 5% or much less. That estimate was fairly good! These base stealers had been caught just one.2% of the time. These are the simple cash steals, the $10 you make on the primary funding.
However, Statcast tabulated 184 steals the place the mannequin predicted a caught stealing proportion between 31% and 35%. Once more, the mannequin was fairly good – catchers threw out 38.6% of these would-be base stealers. That’s the unfavorable $2 funding on this instance. These steals in all probability weren’t a good suggestion.
Now, a stolen base breakeven level nonetheless has that means. Per our play-by-play database, the common profitable stolen base occasion added 0.169 runs to a group’s anticipated run scoring. The typical caught stealing occasion value a group 0.394 runs. Do the maths, and that signifies that a 70% success fee has zero anticipated worth. Exclude double steals from the evaluation, and it’s about 71%.
Anticipated worth isn’t the one factor figuring out whether or not it’s a great time to steal, after all. Who’s batting subsequent issues. Sport state issues. Whether or not the pitcher will get spooked by profitable steals in all probability issues, although undoubtedly not in a method I’d really feel comfy saying we may measure. However in a broad sense, you possibly can consider 70% as a rule of thumb line. It is best to want a great cause to try a steal for those who suppose it’ll achieve success lower than 70% of the time, and likewise, it’s best to want a great cause not to steal for those who’re going to achieve success much more than 70% of the time.
What does that imply for the league-wide stolen base success fee? Let’s return to my marginal return instance from earlier. The makes an attempt with a caught stealing proportion beneath 5%? They’re the $10 funding. The steals with a caught stealing fee between 5% and 10%? They’re extra just like the $8 funding, and so forth. I tabulated all that knowledge (see the appendix beneath for a fast dialogue of that) and used that to estimate what the general stolen base success fee would appear to be if gamers solely stole when the marginal returns had been above zero.
In different phrases, I took all the stolen base makes an attempt with an estimated caught stealing proportion of 30% or beneath and added them collectively. That’s many of the tracked steals within the database, consider it or not. Statcast estimated possibilities for 3,410 steals in 2024. A full 2,764 of these carried caught stealing possibilities of 30% or decrease. These 2,764 alternatives resulted in 2,397 steals and 367 occasions caught stealing, an 86.7% success fee.
All of the stolen base alternatives with optimistic marginal worth – those the place the batter is on the fitting facet of breakeven – have an mixture common success fee of roughly 87%. If the league is beneath that, there are some dangerous steals within the combine. On condition that the general success fee in Statcast’s pattern is 80.8% (once more, it excludes some sorts of steals), it’s clear that some quantity of dangerous stolen base makes an attempt are bringing the entire pattern down.
Right here’s one other mind-set about it: Utilizing my common run expectancy modifications from up above, the “good steals” added 260 runs of anticipated scoring to their groups. However for those who have a look at all tracked stolen base makes an attempt as an entire, you get solely 207 runs of whole worth. The “dangerous steals” value groups 53 runs, in different phrases.
Curiously sufficient, the “dangerous steals” had been about as dangerous because the “good steals” had been good. The typical good steal added 0.090 runs per try. The typical dangerous steal value 0.082 runs per try. There have been way more good makes an attempt than dangerous – 81% of steals tracked by Statcast fell on the fitting facet of the breakeven line – however that backside 20% is dragging down the general numbers.
That 70% line is hardly a vibrant dividing line. There are stolen base makes an attempt with a breakeven effectively beneath 70%, and ones with a breakeven above it. It’s an mixture quantity solely, and I received’t declare to have an opinion on each single steal try all 12 months. However as a common rule of thumb, it’s truthful to say that roughly a fifth of the steals that had been tried this 12 months had been negative-expectation undertakings.
One other complication: It’s not like there’s a blinking purple gentle telling you the chances of efficiently stealing a base on each play. Tiny fractions of a second separate an 80% probability from a 65% probability. The pitcher throwing a fastball up as an alternative of a changeup down may simply account for it. If you happen to’re keen to finish up with a number of makes an attempt with marginally unfavorable anticipated worth in change for being extra aggressive total, that might change the calculus barely.
Let’s say groups are advantageous with stolen base makes an attempt which might be solely 65% prone to succeed – breakeven plus a margin of error. Add that bucket in to our hypothetical group of good-decision stolen base makes an attempt, and we get an total success fee of 85.1%, and a complete of 252 runs added. That feels nearer to an affordable estimate to me – I’d quite have my baserunners be aggressive with the brand new guidelines, personally.
You may quibble with numerous the actual assumptions right here. Perhaps the breakeven fee is a bit totally different than my estimate. Perhaps the price of steals on the participant on the plate – taking pitches to present the runner an opportunity, getting distracted by a shifting protection, and so forth – modifications the maths. Baseball is much more advanced than my little simplification. However one factor is for certain: In case your group is succeeding in its stolen base makes an attempt on the breakeven fee, it’s stealing too usually. Don’t concentrate on getting your total numbers to breakeven – concentrate on the marginal breakeven steal, and cease stealing after that.
Appendix: The pattern is your pal, besides on the finish when it bends
Right here’s a chart of Statcast’s estimated caught stealing proportion in comparison with precise charges, bucketed out in 5 % teams:
Whoa, the fitting facet is fairly funky, huh? The primary half of the graph appears nearly good, after which issues get bizarre. Is one thing unusual with the numbers?
Not likely! There are two issues occurring right here, every of which highlights a limitation of the sort of evaluation. First, the graph is mendacity to you. The info follows a pattern line proper up till round 50% caught stealing, at which level it will get wild. However that’s not half the pattern – it’s 94% of the pattern. Almost each steal try leads to a caught stealing proportion estimate beneath 50%. In fact it does! That’s the way you get an precise caught stealing fee of 20%. There’s an inordinate quantity of noise in the fitting half of the graph – there are a 3rd as many observations in all the proper half than within the left-most datapoint. Right here it’s in desk kind:
Caught Stealing Charges, Modeled vs. Precise
| Bucket | Rely | Modeled CS Fee | CS Fee |
|---|---|---|---|
| 0-5% | 644 | 2.1% | 1.2% |
| 6-10% | 527 | 8.1% | 4.9% |
| 11-15% | 543 | 13.0% | 12.9% |
| 16-20% | 447 | 17.9% | 22.4% |
| 21-25% | 356 | 22.9% | 24.2% |
| 26-30% | 247 | 27.8% | 31.2% |
| 31-35% | 184 | 32.9% | 38.6% |
| 36-40% | 122 | 37.7% | 45.1% |
| 41-45% | 86 | 42.5% | 50.0% |
| 46-50% | 57 | 48.2% | 50.9% |
| 51-55% | 54 | 53.1% | 44.4% |
| 56-60% | 32 | 58.2% | 43.8% |
| 61-65% | 26 | 62.4% | 53.8% |
| 66-70% | 22 | 68.1% | 40.9% |
| 71-75% | 21 | 73.1% | 42.9% |
| 76-80% | 16 | 77.3% | 56.3% |
| 81-85% | 13 | 83.3% | 46.2% |
| 86-90% | 7 | 88.4% | 28.6% |
| 91-95% | 5 | 92.6% | 40.0% |
| 96-100% | 1 | 96.0% | 100.0% |
Second, think about what a play with a 75% caught stealing probability appears like. Perhaps it’s a busted hit and run try, or perhaps the runner fell down. Most certainly, although, it’s a delayed steal, and belief me once I say {that a} mannequin that relies upon totally on runner place and pace goes to have hassle with delayed steals, significantly once they’re a tiny a part of the pattern.
I watched each stolen base try with an estimated caught stealing probability of upper than 50%. The overwhelming majority of the bizarre ones – the 85-90% bucket has seven steals in it, and 5 had been profitable – had been delayed makes an attempt that preyed on defensive inattention. If the catcher was firing right down to second base at full pace each time, I’ve little question that it’d be an out virtually each time. In my eyes, it is a basic case of a mannequin that is excellent within the common case having hassle with some trend-breaking outliers.
