I don’t know the title for this phenomenon, however I’m guessing everybody has skilled it in some unspecified time in the future. 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 charge. I’ve heard that time period so many occasions over time, usually in reference to whether or not groups have been stealing an excessive amount of or not sufficient, that I integrated it into my thought processes prefer it was my very own.
However then somebody requested me why the optimum stolen base success charge was round 70%, and I noticed that I’d been improper. It was a bolt-of-inspiration form of second – you solely want to listen to the counter-argument as soon as to re-assess your outdated, uncritically assumed thought.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 charge within the combination, is extremely straightforward to grasp. There’s a distinction between marginal return and complete return. Contemplate 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 possibly can maintain investing till your online business breaks even – till you make a detrimental $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 resolution. You need to cease when your marginal return stops being optimistic – when an funding returns you $0, you’ll be able to simply cease going and pocket the $30 ($10+$8+$6+$4+$2+$0).
In relation to stolen bases, not each alternative is created equal. Statcast data caught stealing chances 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 yr’s information set, which doesn’t comprise each steal (double steals, steals of house, and failed pickoffs are notable exclusions), there have been 644 steals the place Statcast estimated a caught stealing chance of 5% or much less. That estimate was fairly good! These base stealers have been caught only 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 detrimental $2 funding on this instance. These steals in all probability weren’t a good suggestion.
Now, a stolen base breakeven level nonetheless has which means. Per our play-by-play database, the typical profitable stolen base occasion added 0.169 runs to a staff’s anticipated run scoring. The typical caught stealing occasion value a staff 0.394 runs. Do the maths, and that implies that a 70% success charge 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, in fact. Who’s batting subsequent issues. Sport state issues. Whether or not the pitcher will get spooked by profitable steals in all probability issues, although positively not in a manner I’d really feel comfy saying we might measure. However in a broad sense, you’ll be able to consider 70% as a rule of thumb line. You need to want a great cause to aim a steal for those who assume it’ll achieve success lower than 70% of the time, and likewise, it is 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 charge? Let’s return to my marginal return instance from earlier. The makes an attempt with a caught stealing proportion under 5%? They’re the $10 funding. The steals with a caught stealing charge between 5% and 10%? They’re extra just like the $8 funding, and so forth. I tabulated all that information (see the appendix under for a fast dialogue of that) and used that to estimate what the general stolen base success charge would seem like if gamers solely stole when the marginal returns have been above zero.
In different phrases, I took the entire stolen base makes an attempt with an estimated caught stealing proportion of 30% or under and added them collectively. That’s a lot of the tracked steals within the database, imagine it or not. Statcast estimated chances for 3,410 steals in 2024. A full 2,764 of these carried caught stealing chances of 30% or decrease. These 2,764 alternatives resulted in 2,397 steals and 367 occasions caught stealing, an 86.7% success charge.
All of the stolen base alternatives with optimistic marginal worth – those the place the batter is on the fitting facet of breakeven – have an combination common success charge of roughly 87%. If the league is under that, there are some dangerous steals within the combine. Provided that the general success charge in Statcast’s pattern is 80.8% (once more, it excludes some varieties 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 take a look at all tracked stolen base makes an attempt as an entire, you get solely 207 runs of complete worth. The “dangerous steals” value groups 53 runs, in different phrases.
Apparently sufficient, the “dangerous steals” have been about as dangerous because the “good steals” have 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 much 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 brilliant dividing line. There are stolen base makes an attempt with a breakeven nicely under 70%, and ones with a breakeven above it. It’s an combination quantity solely, and I gained’t declare to have an opinion on each single steal try all yr. However as a basic rule of thumb, it’s truthful to say that roughly a fifth of the steals that have been tried this yr have been negative-expectation undertakings.
One other complication: It’s not like there’s a blinking purple gentle telling you the percentages 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 might simply account for it. When you’re keen to finish up with a number of makes an attempt with marginally detrimental anticipated worth in change for being extra aggressive general, that would change the calculus barely.
Let’s say groups are wonderful with stolen base makes an attempt which can 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 general success charge of 85.1%, and a complete of 252 runs added. That feels nearer to an inexpensive estimate to me – I’d reasonably have my baserunners be aggressive with the brand new guidelines, personally.
You’ll be able to quibble with a variety of the actual assumptions right here. Perhaps the breakeven charge is a bit totally different than my estimate. Perhaps the price of steals on the participant on the plate – taking pitches to provide 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 positive: In case your staff is succeeding in its stolen base makes an attempt on the breakeven charge, it’s stealing too usually. Don’t give attention to getting your general numbers to breakeven – give attention to the marginal breakeven steal, and cease stealing after that.
Appendix: The development is your good friend, 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 to be like 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 this kind of evaluation. First, the graph is mendacity to you. The info follows a development 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. Practically each steal try leads to a caught stealing proportion estimate under 50%. After all it does! That’s the way you get an precise caught stealing charge of 20%. There’s an inordinate quantity of noise in the fitting half of the graph – there are a 3rd as many observations in your complete proper half than within the left-most datapoint. Right here it’s in desk type:
Caught Stealing Charges, Modeled vs. Precise
| Bucket | Rely | Modeled CS Price | CS Price |
|---|---|---|---|
| 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 to be like like. Perhaps it’s a busted hit and run try, or perhaps the runner fell down. Most definitely, 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 have been profitable – have 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 doubt that it’d be an out nearly each time. In my eyes, this can be a traditional case of a mannequin that is excellent within the basic case having hassle with some trend-breaking outliers.
