THE BOOK--Playing The Percentages In Baseball

I should also point out that since this data shows a definite improvement at each age:

22 0.064 39879
23 0.070 64129
24 0.070 90850
25 0.072 115991
26 0.076 130124
27 0.076 134617

(Higher war per game, and more innings pitched)

This shows a definite decline at each age:
30 0.087 97852
31 0.085 83333
32 0.084 72144
33 0.083 60879

So, you are definitely on the down slope starting at age 30.  And you are on your way up by age 27.

***

As I explained from age 27 to 30, you are also going down, but it’s not so unambiguous without looking at the data more carefully.

In no way is the peak age of a pitcher anything less than 27.

***

Tango, this is pretty much wrong. This is the conclusion you would reach from your data, but since it is biased by the fact that it does not include anything but major league numbers, it is not necessarily the correct conclusion. I wouldn’t make such a strong statement if I were you…

Correction: In no way is the peak age of a MLB pitcher anything less than 27.

Doesn’t this contradict what MGL said two days ago?

http://www.insidethebook.com/ee/index.php/site/comments/no_matter_how_i_slice_or_dice_it_pitchers_get_worse_every_year/

I was thinking the same thing.

I was ALSO thinking the same thing.
vr, Xei

It’s because we’re looking at two different populations. right?

We’re looking at populations a different way.  I’m throwing out NO data.  On the other hand, I can look at the same data, but ensure that I keep the pools of player data the same in adjacent seasons, like here:
http://tangotiger.net/adjacentPitching.html

Personally, I like this thread’s process the best.  I don’t see any selection biases, other than the pitcher having to be in MLB.

I am confused as to the difference between my work (and your old work) and your new work.

I thought MGL’s analysis was using all pitchers, minor and major using MLEs as a common yardstick. right???

This new work is simply a sum of ALL pitchers at those ages, with NO control in making sure that there’s equal representation at each age.

The idea is that if you peak at age 27, you will have both the most number of pitchers pitching AND their rate stats are the best.  Comparing age 27 to 26, and that’s true.  That is, I have more innings thrown and they pitched better.  Even though I don’t have the same population of pitchers, it must mean something that the guys at age 27 are better than those at age 26.

Same for 26-25, 25-24, 24-23, 23-22.

For example, without looking at data year-to-year, are players better at age 20 or 19 (in any sport).  Well, you have alot more players at age 20 than 19.  AND the rate stats of the 20-yr olds is higher than the 19-yr olds.  Just on that fact, you would conclude that 20-yr olds are better.

Do you even need to do a matched-pair study, making sure you have the same players in the same proportion at each age?  I say no, especially since you have huge overlap between the 20 and 19 yr olds anyway (the 20yr olds were 19, and the 19yr olds turn 20).  The pools is not the same proportion, but I say that doesn’t matter to establish PEAK.  It only matters to establish SHAPE.

I still don’t see how that reconciles with the results we get when we do curves using the “delta” method which shows that pitchers decline every year after age 25 or so.

IOW, answer me this question (batman):  If all I told you was that we have a pitcher who was a true 4.00 RA pitcher at age 26 in the major leagues.  IOW, he pitched at age 26 in the majors and that is all you know.  Will his projected true RA going into his 27th year, whether he ends up pitching or not in the majors, be more than or less than 4.00? The results of the delta method say that it will be worse.  That is easy to figure out (with one caveat).  There is only one correct answer of course for that question.

The caveat of course is that even though all I have to do is look at all 26 yo pitchers who pitched in any year X and see how they pitched in year X+1 and take the average difference (the delta method of course), my question was what was his true talent going into year X+1, but there are some pitchers in our sample who did not actually pitch in Year x+1 so we don’t know what their performance would have been if they pitched. But we can CERTAINLY answer the question precisely by using the delta method if we rephrase the question to, “....if he pitches in his age 27 season...”

Couldn’t this be a relic of an information problem in giving the younger pitchers the appropriate number of innings? For example, say we have 2 19yos, one worth 0 WAR, the other .03 WAR/G. They both get a shot and at the end of the year the first has 50 IP, the second 100 for a total of 150 IP at .02 WAR/G. Next year the first guy is out of the league and the second deteriorates to .025 WAR/G, but is in the rotation the whole year for 200 IP, so our total IP and WAR/G at 20yo are both higher despite the pitchers being worse.

This is what you have (math at bottom):

Lets say you have 6 pitchers aged 24, 3 with true talent of ERA+ of 90 and 3 with ERA+ of 85 - from each group one is lucky, one has average luck and one is unlucky, with luck = 5 ERA+. The 24 year olds with observed talent of 90 or higher get 100 ip, the 85s get 50 ipm and the 80 gets 0.

In year 2 everyone improves by 2 ERA+, and luck evens out - the minus go plus, the plusses go minus. The guy who was obs 95 last year gets 150 ip, the guy who is 97 this year gets 150 ip, the 2 medium guys get 100 ip and the 2 low guys get 50

We have all the players getting better. We have year-to-year showing worse. We have more ip and a better performance at age 25 versus age 24. We have more guys in the majors at age 25 versus 24.

One of the big problems is that pitching performance is so inconsistent year to year make yr to yr comparisons full of problems. You also get a sample bias because not everyone is good enough pitch in the majors at age 22. You get a mss of guys not good enough at age 22 to pitch in the minors who will in a few years. But yr to yr comparisons on an individual basis is affected by the deviation in performance yr to yr.

If Tango wasnt right, then there would be some 22 year olds ready to pitch in the majors each year that would have fantastic MLEs in AA or AAA ball.

24
TT Luck Obs Tal ip weighted
1 90 5 95 100 9500
2 90 0 90 100 9000
3 90 -5 85 50 4250
4 85 5 90 100 9000
5 85 0 85 50 4250
6 85 -5 80 0 0

400 36000 90



25
TT Luck Obs Tal ip weighted
1 92 -5 87 150 13050
2 92 0 92 100 9200
3 92 5 97 150 14550
4 87 -5 82 50 4100
5 87 0 87 50 4350
6 87 5 92 100 9200

600 54450 90.75

min of change in weighted
ip obs tal change

1 100 -8 -800
2 100 2 200
3 50 12 600
4 50 -8 -400
5 50 2 100
6 0 12 0

350 12 -300

I think we can reconcile Tango and MGL’s findings.  The missing element is that a lot of pitchers “audition” in MLB between ages 22 and 25.  They are given a chance to succeed, but many fail.  This largely stops happening by age 27.  So Tango’s data is the outcome of two different curves:  the percentage of permanent hires (as opposed to temps) at each age, and the talent level of the regulars at that level. 

Take a simple model where the % of permanent players starts at 20% at age 22 (i.e. 80% of them will fail) and rises to 100% by age 27 and thereafter.  Assume the permanent players peak at 24 (.07 WAR/G) and decline gradually after that.  And the temps make a minimal contribution (.01 WAR).  What you then get is exactly what we observe:  a rising performance that peaks at age 27, driven by the declining % of temps in each group compared to earlier ages, but thereafter the age curve drives down the performance level each year. 

Basically, before age 26 the players are going through a sieve as MLB pans for gold.  The good pitchers survive to the next age, while some new tryouts are added to the mix.  Each successive age group has more long-career (i.e. good) pitchers, hitting a plateau of nearly 100% around age 27.

To follow up, pitchers who face fewer than 2000 batters in their careers account for about 12% of all PAs.  This group performs quite poorly, as you’d imagine (some of it bad luck, some skill, but the performance stats are poor).  I don’t know how they are distributed by age, but it must be highly concentrated at young ages.  These pitchers might provide 50% of the PA at age 23, but only 7% at age 28 and 2% at age 35 (#s for illustration only).  So when Tango compares age 23 to age 27, the underlying quality difference is potentially very large.

Let’s create a simple model, where the % of short career pitchers looks like this:
Age &#xTr;youts
22 0.5
23 0.4
24 0.3
25 0.2
26 0.1
27 0
28+ 0

Let’s assume that the short career pitchers contribute 0.5 WAR on average. And the long-career guys age like this, with a peak at 24, then gentle decline, then sharper decline:
Age WAR(long-career)
22 1.9
23 2.2
24 2.5
25 2.4
26 2.3
27 2.2
28 2.1
29 2
30 1.8
31 1.6
32 1.4
33 1.2
34 1
35 0.8
36 0.6
37 0.4
38 0.2
39 0

Combine this, and the average WAR for each age looks like this:
Age Total WAR
22 1.2
23 1.52
24 1.9
25 2.02
26 2.12
27 2.2
28 2.1
29 2
30 1.8
31 1.6
32 1.4
33 1.2
34 1
35 0.8
36 0.6
37 0.4
38 0.2
39 0

Pretty much what we observe in MLB.  Maybe someone can test my theory by calculating the percentage of PAs provided by short-career pitchers at each age?

Guy/16 marked for moderation and is now open.

” I don’t know how they are distributed by age, but it must be highly concentrated at young ages.”

Huh?

Players who perform in the majors at a young age are usually pretty good. I took all the pitchers age 23 from the years 1982-1991 and got a total of 89,526 bfp. Of that 80% (71,279) were done by pitchers with more than 2,000 bfp.

Age 22 I got 84% (43,407 out of 51,670)

For comparison sake, I took 1991, and found 160,746 bfp, of those 82% were done by players with 2,000 bfp

And your top pitchers at a young age represent a lot more of the total - the top 20 pitchers age 22 did 33% of the bfp, the top 20 age 23 22%, the top 20 in 1991 did 12%.

I would find it very surprising to learn that short-career pitchers do not mainly pitch during their 20s.  If you look at age 28 pitchers, are 20% of the BF also from short-career pitchers? What about age 32?

Maybe Tango can easily tell us the average career WAR for each age cohort.  That would be another way to assess whether the younger cohorts make up lesser talent pools.

Guy, are you asking for the total career WAR for pitchers at each age?  So, for pitchers who pitch at age 22, what is their career WAR from age 22 to the end?  If not, give me the exact spec.

In addition to the post above from dq, what 16/Guy stipulates doesn’t seem to make much logical sense.

We know that IP are evenly distributed in thirds, from 17-26, 27-30, and 31+. If 12% of all PAs are from pitchers with fewer than 2,000 BFs, then assuming that all of these pitchers are younger pitchers would mean that “long career pitchers” aren’t pitching until later in their careers.

Tango: I was looking for something that would shed light on the average talent level of each cohort.  Career WAR would be OK, or career WAR/Game.  Weighted by innings/batters at that age.

I see.  So, career WAR (past, present, future), weighted by IP at age X.  Correct?

The career WAR is the average WAR of the pitcher weighted by his innings.  So, you take the career WAR of each pitcher who pitched at age 21, figure out how many innings he pitched at age 21, and that becomes his weight. 

So, from the age of 23 to 27, the career WAR for our pitchers at each age was 15 wins.  We can say therefore that the talent level of pitchers who pitched at those ages is roughly the same.  And so, that we witnessed a rise in performance from each age tells us that pitchers were pitching better.

Starting at age 28, good pitchers started to remain, so we’re getting a biased pool of pitchers.  But if you are looking for an unbiased pool of pitchers, it seems to me that pitchers aged 23-27 (or 22-28 if you want to stretch it a bit) are pretty much equal in terms of overall talent.

Age careerWAR
16 2
17 0
18 7
19 23
20 22
21 19
22 16

23 15
24 15
25 15
26 15
27 15

28 16
29 18
30 19
31 21
32 23
33 25
34 27
35 30
36 33
37 36
38 41
39 47
40 50
41 56
42 59
43 66
44 68
45 74
46 65
47 97
48 97

Ok, I think you’ll like this one.

I figured the weighted career WAR per game (career through age 29) for pitchers at each age.  (Weighted by IP at that age.)

This tells us what we EXPECTED to have as a WAR for a pitcher, if aging was not an issue. 

Next to it is the OBSERVED WAR per game at that age.

So, if the observed is lower, then we know pitcher is in decline.

Age WAR29 WAR_per_Game diff
16 0.011 -0.474 -0.485
17 -0.015 -0.074 -0.059
18 0.017 -0.039 -0.056
19 0.076 0.034 -0.042

20 0.080 0.058 -0.022
21 0.070 0.073 0.003
22 0.068 0.064 -0.004

23 0.066 0.070 0.004
24 0.068 0.070 0.002
25 0.069 0.072 0.003
26 0.072 0.076 0.004
27 0.074 0.076 0.002

28 0.081 0.077 -0.004
29 0.090 0.081 -0.009
30 0.090 0.087 -0.003
31 0.091 0.086 -0.005
32 0.092 0.085 -0.007

33 0.095 0.083 -0.012
34 0.098 0.090 -0.008
35 0.102 0.085 -0.017
36 0.104 0.094 -0.010

37 0.110 0.091 -0.019
38 0.112 0.096 -0.016
39 0.116 0.090 -0.026
40 0.124 0.086 -0.038
41 0.133 0.088 -0.045
42 0.128 0.068 -0.060

43 0.122 0.065 -0.057
44 0.117 0.077 -0.040
45 0.119 0.086 -0.033
46 0.109 0.003 -0.106
47 0.149 0.030 -0.119
48 0.149 -0.026 -0.175

Nice right?  So from age 23 to 27, pitchers performed slightly above expectation, and by the same amount.  If you smooth it out, this sets the peak at age 26.

Tango:  I actually think your WAR/game data nicely confirms my theory.  The talent difference between age 23 and age 27 is large enough to explain all of the apparent performance gain in your original table.  (WAR/game is a better measure than career WAR, because pitchers whose MLB careers start at younger ages—part of which is luck—will have more opportunity to boost their career total).

Regarding your difference column you say “if the observed is lower, then we know pitcher is in decline.” But these arent’ y-t-y deltas—the difference tells you how well the player performed compared to his career mean.  So your data actually shows that pitchers on average are as good at 23 as they ever will be (+.004). Then they stay at that same level (relative to career mean) thru age 27, and decline after that. 

A question on starting vs. relief roles:  does Rally set an appropriately higher replacement level for relief innings in his WAR calculations?  I assume he does, but don’t know where his methodology is posted.  If not, then these numbers will tend to overstate performance as players age.

So MGL says “pitchers get worse every year,” and Tango says “In no way is the peak age of a pitcher anything less than 27.”

Are we just going to leave it there?

How about:

the .600 pitchers peak at age 29

the .550 pitchers peak at age 28

the .500 pitchers peak at age 27

the .450 pitchers peak at age 26

the .400 pitchers peak at age 25

the .350 pitchers peak at age 24 (avg AAA pitcher)

the .300 pitchers peak at age 23 (Avg AA pitcher)

the .250 pitchers peak at age 22 (avg A pitcher)

the .200 pitchers peak at age 21 (avg college pitcher)

And depending what kind of pitchers are in your sample, you’ll get different kinds of peaks.

(All numbers for illustration purposes only.)

The pitchers who “peak” earlier may not be peaking; they just get cut because they are not good enough to keep playing. A .250/22 player might be .330 at 27, but he wont be in baseball

How about this: pitchers would peak at a high age, like 28, except that they get hurt. Any specific pitcher might be expected to decline from age 24 to age 25, but the top single-season performances will come from 28-year-old pitchers.

I searched for all pitcher-seasons from 1961 to 2009 with at least 200 IP and 150 ERA+. (I would have used WAR except that I didn’t want my data set dominated by 1970s-era pitchers.) There are 162 such seasons, ranging from Dwight Gooden’s 1985 (age 20) to Roger Clemens’s 2005 (age 42). Here are the number that occurred at each age:

Age Count
20 1
21 2
22 4
23 10
24 12
25 15
26 18
27 20
28 16
29 14
30 5
31 11
32 9
33 6
34 3
35 7
36 2
37 3
38 2
39 0
40 1
41 0
42 1

The mode is at age 27. The median is between ages 27 and 28: 82 of the 162 seasons occur during ages 20-27, and 80 of the seasons occur during ages 28-42. The mean is at age 28.2.

The “injury-free peak age” might still be higher, like 29 or 30, but I think we can say with confidence that it’s no lower than 27.

"So MGL says “pitchers get worse every year,” and Tango says “In no way is the peak age of a pitcher anything less than 27.”

Are we just going to leave it there?”

That’s a good question.  I am thoroughly confused.  And no one has answered this question yet:

If all I told you was that we have a pitcher who was a true 4.00 RA pitcher at age 26 in the major leagues.  IOW, he pitched at age 26 in the majors and that is all you know.  Will his projected true RA going into his 27th year, whether he ends up pitching or not in the majors (or maybe there are two different answers - one, if he does pitch at age 27 and one if he doesn’t pitch), be more than or less than 4.00? The results of the delta method say that it will be worse.  That is easy to figure out.  There is only one correct answer of course for that question.

"does Rally set an appropriately higher replacement level for relief innings in his WAR calculations?”

Yes.  I think I have starting replacement level at 20% higher than average, relief at 5% higher.

Tango’s conclusion clearly conflicts with MGL’s findings.  But I don’t think Tango’s DATA conflicts with it—they actually tell the same story.  MGL reported:  “linear weights against is flat until age 26...and then a sharp, almost linear curve downward to the tune of around .2 runs a year.” Now look at Tango’s WAR/game data in post 25:  it shows players performing below their career rate through age 22 (suggesting they are improving in these years), then a flat performance from 23-27—above the career mean --and then a decline after that.  Tango’s decline is more gentle, but his data includes a big survivor bias so we expect it to show slower decline than the delta method.  The stories are identical.

The reason Tango’s original data suggested a peak of 27 is that the overall talent level rises steadily after age 23.  In the 20s, weaker pitchers get screened out each year, and this Darwinian process improves the gene pool each year.  And after age 27, the aging curve starts driving weaker players below replacement level, so the survivors are better players and the talent level continues to rise. 

It would be interesting to see if hitters follow the same pattern:  good players at ages 18-21 (because only good players make it that young), then a weak talent pool from 22-25, then steadily better every successive year.  I’ll bet it’s similar.

Another point:  if peak age is 27, that is when the career WAR/game should be at its lowest rate.  Peak age is when the weakest players are—briefly—good enough to play in MLB.  Every other age should have a higher average talent level.  But 27-yr-olds are better, not worse, than younger pitchers in terms of career talent.

When does career talent hit its lowest level?  Age 23!  This is also the age at which pitchers most overperform their career rate (tied with age 26).

Thanks, Rally.  BTW, is there a place where you explain your full methodology?  Would be nice to have that (or a link) on your site.

"if peak age is 27, that is when the career WAR/game should be at its lowest rate. “

Career WAR/game is lowest at age 16-20.  And it’s easy enough to see why.

That’s not right.  It’s low at 16-18, then much higher at 19-20, and declines thru age 23.  And I think we can all agree the age 16-18 MLB data won’t tell us much useful, if only because your total sample is <700 IP.  The talent level clearly hits a low point at age 23, which makes complete sense:  most pitchers are about as good as they’re ever going to be, so teams may as well find out if they can succeed in MLB.  Further delays just risks injury and loss of value to the team.

Age WAR29 WAR_per_Game diff
16 0.011 -0.474 -0.485
17 -0.015 -0.074 -0.059
18 0.017 -0.039 -0.056

19 0.076 0.034 -0.042
20 0.080 0.058 -0.022

21 0.070 0.073 0.003
22 0.068 0.064 -0.004
23 0.066 0.070 0.004

Major league teams do not debut 23 yearolds because they think they are as good as they are going to be; they debut them because they think they are ready. They might be wrong.

If they have to be at 4.50 ra to make the ml, they will pitch them then, but if they are 23 with a 4.50, they assume they will get better.
They might be wrong.

You don’t think someone is going to be as good as they are going to be when they first try something; you think they will improve.
They might be wrong.

1st season with 20 ip, 19801-1999

age #

19 4
20 20
21 63
22 121
23 165
24 155
25 147
26 100
27 72
28 20
29 13
30 9
31 + 4

893

dq:  I’m not sure what you’re quarreling with. I made no claims about what teams THOUGHT, only that most pitchers will in fact be at or close to their peak by 23.  So it makes sense to give a chance to those who seem to have the potential for MLB success.  And if you haven’t made it by age 26, teams seem to recognize, you probably won’t ever make it.  (If peak were 27, there would be a lot of guys still improving at ages 28 and 29—but that seems to be rather rare).  The result is that the pitcher talent pool is weaker from ages 22-25 than at other ages.

Your data is perfectly consistent with my argument. Teams give “tryouts” to lots of pitchers aged 22-25.  Many of these pitchers will not succeed, and are screened out of MLB.  That leaves a superior pool of pitchers at age 27, because by that age very few rookies are getting a tryout, which in turn creates the illusion of a later peak age.

The effect Guy talks about is likely part of what is going on, but I don’t think the discrepancy can be explained away just by weaker pitchers being weeded out in their early- to mid-twenties.  There are also a lot of pitchers who were not in the Majors in their early 20s who do enter the majors later, presumably because they got better and became good enough to pitch at 27, so it’s not just weaker pitchers dropping out of the sample leaving the older groups of pitchers as the best crop of talent from the previous samples.  Tom has pitchers at 27 throwing over twice as many innings as pitchers at 23 in the original post, so the new pitchers coming into the sample at later ages are probably having just as large an effect as the ones dropping out after being auditioned at a young age.  It would also only make sense for that many extra innings to come from age 27 if there are a lot of pitchers who are legitimately improving, so that discrepancy still exists too; how are there enough pitchers improving up to 27 to give that age the most innings and WAR if we know that pitchers who are already in the Majors, as a group, don’t improve through their mid-20s?

It could be that pitchers just have a wide variety of aging curves, where some peak in their early 20s and some in their late 20s, and that the pre-peak curve is steep enough that pitchers who peak later are simply not good enough pre-peak to compete with the pitchers who peak earlier.  In other words, someone who has a natural peak at 27 is unlikely to be good enough to compete for a Major League spot at 23 or even 25 or 26 because, a year or more prior to his peak, he is still far enough below peak level that he can’t compete with pitchers of comparable skill who have already peaked.  If that’s true, then it could simply be that anyone who is in the Majors by his early- or mid-20s is likely to be that good because he is in the group of early-peakers.  There could also be a bias in MLB for selecting pitchers who peaked early and are on the downslope than a comparable pitcher that is peaking at 27.  If you have two pitchers who are the same age and have the same true talent, but one peaked early and is on the decline and the other has yet to peak and is on the rise, teams will probably tend to pick the former because he has a better track record and has ML experience.  Say that both pitchers are 4.00 ERA pitchers at 25, and that in 2 years, the first will decline to 4.2 and the second will peak at 3.7 (and break into the Majors).  By looking at only the pitcher who was already in the Majors, you see a decline, but overall, you get more innings pitched and a better avergae production between the two pitchers combined at 27 than at 25.

When you ask MGL’s question (given that a player was in the Majors at 26, is his true-talent more likely to go up or down at 27?), that means that because you know he both was at a high enough level and had a strong enough track record to be in the Majors at 26, it’s more likely that he is in the group of pitchers who has peaked early than in the group that peaks later.  If he hasn’t yet peaked, he’s more likely to either not be at a high enough level to pitch in the Majors yet or to not have a good enough track record to be chosen for the Majors over comparable pitchers who are now on the decline.

As for 23 year olds having the lowest average career production, that doesn’t have to mean more pitchers are peaking then.  It could be that pitchers who peak at 23 are simply not weeded out as quickly as pitchers who peak later.  Like dq says, teams think that pitchers will improve from 23, so when they decline, they are kept in the Majors longer than if they would have broken in at 26 or 27 and then declined from there.  When someone peaks at 27 and comes into the Majors and then declines, that’s what teams expect, and those players are not allowed to pitch as they approach or pass replacement level.  As a result, you end up with pitchers who pitched at 23 having poor career production because they peaked early and were kept around to decline a lot further, and that’s why they end up with lower career production as a group.

The larger number of innings at 27 doesn’t have to mean pitchers improved (though it could).  If MLB auditions a new set of pitchers at each age 22 thru 25, and keeps the best from each cohort, then you can end up with a larger number of 27-yr-olds.  Plus, a lot of the 27-yr-olds were in MLB at 23, but threw many fewer innings. 

We can only assume the 27-yr-olds improved IF teams do a highly efficient job of talent evaluation.  But we know projecting pitchers is difficult.  When a pitcher arrives in the bigs at 25 or 26 and pitches reasonably well, I don’t think we can assume he was significantly worse at 23.  It may be that he was unlucky at 23, or injured, or pitching in a hitters’ park in AA, or something else.  It may just have taken time for his talent to be identified—it’s not like teams have unlimited opportunities to offer MLB playing time to young pitchers in their system.  In any case, to answer this you would have to look at minor league stats, and try to demonstrate that pitchers who establish themselves at 26 or 27 were clearly worse when they were in the minors.  Tango’s and MGL’s data both show pretty clearly that pitchers already in the majors at 23 are not any better at 27 (on average, of course).

dq:  It would be interesting to compare the quality of each “incoming class” you identify.  Do you have the ability to report the WAR/Game or OPS+ (or any good career rate stat) for each age group?  It could be that the guys arriving at 25 and 26 are actually better than those arriving at 22-24, which would be interesting.

For 27 year olds to maintain a higher average production while throwing more than twice as many innings as 23 year olds without at least some of that population legitimately improving (as opposed to getting lucky or whatever other reason), teams would have to be Royally screwing up (i.e. Dayton Moore is running every team).  That goes both for pitchers to be stuck in the minors throughout their mid-twenties getting worse every year for several years before finally getting called up at 26 or 27 and still being better than the pitchers who debuted earlier, and for pitchers in the Majors at 23 to get worse every year and still be given way more innings at 27 if those are both big enough issues to throw the results of Tango’s analyses off by that much.  There probably is some inefficiency in how teams identify pitching talent, but probably not so much that by inefficiency alone (or maybe even by primarily inefficiency) they are so frequently leaving pitchers in the minors for years after they peak before calling them up that by age 27 there are over double the IP that are given to pitchers at their true peaks.  And if that were the case, then they would likely not be getting better average production from the 27 year olds.

If it’s true that a lot of bad pitchers are given chances at a young age and then weeded out (or pitchers who are only good enough to pitch for a short time at their peaks), and that the pitchers who debut later actually peaked at the same time as the pitchers who debuted early and then got weeded out, then that would create another issue.  If the pitchers debuting later don’t age any differently as a group than the ones who got weeded out after a young debut, then either they were better than the group of pitchers who got called up earlier all along (which makes no sense-surely some of the pitchers from the late-debut group were better than some of the pitchers from the early-debut group at a young age and were simply unlucky or mis-identified or whatever, but for that to be true of the group as a whole makes no sense), or they are even worse now than the pitchers they are replacing who got weeded out.  In which case, the age 27 pitchers are not going to have better average production, unless all of the pitchers who were not weeded out are tripling their innings or something like that.  It just doesn’t make sense for a discrepancy that large between the innings at 23 and 27, along with better average production from age 27 pitchers, to occur if everyone is peaking at 23.  There almost has to be some significant portion of the population of pitchers at 27 whose true talent improved from 23, even if it turns out that that segment of the population was mostly not in the Majors before they hit their peak.

I don’t know if it is actually true that teams try out pitchers from ages 22-25 and them weed them out quickly, and that there aren’t as many short-career pitchers debuting after that.  There number of pitchers with 3 or fewer seasons of at least 20 IP is highest for pitchers whose first 20 IP season came at age 26 (at least for pitchers who debuted between 1960 and 2000), even though there are more pitchers debuting at younger ages.  The following table gives the number of pitchers who had 3 or fewer (and 2 or fewer, and just 1) seasons of at least 20 IP, grouped by the age of their first season throwing at least 20 IP (debut between 1960 and 2000):

http://spreadsheets.google.com/pub?key=tLRkGHUumeJ7gylk8YboNjA&output=html

That’s without accounting for there being more pitchers who debut at a younger age, so the percentage of pitchers who are weeded out quickly after debuting at 26 or 27 will be higher than just showing the total number of pitchers would indicate.  Pitchers who debut at 26 or 27 are more likely to be out of the Majors quickly than pitchers who debut at 22-25 by enough that, despite there being fewer overall pitchers debuting at 26-27, there are just as many of those pitchers who are short career pitchers.  Based off that table, I would put the ages where short-career pitchers are entering the league the most at either 23-27 or 24-27 rather than 22-25.

Kincaid:  MGL did not claim that pitchers peaked at 23.  He said they were “flat” until age 26.  Tango’s data suggests they perform similarly until 27.  So we’re basically talking about a plateau from roughly 23-27.  And of course that’s an average—no one would dispute that SOME pitchers improve over those ages (while others are declining). 

So this does not require any massive inefficiency on the part of decision-makers.  Keep in mind how small these talent differences are:  the performance difference between 23 and 27 is .06 runs/game!  And think about the distribution of talent:  after a relatively small number of clearly-talented pitchers, you have a huge fog of pitchers who may or may not succeed in the majors, with true talent somewhere between -1 and +2 WAR.  So teams give them a try, some succeed, and some fail.  It doesn’t seem surprising that the talent level of the survivors in every cohort is a little bit higher with each successive age. 

What this may show is that teams are still too slow to give innings to 23-yr-old pitchers.  But not necessarily.  Giving them innings requires you to take innings away from older guys who have a track record in the majors. and taking a gamble.  If there was a way to have every 22-yr-old throw 1,000 innings against MLB hitters and measure the results, my guess is 23 yr-olds would log nearly as many innings as 27-yr-olds.

Your data seems entirely consistent with the idea that short-career pitchers throw most of their innings before age 27.  But if you don’t think that’s true, why do you think younger pitchers have a lower career talent level?

mgl said,

“All pitchers from around age 21 to 26 are completely flat in runs allowed (against linear weights against).  After that, they simply skyrocket in a nice smooth pattern to the tune of around .2 runs per 9 innings per year. “

So, that says that (on average) pitchers are as good as they are going to get at age 21. It is a pretty long peak, around 5 years.

At this point, I dont have much to add to what 42/Kincaid said. Ill try playing around and see what I get.

I am in agreement with the last few comments.

Let me remind that when I did a basic delta including minor leaguers (no MLEs, just same team in consecutive years) I found a fairly flat wOBA allowed for 22-26, but not as flat as MLB alone. At all levels of the minor leagues the first season of decline was 24.

I duplicated MGL’s observation that MLB pitchers declined at every age, but I still believe this is because at age 23 and before fewer than 5% of professional pitchers are in MLB, and many of those likely because they had an above average performance which then regressed towards the mean the following year. To reduce the bias in the selective sample of young major leaguers, one could use multi year projections at each age (necessitating MLEs) compared to the following season.

This is probably my all-time favorite research:

http://www.insidethebook.com/ee/index.php/site/comments/true_aging_patterns/

Where I conclude in post 24:

So, I think I’m reasonably confident in saying that between 1954-2008, that the peak age for hitters and for pitchers is 27, and that this can be verified by looking at all samples of data (totalling 500,000 PA) by matching in back-to-back years on the identity of the pitcher, batter, park, role, and that they each faced each other under those conditions at least 4 times in each year.

I also point to a possible .003 wOBA familiarity factor that the batter gains in seeing the same pitcher.  So, a possible reason the pitcher appears to “age” is that he’s not aging… the batter simply has a performance advantage in seeing him more.  It’s like when a pitcher “ages” during a game.

Reconciling mgl and Tango:

Okay, I took all the pitchers that started in 1970 or later and did not pitch in 2008. I then grouped them by age, and computed ERA+ (using the “new”
method, which is not used in Baseball Reference yet).

All Pitchers, starting 1970+, ended by 2008:

BRef
Age ip era+
a18 116 53.81
a19 1,035 96.84
a20 4,943 102.03
a21 18,271 96.68
a22 38,650 94.44
a23 65,986 95.56
a24 89,826 95.85
a25 107,809 97.57
a26 111,182 99.26
a27 104,476 98.27
a28 95,781 99.60
a29 83,521 101.05
a30 71,225 102.00
a31 60,954 101.41
a32 51,222 101.89
a33 39,852 101.63
a34 31,628 99.59
a35 23,920 99.62
a36 18,425 105.16
a37 12,418 100.54
a38 8,071 99.98
a39 6,295 100.67
a40 4,329 104.08
a41 2,830 100.60
a42 1,792 99.98
a43 834 98.57
a44 464 88.81
a45 231 103.43
a46 148 67.58

Which would show a slight rise in overall performance thru age 30. Additionally, I looked at the players debuting each year, and came up with an
overall ERA+ for a 1st year player of 91.23 (take note Marcel), done by age as:

Debut
Age ip era+
a18 116 53.81
a19 840 103.50
a20 3,012 94.89
a21 10,369 92.12
a22 16,128 91.20
a23 20,079 89.16
a24 17,153 89.81
a25 13,542 91.73
a26 9,250 90.98
a27 6,560 92.28
a28 2,357 92.59
a29 1,874 101.99
a30 967 87.31
a31 125 56.64
a32 403 129.28
a33 189 94.40
a34 6 45.00
a35 93 134.76
a36 106 74.73
a37 20 36.07
a38 3 na
a39 21 na
a40 1 na
a41 3 99.45

103,219 91.23

The 32 year-old group has some foreign pitchers, the real old groups include fielders like Wade Boggs pitching.

So, the average by age increases from 22-26 with increasing innings, yet the average new pitcher is only a 91.23.

Why?

Survivor.

The players who return average a 102.39 ERA+ that year, while the guys who don’t pitch the following year are a 74.20.
So, the 74.20s get replaced by 91.23s. And the 102.39 do show a slight decrease, going 99.98

Guys Returning:

Year Year + 1 Improve?

a19 102.73 113.17 1.102
a20 109.63 102.66 0.936
a21 100.48 96.76 0.963
a22 97.45 98.36 1.009
a23 98.28 97.27 0.990
a24 99.19 98.41 0.992
a25 100.47 100.01 0.995
a26 102.35 98.68 0.964
a27 101.51 99.78 0.983
a28 102.98 101.03 0.981
a29 104.07 102.20 0.982
a30 104.85 101.50 0.968
a31 105.27 101.68 0.966
a32 105.05 101.66 0.968
a33 104.91 99.59 0.949
a34 102.56 99.49 0.970
a35 104.40 105.34 1.009
a36 110.20 100.64 0.913
a37 105.27 100.10 0.951
a38 105.06 101.05 0.962
a39 107.47 104.13 0.969

Average 102.39 99.98 ,976

Non Returnees

ip era+

a19 129 55.54
a20 700 56.02
a21 2,083 67.11
a22 4,301 70.41
a23 6,099 68.85
a24 8,716 64.73
a25 11,731 73.83
a26 12,294 74.38
a27 10,437 69.09
a28 11,363 74.54
a29 9,317 76.99
a30 7,377 77.32
a31 7,075 71.96
a32 5,964 77.92
a33 5,341 80.45
a34 4,495 81.64
a35 4,186 77.13
a36 3,268 81.80
a37 2,468 81.48
a38 1,824 82.61
a39 1,731 82.74
a40 798 81.47

So, at age 24 players perform at 95.85; 24 year-olds who average 64,73 don’t pitch the next year. Guys who debut at 25 average 91.73. GUys who return went
99.19 at age 24, they go 98,41 at age 25. Since the new guys do much better than the dropouts, the overall group of 25 year-olds do better than the
24 year-olds.

This is largely because the guys who do poorly get thrown out, and they get replaced by a new group. The new group is still below the overall average,
but they do much better than the guys who were let go