THE BOOK--Playing The Percentages In Baseball

These are the sorts of things that lead me to the theory that pitchers should be pushed fast through the minors. Given the fact that throwing overhand is an unnatural motion, I feel there’s a limited number of pitches a typical pitcher has in their arm/elbow/shoulder. Add in that there is little (or no) evidence that supports that they get substantially better—like hitters—through their 20’s, and I have no problem with people like the Reds pushing Mike Leake into the rotation without the minors (if they feel he’s mentally ready, then they’re probably the best ones to judge. I think I would’ve gone at least half a year in Double or Triple-A).

Teams should look for mental preparedness the most because pitchers are pretty maxed out physically (in my, untrained opinion) pretty early in their 20’s. Like, 20 or 21 or 22.

The attrition rate and little evidence that they get better with age means push them quickly through the minors, let them pitch at their ‘peak’ for you, and ship them off before their big free agent deal. Or after a team-friendly deal that buys up their first year or two of arbitration. Like the A’s did with Hudson/Mulder/Zito, essentially.

There has got to be some chance though that pitchers improve in the minors mentally and then when they get to the majors, the physical decline outweighs any more mental improvement there might be.

Let’s say that that pitchers decline .1 run per year physically but that they improve .1 per year mentally while in the minors and then .05 per year the first 3 years in the majors.  So there is no decline in the minors and then we see small decline in the majors for the first 3 years and then a larger decline after that.  So bringing up a pitcher earlier won’t help.

Plus, I found more of a stagnation until age 25 or 26, and that is in the majors only, which suggests that with a young pitchers who you feel is not ready mentally, it might be worth it to leave him in the minors as you are not risking much in terms of his physical decline.

For a pitcher who is already 25 or 26, it might not behoove a team to leave him in the minors for very long.

Now, some people might say that MLB teams know what they are doing and they might be right.  But, if a person or organization is fundamentally wrong about something or is not privy to an important piece of information, then it is entirely possible that they are doing something wrong.  I doubt that many (if any) baseball people will acknowledge that pitchers uniformly get worse with age.  They ALL think that young pitchers get better with age.

The best counterexample I could think of is Randy Johnson. His velocity was there when he was in the minors and he started to have better control after age 29, then he had another climax in age 35-38.

And we kept hearing the statement that young wild throwers could learn to control their fastball and become better pitchers. Maybe young pitchers with high K/9 and BB/9 could have some chances to age better? My two cents.

I like the mental/physical theory.  Evidence for or against has got to be somewhere in the data, no?

1.  Why are there no 18-year-old pitchers in the major leagues?  What skill are they missing to make them successful?  If you asked a scout, what would he say?

2.  How hard to 18-year-olds throw?  That’s just a radar gun reading.  Is there any PitchF/X-like data for young college pitchers, or high school pitchers of any sort?

And related to the mental/physical theory ... maybe pitchers do have a curve, but it’s so very, very steep on the way up that the transition from not ready to ready takes only a season, or even less.  Then the reason 22-year-old pitchers appear to decline is severe selection bias: the ones who improve from 21 to 22 are so far off the radar at 21 they’ll never make any study of this sort.

What if you look *backwards* instead of forwards?  Subtract every pitcher’s age from 54 so that his career runs the other way.  You’d definitely find a decline at 31 or so, if you correct for survivor bias, as pitchers “collapse” from decent to out of MLB. 

Doesn’t the fact that pitchers are not in MLB at 17, but in MLB at 24, show that there’s an improvement between those years, and that if you don’t find it, it’s just because of selection bias?  I mean, GMs aren’t so stupid that they won’t play a superstar Gooden-like teenager just because he’s only 18.

"Doesn’t the fact that pitchers are not in MLB at 17, but in MLB at 24, show that there’s an improvement between those years, and that if you don’t find it, it’s just because of selection bias?”

First of all, I find the curve (for lwts against, essentially RA) from 21 to 25 to be dead flat, so it is not unreasonable to think that from 18 to 21 pitchers improve.

There are two complications with pitchers:

1. start/relief: it’s a 1-run difference, which will overwhelm the 0.1 run difference you are going to find in year-to-year differences in real aging; you have to do SOMETHING about start/relief: I use the “rule of 17”, which means that pitchers get 17% more K per PA as relievers, allow 17% more HR as starters, improve by .017 BABIP points in relief, and are flat in walks

But, you have to do something.

2. DH and/or league changes.  Again, a big difference. 

***

Without any adjustments, here was my article from a few years ago:

http://www.tangotiger.net/adjacentPitching.html

You might find young pitchers improving if you looked at MLE’s of minor leaguers.  But since the MLEs themselves are an uncertain estimate, any study will be very shaky.  Pitchers who stay at the same level 2 years in a row most likely were pretty bad in year 1, so selective sampling rears it’s ugly head.

Interesting.  Sample size is probably prohibitive, but I would be curious as to the results for converted position players.  As a group, they should log fewer professional innings prior to physical maturity.

I really think this information is of some importance, and says something vital that all of us are missing in some fundamental way.  Does it say something about the entire training methodology employed by most MLB teams for young pitchers?  How far back is the data set going, MGL?  There may only be so much a human can be capable of with overhand pitching, and we may have reached those limits.  If I was an executive seeing this data, I might be tempted to push pitching prospects much faster than has become accepted wisdom.

Even at the professional level, many instructors approach pitching as more art than science.  Hitting instruction is light-years beyond what it was thirty years ago, which I think has been partially responsible for the increase in offense.

"Hitting instruction is light-years beyond what it was thirty years ago, which I think has been partially responsible for the increase in offense.”

I’ll tell you what’s scary, is the credit given to the guy who worked with Zobrist and then Jason Bartlett.  It’s possible that they are just coincidences and are examples of late bloomers or flukes, but if better instruction can really turn light hitting infielders into Chase Utley and Derek Jeter I fear for the pitchers once his theories catch on.

I don’t think it’s all that surprising that pitchers *as a population* get worse from 22+. But that doesn’t mean that *some* pitchers can’t get better over time.

I see it as a race of skills versus injuries and age-decline. Skill-wise, a typical pitcher *is* getting better from 22-26 - enough to offset the degradation from injuries. But you can only milk that so much, and then you see a decline that only gets worse as the pitcher starts to decline from simple aging.

Just speculating here, but a super tall pitcher like Randy Johnson may have an advantage. No matter how old he gets as a baseball player he’s still 6-10 (or close to it). It’s a plus-plus tool he has that’s age-proof.

This is truly one of the things in baseball we understand the least (as opposed to the myriad things that Bill James says we don’t understand).

I believe that for younger (pre-peak) pitchers you need to look at minor league numbers, as the small percentage of players at those ages who are in MLB biases the sample. I don’t have the numbers handy for pitchers, but only 1% of age 21 batters and 5% at age 22 are in MLB. These are likely the elite players, early bloomers or those with an outlier season. If you are looking at only MLB in the younger years, it is possible that regression to the mean is outweighing any growth for those players.

To determine the aging curve I used or Oliver I used the delta method of matched pairs for any player on the same team in consecutive years, weighted by smallest PA of BF (no minimum), regardless of league or level. I realize, as Rally stated in #7, that year 2 could show upward regression to the mean as the player repeating might correlate with a below average performance in year 1. So yes, I found growth up to age 24, but decline after that, and pitchers peaked at the same age as batters.

Pitchers allowed the fewest base hits and HRs at 23, fewest BB at 25 and most SO at 25. For the anti-Dips folks, I showed an decrease in BABIP every year to 23, then an increase in every year after.

MGL, I sent you a spreadsheet of my results in Jan 2010.

If someone can tell me how to insert an image here, I will post a graph of the component curves.

Matt Lentzer/11: I think being 6’10 is actually a hindrance and part of the reason he struggled with control. I can’t remember exactly where, but I recall him saying something to the effect that being so damn tall lead to him never really knowing how to coordinate his body properly to get consistent release points (as consistent as pitchers get, anyways), or know where his heater was going. I think he said something also to the effect that being tall is good as a pitcher, only to a certain point.

I wonder if there’s something to that or not. I don’t know and I possibly/probably am not remembering the quotes properly. Don’t know where they came from, either.

Also, can anyone point me to other studies on this?

Brian, can you resend that spreadsheet to me?

I don’t see how selection bias is a huge factor for younger players.  You get promoted to the majors after a lucky season in the minors, but that does not factor into my aging curves since I am not looking at the minor league data.  Of course if you are a young player and you get more than one season in MLB, it is likely you got a little lucky in your first year, but, that is the case for all years and for all players (hence, the survivor bias) PLUS I am trying to control for survivor bias by inserting that “phantom” year.  So for all the young players who never got a second year (or came up again 2 or 3 years later), I am inserting that “phantom” second year anyway, which should show an improvement on the average, thus negating some or most of the effects of survivor bias.

I agree that pitchers (and hitters) who make it to the majors at a young age are likely to be early bloomers, but if we going to use these aging curves for forecasting MLB players and for decisions at the major league level, then we WANT to use whatever aging curves apply to players that are IN the major leagues!  So we WANT to include this selection bias in our aging curves.

We don’t, of course, necessarily want to apply those aging patterns to players still in the minors.  But, for them, as Brian does/did, you can construct aging curves for players in the minors.  I would agree that they would probably be shifted more to the left, as these players would tend to be late bloomers (that is why they are still in the minors). 

But, I would be skeptical about crossing over from the minors to the majors in constructing the aging curves, Brain.  For one thing, you are mixing late bloomers and early bloomers (which may be fine actually).  For another thing, our MLE’s may be too biased (and certainly not that accurate, especially for pitchers), since they are based on players who have played in the major and minor leagues already, and in some sense already include aging (or at least it is hard to tease the aging out) to be used effectively when trying to infer subtle and small aging changes. 

I feel much comfortable doing aging curves separately for the minors and majors and then see if I can figure out how they relate.

Brian:

“So yes, I found growth up to age 24, but decline after that, and pitchers peaked at the same age as batters.”

That does not make sense. You say that pitchers start to decline after age 24 and then you say that pitchers have the same peak age as hitters.  How can those two statements be reconciled?  Hitters don’t start to decline after age 24.

One thing that might help with the pitcher curves is some kind of TBF minimum.  Certainly pitching curves are greatly affected by those pitchers who get hurt, pitch horribly for a short while (or a long while) and then are put on the DL.  If you knew that a pitcher was healthy from one year to the next, it might drastically change the aging curve.  But again, you have huge selective sampling issues when you try and use min PA or TBF, as we find with batters.  If you use large min PA with batters for aging curves, you find that almost no one declines with age, at least until 30 or 31.  A big part of getting lots of PA or TBF is simply pitching or hitting well, whether you are healthy or not, and playing “well” means getting lucky, for our purposes at least…

MGL—Why not combine with Mike Fast and Jeremy Greenhouse are show with pitch speed and get an aging curve on fast ball speed.  Maybe it stays constant for until 26 when injuries start catching up.

What is the problem with the idea that pitchers peak early?  The tone of the discussion is, “hey, that can’t be right!” Why can’t it be right?

What’s wrong with this simple model: physical skills peak at (say) 19, and mental skills improve steeply until they peak at (say) age 24, at which point they stay at the high plateau forever. 

The sum of a pitcher’s effectiveness is Physical+Mental.  The exact peak ages for both vary by pitcher, with (as mentioned) means at 19 and 24, respectively.

Why can’t that model be approximately true?

I don’t think that anyone here is strongly questioning that model.  Most traditional baseball people would tell you that you were crazy, though, and that is a little bit of a hard nut to crack. 

If a pitcher enters the majors at age 24 and has an average season (I say that to put regression aside), is there any manager, coach, player, commentator, or writer alive who doesn’t think that he is likely to improve with more “seasoning?” I think not…

IOW, we have had it drilled into our heads that a young pitcher, even one that is 25 or 26, learns a lot in the major leagues and needs 2 or 3 years experience in the majors to reach his potential, etc., etc., etc.  And no one (in a traditional context) thinks that a 25 or 26 year old pitcher is past his physical prime.  And all of that seems to make intuitive sense.  And of course, the pundits and experts can point to many, many pitchers for whom that is true.  Of course for maybe 25-40% of all pitchers that WILL be true, so you would have a large sample to choose from in order to prove your point about pitchers needing age and experience to mature and reach their potential…

Different players peak at different ages. Some peak early, some late. The average for all professional players, batters and pitchers, appears by my study to be at 24. When looking at MLB only or even Japan only, it’s about 27. There are two parts to a peak, when and how high. If we have two players starting at the same point, with Player A peaking at 24 but player B continue to improve to 27, then B will have a higher peak and thus is more likely to be in MLB. Guys who have successful careers lasting 10 or more years qualify for JC’s study and show a peak near 30.

Different skills age differently. Physical traits such as speed peaks the earliest, perhaps 20 or 21, with power around 27. Walks and strikeouts are the latest peaking for batters and pitchers, as perhaps their mental skills can outweigh their declining physical skills for a few years.

The age with the most PAs and BFs is also 24. I think what happens is that if a guy is not MLB quality at 24 management knows the odds are against him at 25 or later (save some like Garrett Jones), and players start getting released at a higher and higher rate.

Cuba has an interesting league with a wide variety of skill level, from college to MLB equivalent, and where it is very difficult to advance out of the league. Basically, you have major and linor league quality players in the same league year after year. I have the batting for the past five seasons, and ages for 75-80% of the players. I’m at the point where I can do an age study of the batters, and hopefully can have results by tomorrow evening.

Mike Rogers/14

I’m sure being so tall had its challenges for Randy, but I think it is more accurate to look at it as a tool to be mastered than as a handicap. Guys with lots of movement on their pitches tend to have control problems as well. Being tall or having lots of movement is being projectable or having upside.

Being tall means your stride is longer and you release the ball closer to the plate. Just a few inches makes a big difference. 3” = 1 mph IIRC. Your release point is also higher which makes the ball harder to pick up for the batter. You also have a mechanical advantage pitching with a longer arm which means less wear and tear on your shoulder. 

There’s many good reasons why the pitcher is usually the tallest guy on the field.

MGL:

It’s a fascinating subject.

I’ll take a stab at it if someone can point me in the direction of a competition matrix.  Pitchers x Batters x Ballpark would be a start.  Handedness is available everywhere. 

Going by Tango’s remark above, it looks like I’ll need to know which innings were pitched in relief as well, unless they are explained by the three simple competition effects already mentioned.  I don’t want to make the model too complicated, but is there anything else of extreme importance that would need to be added?

Mike Rogers:

This is for batting, but to my mind the seminal work on the subject is Jim Albert’s study here.

The reasoning is clear and the model is explicit.  As is the execution.

Also he produces career trajectories for a number of players.  The objection will be that he has only used players with 5000PA.  The correction will be to only use those players who were established as star players by age 28, this by some objective measure.

From there you could get the trajectories for all the players that met the criteria from Jim himself.  You would have a real sense of how these guys aged, and how different types of players age differently by different measures of performance.

From there we could ask some physiologists if there is a reason that especially gifted athletes should peak at a later age, or sustain their abilities longer.  Does the phenomenon exist in other sports?  Specifically in other sports that are less riddled with context and censorship bias issues.

I mean before any of us looked at this in a mathy way, would it have been intuitively obvious to anyone that great players should peak at a later age?  It wasn’t to me.

I wonder how much of this has to do with the fact that the pitchers 29+ could be multiple year veterans. I imagine that hitters could improve after multiple attempts with the same pitcher.

MGL

I loved your articles on age effects and MLB batters, the ones posted at The Hardball Times around Christmas.

I am struggling to understand the treatment of survivor bias, though.  With your model you would appear to be culling mainly the shorter trees from the forest, no?  So we would expect the distribution of the remaining trees to be taller, and with fewer runt trees (smaller left tail).  That doesn’t happen, not even a bit.  Granted that was with a few crude checks, I didn’t do a rigorous analysis.

That, combined with the fact that underlying hitting and pitching abilities seem to drift randomly, as quite rightly noted by Brad Null and as implied by the structure of the Marcel predictor model.  Not only that, but this Brownian movement in underlying ability appears to occur mostly in the offseason, as suggested by the streakiness analysis articles on in-season baseball hitting (I’ve yet to find any on pitching, but would love to be linked to any that are available).

The simple answer would be that I have underestimated the level of impact that context provides to baseball results.  Whether it be managerial, team effect, schedule or randomly enforced.  Perhaps other commonsensical things that elude me at the moment.  I dunno, something’s up though.

One last thing, MGL:

Googling for the age effects on hitters stuff of yours, I see a couple of links to oncology biostatistics articles by M. Lichtman.

If this is you; couldn’t you analyse the problem by treating the data as clinical trial with systemic censoring bias?  I’m a babe in the woods with that type of math, but surely stochastic models using counting processes would have value here, no?

As a crude example, by chance alone, we would expect some pitchers in their late 20s/early 30s to have opposition wOBA of .300, .330, .360, .330 in four consecutive years.  But in our sample we’ll have too few, because the pattern of the first three years eliminates some guys from the process.  So that modelling could capture that sort of thing.  Wouldn’t it.

As I say, that’s beyond the scope of what I can do mathwise, and the difficulty of opposition would have to come from fangraphs or similar I suppose, raw data doesn’t seem to be anywhere.  But hopefully someone else takes the ball on that, it would seem reasonable to me.  And would be a completely different way of looking at the problem, which is always nice.

I ran the aging on the past five years of Cuban batting, but it appears that sample sizes at each age (max 15k weighted PAs) was not sufficient to identify any clear trends.

Looking at distribution of PAs by age, the bulk were age 20-24, then a smaller peak at 28-29. I interpret this as the best players (MLB or close in quality) keep their playing time to 28, then start declining. Every one else starts attriting at 24, replaced by the next wave of younger players.

I have not yet entered the pitcher’s ages into their table.

PAs by Age (in thousands), Cuba 2005-2009

unk 8.8
17  1.2
18  3.6
19  7.2
20 11.4
21 13.2
22 13.7
23 15.2
24 11.2
25  8.5
26  9.2
27  9.2
28 10.4
29  9.7
30  8.4
31  6.7
32  3.5
33  3.5
34  2.4
35  1.9
36  1.7
37  1.3
38  0.8

"The age with the most PAs and BFs is also 24.”

Brian, that’s interesting.  Can you explain exactly what you mean by that?

The idea that hitters peak as early as 24 would obviously contradict a lot of prior research.  As a simple sanity check, what does age 27 performance look like for players who are regulars at age 24?  Are they any better?  Obviously, we’re leaving out guys who don’t break in until after age 24.  But almost all the players we care about are playing by 24.

Let me phrase the statement precisely
“The most common peak age for professional players (both major and minor league), both batters and pitchers, is 24. The group of players who have later peaks are more likely to attain a higher level of production and thus are more likely to be major league players.”

I may not be the only one to find that. If you look at BP’s PECOTA cards, down to the ‘Career Projection’ and ‘Ten Year Forecast’ charts, they have their projections peaking at 23 or 24.
http://www.baseballprospectus.com/card/card.php?id=HEYWARD19890809A.

Guy, I will look into your question of 24 to 27, but of course that can introduce a selection bias. If we look at the 24 year olds who were still playing at 27, they are likely to have improved because we are excluding the players who were released (or sent to the minors) before they got to 27.

Agreed. One solution is use WAR, and count guys as zero if they don’t play.  (I do think the fact that almost all aging analysis uses rate stats is one reason that post-peak declines get understated.  Players play less as they age, and while there are selective sampling concerns to be sure, the bottom line is they contribute less.)

Here is a typical refrain by a mainstream sportswriter (Dave Kaplan), which reflects the prevailing wisdom about MLB pitchers:

Zambrano was simply awful Monday as he was pounded by the Atlanta Braves giving up 8 earned runs in less than 2 innings of work. Can he rebound? Certainly. He is only 28 (he turns 29 in June) and he should be entering the prime of his career.

Interestingly, I think that conventional wisdom holds that pitchers peak later than hitters, due to their perceived need for many years of experience and seasoning.

This year was the first time I did pitching aging curves, and I did them for all levels combined, and by component. For the purposes of this thread, I did a query to do wOBA change for batters and pitchers, for all professionals, and for each level.

Damn if MGL wasn’t right - MLB pitchers show no improvement, except for a 0.98 at age 22.

There is improvement in wOBA allowed by pitchers in the minor leagues at younger ages - but from A to AAA, age 24 is the year they turn worse.

In the case of Zambrano at age 28, all pitchers that age are 110% of peak (111 in MLB, 108 in AAA, 115 in AA).

I hadn’t organized the data in this way before, and there’s a lot of good numbers. Give me the weekend to stare at them some more and I’ll get an article together for THT. Fascinating sh!t.

Brian, in my original post in green above (I don’t know what that is called - the original post in a thread on a blog like this) I give a description of the trajectories of all the components.  I also have polynomial regression equations for all of them.  If I knew how to post graphs, I would have done that.

Just want to reiterate that I love this blog for these kinds of things.

I looked at pitchers from 1993-2006 who were 24 years old, pitched at least 162 innings, and had an ERA+ between 95 and 105.  There were 19.

How did they do at 27?

6 were improved.  Ranging from CC Sabathia (157) to Kelvim Escobar (110), all of these guys pitching a full season.

6 were about the same, ERA+ between 99 and 103, but I also counted Ben Sheets and AJ Burnett in this class.  Their ERA+ were improved (119, 112) but each only pitched a little over 100 innings.  I interpret this as their overall value not much different from a guy who makes 30 average starts.

1 went to the bullpen and pitched well (Baez).  2 were worse, and pitched at least 100 innings, Kyle Lohse and Tony Armas.  4 were terrible, and pitched between 3 and 50 innings.

So roughly, their chances of improving were the same as getting hurt and losing effectiveness, which were about the same as their chances of treading water.  But we remember the maturation of guys like Lackey and Sabathia from mid rotation guys to aces, and forget about the Jim Parques, Ismael Valdeses, and Felipe Liras.

looking at both MLB and minor league numbers, I found pitchers very flat from 22 to 26.

Anyone remember the specifics of the study that found lefthanded pitchers peak later than righthanded pitchers?  If my memory serves me well the peak for MLB LHPs was 28 or 29.  It was probably from an article on Hardball Times or the like.

It would be interesting to know if height played a part in how well a pitcher did over the 22-26 plateau.

Matt

I don’t see any difference in the aging of LHP vs RHP

All pitchers (MLB & MiLB)
by throwing hand, by wOBA allowed
percent of peak

    Left Right  
17  1.22  1.26
18  1.15  1.18
19  1.11  1.13
20  1.07  1.07
21  1.04  1.04
22  1.02  1.02
23  1.00  1.00
24  1.01  1.01
25  1.02  1.03
26  1.05  1.04
27  1.08  1.07
28  1.13  1.11
29  1.15  1.14
30  1.18  1.17
31  1.22  1.22
32  1.27  1.27
33  1.31  1.31
34  1.39  1.37
35  1.46  1.39
36  1.48  1.48
37  1.50  1.51
38  1.53  1.50
39  1.46  1.52
40  1.55  1.55

I performed some cursory Google searches to jog my memory about where I saw different peaks for RHP versus LHP. That quest proved fruitless, but I did come across a couple of articles related to aging curves for pitchers.

An older one from 2005 by Chris Jaffe:

http://www.baseballthinkfactory.org/files/primate_studies/discussion/a_new_look_at_pitcher_aging_patterns/