Breaking Even Is for Suckers

I don’t know the identify for this phenomenon, however I’m guessing everybody has skilled it in some unspecified time in the future. You hear one thing sufficient instances, and also you begin to repeat it with out actually pondering critically about it. My instance: the breakeven stolen base price. I’ve heard that time period so many instances over time, typically in reference to whether or not groups had 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 price was round 70%, and I noticed that I’d been mistaken. 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 previous, 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 needs to be profitable at much better than the breakeven price 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 possibly can maintain investing till your small business breaks even – till you make a damaging $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 unhealthy resolution. It’s best to cease when your marginal return stops being optimistic – when an funding returns you $0, you may 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 data caught stealing chances that keep in mind runner velocity, distance from second, batter handedness, and all types of different variables you’d need to embody to get a great estimate of success. On this yr’s information 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 chance of 5% or much less. That estimate was fairly good! These base stealers had been caught only one.2% of the time. These are the straightforward cash steals, the $10 you make on the primary funding.

Then again, 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 damaging $2 funding on this instance. These steals most likely 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 signifies that a 70% success price 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. Recreation state issues. Whether or not the pitcher will get spooked by profitable steals most likely issues, although positively not in a manner I’d really feel snug saying we may measure. However in a broad sense, you may consider 70% as a rule of thumb line. It’s best to want a great purpose to aim a steal in the event you suppose it’ll achieve success lower than 70% of the time, and likewise, you need to want a great purpose to not steal in the event you’re going to achieve success much more than 70% of the time.

What does that imply for the league-wide stolen base success price? 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 price between 5% and 10%? They’re extra just like the $8 funding, and so forth. I tabulated all that information (see the appendix beneath for a fast dialogue of that) and used that to estimate what the general stolen base success price would appear to be if gamers solely stole when the marginal returns had been above zero.

In different phrases, I took the entire 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 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 instances caught stealing, an 86.7% success price.

All of the stolen base alternatives with optimistic marginal worth – those the place the batter is on the precise facet of breakeven – have an mixture common success price of roughly 87%. If the league is beneath that, there are some unhealthy steals within the combine. Provided that the general success price in Statcast’s pattern is 80.8% (once more, it excludes some sorts of steals), it’s clear that some quantity of unhealthy 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 adjustments from up above, the “good steals” added 260 runs of anticipated scoring to their groups. However in the event you take a look at all tracked stolen base makes an attempt as an entire, you get solely 207 runs of whole worth. The “unhealthy steals” value groups 53 runs, in different phrases.

Curiously sufficient, the “unhealthy steals” had been about as unhealthy because the “good steals” had been good. The typical good steal added 0.090 runs per try. The typical unhealthy steal value 0.082 runs per try. There have been much more good makes an attempt than unhealthy – 81% of steals tracked by Statcast fell on the precise facet of the breakeven line – however that backside 20% is dragging down the general numbers.

That 70% line is hardly a vivid 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 yr. However as a common rule of thumb, it’s honest to say that roughly a fifth of the steals that had been tried this yr had been negative-expectation undertakings.

One other complication: It’s not like there’s a blinking purple mild 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. When you’re prepared to finish up with just a few makes an attempt with marginally damaging anticipated worth in change for being extra aggressive total, that would change the calculus barely.

Let’s say groups are superb with stolen base makes an attempt which are 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 price of 85.1%, and a complete of 252 runs added. That feels nearer to an affordable estimate to me – I’d somewhat have my baserunners be aggressive with the brand new guidelines, personally.

You possibly can quibble with a variety of the actual assumptions right here. Perhaps the breakeven price 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 – adjustments 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 price, it’s stealing too typically. Don’t deal with getting your total numbers to breakeven – deal with the marginal breakeven steal, and cease stealing after that.

Appendix: The development 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 p.c teams:

Whoa, the precise facet is fairly funky, huh? The primary half of the graph seems 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 any such 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. Almost each steal try ends in a caught stealing proportion estimate beneath 50%. In fact it does! That’s the way you get an precise caught stealing price of 20%. There’s an inordinate quantity of noise in the precise half of the graph – there are a 3rd as many observations in your entire proper half than within the left-most datapoint. Right here it’s in desk type:

Second, think about what a play with a 75% caught stealing probability seems like. Perhaps it’s a busted hit and run try, or perhaps the runner fell down. Most probably, although, it’s a delayed steal, and belief me after I say {that a} mannequin that relies upon totally on runner place and velocity goes to have hassle with delayed steals, significantly after 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 all the way down to second base at full velocity each time, I’ve little question that it’d be an out nearly 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.