### Should you always expect pitchers to decline?

How should you change your expectations of a pitcher's performance as he ages?

For hitters, it's pretty much been established that, as a group, they will improve up to about age 27, then begin to decline. Is the same true for pitchers?

Studies of the history of some of the best pitchers, the ones with long careers, seem to suggest so. One such study comes from the study Justin Wolfers co-authored, then wrote about in the New York Times. I don't agree with the study's conclusions, but, even so, the diagram in the article does show the expected aging curve – better in the middle, and worse at the ends.

Last week, at the JSM convention in Denver, Jim Albert fitted some spline curves to various pitchers' careers (his study isn't online yet). He found a similar pattern for most pitchers – better in the late 20s and early 30s, and worse at the beginning and end of their careers.

But my little study showed something different. I used the "paired seasons" method, where you see what a pitcher did at (say) 25, and compare to what he did at 26. You repeat for all ages, and then chain everything together (by multiplying the improvements/declines) to get a career curve.

Here's the career curve that I got. It's in Component ERA, so higher is worse:

(Technical note: As Tom Tango has demonstrated, that method winds up biased, showing larger declines or smaller improvements than it should, because of the selective sampling problem whereby luckier pitchers get more playing time. That problem is attenuated somewhat if you regress the first-year performance to the mean, which I did. The above curve is after regressing 10% to the MLB mean. The basic shape is the same if you regress 0% or 30%.)

This is NOT the typical U-shaped curve you would expect. Indeed, it seems to show that pitchers get worse every year, regardless of their age. When you see a group of pitchers of age X, you *always* expect them to be worse at age X+1. (Actually, there was a very slight improvement from 19 to 20, I think, but it was negligible and the sample size was small.)

This contradicts the earlier studies. It also contradicts empirical data somewhat. Because, if 22-year-old pitchers are better than 27 year olds, how come there are so many more major-league pitchers who are 27? It doesn't make sense to suggest that teams are so dumb that they leave young pitchers in the minors who are better than their established staffs.

So what's going on? How can the two curves be consistent?

One suggestion (at The Book blog) was that all pitchers actually are physically better at young ages, but younger pitchers aren't ready for the majors until they learn to master their pitches and learn how to handle major-league hitters. Only once they have that experience do they get called up, at which point they start to decline in performance.

It's a nice theory, but it's contradicted by the Wolfers and Albert studies, which found U-shaped curves for the better pitchers.

So I'm leaning towards another theory (which was "#2" in a previous post on this subject), that the above curve is actually the sum of two separate curves. First, the Wolfers/Albert curve, which shows that, in retrospect, after analyzing a full career, pitchers do improve when young. And, second, the records of pitchers who did NOT have long careers, which led to them getting injured when young, and seeing their performance get much worse before they were forced to retire.

For instance, consider these pitchers at 23, 27, 30, and 33:

Pitcher A: 3.50, 3.00, 3.50, 4.50

Pitcher B: 3.50, 3.00, 3.50, 4.50

Pitcher C: 3.50, 3.00, 5.50, retired

Pitcher D: 3.50, 5.50, retired, still retired

If you take the average of those four pitchers, you get:

Average: 3.50, 3.625, 4.17, 4.50

And so even though the guys with the long careers have U-shaped curves, the average is worse at every subsequent age.

If that's true, it means that

(a) if a pitcher stays healthy, he improves into his late 20s before declining, but

(b) enough pitchers get injured that the odds are that the pitcher will actually decline.

Both curves are correct. But if you have a 25-year-old pitcher, and you're thinking of offering him a long-term contract, you have to keep in mind that his expected contribution is LESS than his talent at 25, because of the chance of career-ending injury.

That would also explain why pitchers are such a bad draft gamble, as Bill James showed back in 1985.

For hitters, it's pretty much been established that, as a group, they will improve up to about age 27, then begin to decline. Is the same true for pitchers?

Studies of the history of some of the best pitchers, the ones with long careers, seem to suggest so. One such study comes from the study Justin Wolfers co-authored, then wrote about in the New York Times. I don't agree with the study's conclusions, but, even so, the diagram in the article does show the expected aging curve – better in the middle, and worse at the ends.

Last week, at the JSM convention in Denver, Jim Albert fitted some spline curves to various pitchers' careers (his study isn't online yet). He found a similar pattern for most pitchers – better in the late 20s and early 30s, and worse at the beginning and end of their careers.

But my little study showed something different. I used the "paired seasons" method, where you see what a pitcher did at (say) 25, and compare to what he did at 26. You repeat for all ages, and then chain everything together (by multiplying the improvements/declines) to get a career curve.

Here's the career curve that I got. It's in Component ERA, so higher is worse:

(Technical note: As Tom Tango has demonstrated, that method winds up biased, showing larger declines or smaller improvements than it should, because of the selective sampling problem whereby luckier pitchers get more playing time. That problem is attenuated somewhat if you regress the first-year performance to the mean, which I did. The above curve is after regressing 10% to the MLB mean. The basic shape is the same if you regress 0% or 30%.)

This is NOT the typical U-shaped curve you would expect. Indeed, it seems to show that pitchers get worse every year, regardless of their age. When you see a group of pitchers of age X, you *always* expect them to be worse at age X+1. (Actually, there was a very slight improvement from 19 to 20, I think, but it was negligible and the sample size was small.)

This contradicts the earlier studies. It also contradicts empirical data somewhat. Because, if 22-year-old pitchers are better than 27 year olds, how come there are so many more major-league pitchers who are 27? It doesn't make sense to suggest that teams are so dumb that they leave young pitchers in the minors who are better than their established staffs.

So what's going on? How can the two curves be consistent?

One suggestion (at The Book blog) was that all pitchers actually are physically better at young ages, but younger pitchers aren't ready for the majors until they learn to master their pitches and learn how to handle major-league hitters. Only once they have that experience do they get called up, at which point they start to decline in performance.

It's a nice theory, but it's contradicted by the Wolfers and Albert studies, which found U-shaped curves for the better pitchers.

So I'm leaning towards another theory (which was "#2" in a previous post on this subject), that the above curve is actually the sum of two separate curves. First, the Wolfers/Albert curve, which shows that, in retrospect, after analyzing a full career, pitchers do improve when young. And, second, the records of pitchers who did NOT have long careers, which led to them getting injured when young, and seeing their performance get much worse before they were forced to retire.

For instance, consider these pitchers at 23, 27, 30, and 33:

Pitcher A: 3.50, 3.00, 3.50, 4.50

Pitcher B: 3.50, 3.00, 3.50, 4.50

Pitcher C: 3.50, 3.00, 5.50, retired

Pitcher D: 3.50, 5.50, retired, still retired

If you take the average of those four pitchers, you get:

Average: 3.50, 3.625, 4.17, 4.50

And so even though the guys with the long careers have U-shaped curves, the average is worse at every subsequent age.

If that's true, it means that

(a) if a pitcher stays healthy, he improves into his late 20s before declining, but

(b) enough pitchers get injured that the odds are that the pitcher will actually decline.

Both curves are correct. But if you have a 25-year-old pitcher, and you're thinking of offering him a long-term contract, you have to keep in mind that his expected contribution is LESS than his talent at 25, because of the chance of career-ending injury.

That would also explain why pitchers are such a bad draft gamble, as Bill James showed back in 1985.

## 2 Comments:

I think that this is right, in general. Pitching a baseball clearly causes a lot of injuries, and that biases the results. I think the key is to try to figure out what causes injuries-- usage, delivery, etc.-- and decrease the odds of injury.

I also suspect that certain kinds of pitchers have different aging curves. Those who peak early may have lower peaks than those who peak late. If this is true, then the average picher-- even if uninjured-- may peak early and decline on average over the course of his career, even though the average pitcher who is successful enough to make the majors may peak much later on. There are probably many mental and physical skills that start to depreciate for most people in their early twenties, but those who are successful at employing these skills may be those who able to learn and adjust, and they probably peak later.

Has anyone figured out what the "natural" or "background" attrition rate is for pitchers? We tend to associate career-altering arm injuries with overuse or other decision-controlled causes. But pitchers get sore arms in April as well as September, and it may occur at 22 or 32 or 42. The risk of arm injury seems to be inherent in the act of pitching, random and independent of other identifiable causes. But I've never seen a study quantifying the risk, controlled for things like innings pitched or games played or other usage factors. Anyone know?

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