THE BOOK--Playing The Percentages In Baseball

Hmm, maybe I’m not reading the numbers right, but I find it interesting that players “breakout” and hit their peak, but then gradually decline (age 24 and 30 are equidistant from 27, but 30 is far more productive. That type of thing). It’s not an even curve. Is this known/expected?

Also, why are people still debating the age 27 thing? Hasn’t this basically been proven time and time again?

For the record, I’m not really saying that those are the peaks.  Rather, *according to the method that J.C. Bradbury used*, those come out as the peaks. 

I’m certainly not coming out as an advocate of J.C.’s method.  Just making the point that the method agrees with us that shorter careers have earlier peaks.

JD: the slope is steeper on the upswing and gentler on the downswing.

So, age 25 and age 31 are equivalent in terms of total production, but from age 27, we can see the slope is obviously steeper from 25 to 27.

Tango:  I think the pre-peak curve is steeper.  But the WAR curve might overstate it a bit, because younger players sometimes get stuck in the minors longer than they should (Ryan Howard, Wade Boggs) while a good 31 yr old never loses his job. 

It would be interesting to look at minor league careers and see what kind of pre-27 aging curve that yields.

Guy/4 - Interesting. So these numbers (or any that show the steeper slope going up) might just indicate that players aren’t getting a chance to be good when they’re younger. It’s the Dusty Baker Effect!

It makes sense though, because not only do some potentially good players get stuck in the minors, many others are brought up and platooned, given marginal playing time, etc.

So the real question: Should teams be giving the younger (24-25ish) players starting jobs more often?

Added this post over at Phil’s site: 

A simple way to test Bradbury’s thesis is to compare the performance of players who played at both age 27 and age 30 (300+ PAs).  This removes the injury problem that arguably afflicts the modal peak approach—these guys were all still playing at age 30.  Bradbury projects a very small improvement in OPS over these ages, about 4 points.  However, if we look at players who debuted in 1921 or later and played at these ages (933 players), we find that 55% of them had a higher OPS at age 27.  Their OPS drops 10 points on average, rather than rising 4 points as predicted.  (And the average league OPS change over these years was .000, so that’s not a problem.)

Moreover, this is actually a comparison that should understate the real 27-to-30 performance decline, since a lot of 27-yr-olds decline enough that they aren’t even getting 300 PA at age 30. 

I think we can close this case.....

Guy,

I showed the 5-yr arc data here:
http://www.insidethebook.com/ee/index.php/site/comments/the_ten_year_aging_curve/#41

And this was the LWTS for those players who played at age 26 through age 30, min 300 PA:

26 26 14.3 659
26 27 15.2 659
26 28 15.2 659
26 29 14.5 659
26 30 11.6 659

Peak is at 27/28.

***

Also in that thread, I chose 10-yr arc, but rather then 24-35 age range that JC chose, why not choose age range 23-32:

23 23 17.1 176
23 24 19.4 176
23 25 23.4 176
23 26 25.7 176
23 27 24.9 176
23 28 25.1 176
23 29 23.3 176
23 30 20.8 176
23 31 21.8 176
23 32 17.9 176

And there we see the peak is age 26-28.

Indeed, I showed ALL possible 10-yr arcs, not just the one JC decided to choose.  And the trend is pretty clear.

I am out of town right now, but I am doing some research that suggests that the attrition problem (survivor bias) is significant enough to change the peak age.  Adjusting for this bias pushes the peak age to somewhere around 27-29.

I started to write an article on this before I left.  I’l finish it when I get back and I will probably publish it on Fangraphs.  I think it will change some of the notions we have about peak age.  I also address the idea that there really is no one good, one-size-fits-all definition of peak age.  For example, imagine that there were tons of marginle hitters that enter the league at age 23 or 24 and because they peak at 25 or 26, they are mostly out of baseball by the time they are 28 or 29.  And what if those players brought down the “average” peak age of all players to 26 or 27 but that without these players, the “average” peak age would be 29?  Would you be comfortable saying as a blanket statement that, “Players peak at age 27 and then using that to define the aging curve for all players?” I wouldn’t.

And given that each player probably has his own aging curve, if a player, say, has already played 5 or 10 years, to assume that his peak age was 27 would probably be a mistake.  In fact, if these marginal players who barely play much at all are the ones that are bringing down the “average” peak age, it would be a mistake to apply that lower peak age to anyone but those players.  And those are usually NOT the players we care about. 

Assuming that players like Chase Utley, for example, are well past their peaks is usually the type of “assumption” that we care about and that kind of assumption is probably wrong.

Anyway, I’ll have that article and research done hopefully in a week or so.

I am also going to show how the “delta method” whereby you weight each performance difference from one age to the next by the “minimum of the two PA” is a BAD way to do it.  And of course, why you have to adjust for survivor bias and how to do it.

mgl, sounds like a good read coming.

Each player will peak a little differently, and we are attempting to average them out. However, I believe that a ‘non-survivors’ bias may give a wroong notion of ‘peak’.

“imagine that there were tons of marginle hitters that enter the league at age 23 or 24 and because they peak at 25 or 26, they are mostly out of baseball by the time they are 28 or 29.”

As an alternate theory, look at this instead that you have a lot of marginal hitters who have an outlier season which causes them to be promoted to mlb, but then they regress to their ‘true’ level and are demoted out of mlb before they get to 28 or 29. Was this a true ‘peak’ or a random spike? I think many are, while of course not all are.

Would you be comfortable saying as a blanket statement that, “Players peak at age 27 and then using that to define the aging curve for all players?” I wouldn’t.

Right, this is what we are talking about.  JC’s study is not representative of all MLB players, but representative of the players who played for 10 seasons from age 24 to 35.  If he wants to say he can extrapolate that beyond something else, it’s him to prove it.  Until then, no extrapolation.

And MGL seems to be saying the same thing here.

I do not understand why there is so much discussion on aging curves for hitters but very little for pitchers.  (BTW, it has bothered me ever since looking at data on Bonds and Clemens and wondering why the steroids effect was easier to see for Bonds.)

In April there was a post on a quick-and-dirty aging curve for hitters:

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

Similarly, I looked at single seasons, from 1921 to 2009, to see how many had ERA+ of 100 or more, for at least 60% of games started and at least 120 IP.

The data appear to center, but not neatly, around age 26 or 27.  The rise to the peak (from 23 to 26) seems faster and less “step-wise” than the decline (from 27 to 32).

Age Count
26/27 440/410
25/(28/29) 386/(382/380)
24/(30/31) 303/(318/297)
23/32 233/233
33 202
34 170
35 123

Does this match past findings / other available data / people’s intuitive sense?

I look forward to seeing MGL’ article.  It seems to me what we ultimately want is a series of aging curves, based on a player’s current age and past performance.  Chase Utley’s projection for age 31-35 is now much higher—even relative to his overall skill—than it would have been for Utley after his age 26 season, not to mention when he was a 23-yr-old minor leaguer.

To me, the whole “peak” debate somewhat obscures the more interesting issues, which are the steepness of the pre-peak growth and post-peak decline.  And it’s the post-peak decline where I think past age analysis has most missed the boat.  The problem is that both the delta method and the career quadratic curve method face the same bias, which is fast-aging players disappearing from the samples.  Let’s take Andruw Jones as an example:
Age/WAR/PA
29 6.1 659
30 3.6 659
31 -.9 238
32 .8 331
If you used the delta method and a 300 PA minimum, Jones’ decline vanishes entirely.  In the quadratic, only one decline season appears.  But assuming his career is over, Jones won’t be in anyone’s sample at ages 33, 34, 35, 36, etc.  At each successive age after peak, the proportion of fast-aging players will decline and we are increasingly looking only at players who aged well.

Now, when we’re only trying to project age 34 for a guy who played well at age 33, that probably doesn’t matter—Andruw isn’t relevant.  But if we’re trying to decide whether to give Utley a 7-year contract at age 30, then we do care about Andruw’s precedent.  And while Jones’ decline was unusually abrupt, there are actually a LOT of guys who decline very quickly sometime after age 30.

The other point Andruw illustrates is the importance of incorporating playing time and position/defense.  If you looked only at his OPS+, his decline is much less pronounced (though still there).  But once you factor in a move from CF to DH, and 50% reduction in PT, and the decline is catastrophic.  These rapid-decline players often see reduced PT and/or a move down the defensive spectrum.

Guy, that is another fantastic example.  And yes, Andruw is entirely relevant to forecasting, as are the other players that have been brought up.  You can’t just take him out of the sample!  What a joke that would be.

Correction:  a 300 PA minimum doesn’t totally obscure Jones’ decline—it would capture the 29-to-30 drop (6.1 to 3.6 WAR).  But it would miss the next two years of replacement-level play.

Guy makes some excellent points in post #12.  However, ...

But if we’re trying to decide whether to give Utley a 7-year contract at age 30, then we do care about Andruw’s precedent.

seems to me to be a confusing statement.  Certainly, we should care about Jones career arc in a general sense and, as Tango states in post #13, not exclude that information from analysis of aging because it does not meet some predetermined threshold of participation.  But in the specific sense I am not sure how much relevance an overweight center fielder’s career will have in projecting a 2nd baseman who still seems in excellent fitness.

I have not seen a sabermetric or econometric study of aging that would be suitable for use by a team in projecting a player’s future production in any meaningful way that would be helpful for a team for making decisions on long term contracts.  I have no direct knowledge of what inputs teams use for such analysis, but I would be surprised if this is not tne area where we blogging sabermetricians are not lagging behind teams’ proprietary in house metrics.  The only approach to projecting aging that makes sense is more of an actuarial approach.  Not looking at how often is a 31 year old going to lose playing time, but looking at how often does a 31 year old 2nd baseman lose playing time due to non- baseball related disease or injury, how often due to batting related injury, baserunning injury, and position specific defensive injury.  Not looking at how much a 31 year old hitter’s OPS+ is likely to decline, but looking at how much a 31 year old is likely to decline in eyesight, reaction time, fast twitch muscle fiber, slow twitch muscle fiber and then projecting how those declines might affect batting skills like pitch identification, contact rate, power, speed to 1B, etc.

Clearly JC is wrong to project all MLB players with a similar aging curve and clearly MGL is correct to state that each player will have his own aging curve.  But knowing that is not enough.  If we are to project individual player’s future performance with any meaningful degree of accuracy we must determine what physical attributes are the most important factors in creating the basic baseball skills that determine a player’s current level of success, how those physical attributes are likely to erode over time and what effect that will have on the player’s individual skills and ultimately on his abilty to perform in the future.

Peter/15: That’s an excellent point. Once we’re able to get an idea of what the aging curve looks like in general, we can test some of those ideas.

Do tall players age better than short players?  Do fat players age better than skinny players?  Do players with a steeper ascent trajectory also have a steeper descent?  Do “patient” players with lots of walks age better than “impatient” players?  And so on.

I agree with Peter.

Phil: you should read DAvid GAssko’s articles on those particular topics in HArdball Times.com .  Probably in 2007.

HOWEVER: all these forecasting systems all try to use these various biographical attributes in some form or other (especially PECOTA, which specifically notes in Nate’s article how each type of player has his own trajectory).  AND YET, Marcel, using the most basic of information and methodology is just as good as all other forecasting systems.

Basically, there is so little room in terms of improvement that the answers to the questions being posited will barely move the needle.

Tango:  we know that Marcel is just as good as anything else at predicting OPS/wOBA next season.  Is it also just as good at predicting, say, a player’s total WAR over the next 5 seasons?

Well, I just do a standard -0.5 wins per season.  I haven’t looked at it TOO MUCH, but that seems to be a fairly easy way to do it.

I could try to come up with something a bit less basic, but almost as easy.  For example for starting pitchers, I have the “Rule of 10”, whereby I drop the win% by .010 and the IP by 10% every year.

I could come up with something like that for position players and relievers.

I’m open to any challenge out there, whereby I would provide the open source methodology that is very easy to remember and program, and someone else out there will need alot of computing power and black boxes machinations, and I would bet I would win at least 48% of the time.

Phil/16 - I don’t see much value in trying to determine a generic baseball aging curve.  I think we could profit more from looking at studies that have been done on aging physiology for specific parts of the body for the general population and for athletes in other sports.  I admit that I haven’t done that either, but there must be tons of literature to draw on.  I know weight lifters peak rather late, mid 30s or so, which would be some indication that large muscle strength does as well.  My eye doctor tells me that we start losing some of our eyesight capacity around 20.  Many years ago in drivers ed they had a policeman come in with a machine to test our reaction time.  He claimed that reaction time was as quick as it was ever going to be at age 18.  I am sure a search of physiology journals would yield many articles that would give aging curves for all these traits and more.  If I were a GM I would test every player in my system every year from when they were drafted to after they retire to build a data base relating physiological aging to baseball performance.  The best we can do from the outside is to try and define certain measures of baseball performance that isolate as much as possible specific physiological attributes. 

Tango/19 - Marcel does a very good job overall, but it does not logically follow that there is not much room to improve in specific areas.  One of the things that I hoped that might be done with the raw data from your projection comparison project was to compare how different projection metrics did at forecasting specific catagories of players.  Which system was best at forecasting rookies performance, which was best with players over 30, which was best with players who changed teams, etc.  A single year might not give us much information to help improve projection metrics, but if a projection system was consistently better in a certain area over a period of years it could yield valuable information on where and how improvements could be made.

Tango and MGL,

There are a ton of studies being done about aging curves. Do you foresee any studies being done on characteristics that lend to a longer sustained peak?

Each skill has its own curve. Do particular combination of those curves lead longer peaks?

It does seem to me likely that players who enter the major leagues at age 25 or later (with success), have a significant later peak on average who enter the major leagues at age 22 or younger (with success).

Age of entry creates a somewhat different interaction between the benefit of experience and the effect of aging.

Mike, I think your last point really touches upon the grid that the MLB baseball season is. While those players who enter MLB at a young age do gain more experience, I’d be shocked if a study didn’t show they also deteriorated at a young as well.

My guess is that if you choose two groups of players at age 28 who:
- were great players over the last 3 seasons
- had at least 600 PA in their most recent season, and at least 1500 PA over their last 3 seasons
- but where group 1 started their careers at age 23 and younger, and group 2 started their careers at age 25/26

That you will find no difference in performance from age 29-onward.

One of the reasons of course that a player who enters MLB at a younger age would tend to have an earlier peak is that they probably tend to be physically “older” than their chronological age.  In past studies we have found that experience has little to do with the “aging curve.” And of course when we speak of an aging curve, we are talking about physiological age and not chronological age.  Which is one reason why players have unique aging curves.  They are probably not so unique if we used physiological rather than chronological age.

Bradbury has posted another response to Phil B. here:
http://www.sabernomics.com/sabernomics/index.php/2009/11/aging-and-selective-sampling/.

"It really doesn’t matter to me where peak age for baseball players is. I looked at the data using standard empirical methods to answer the question and I am merely reporting what I found. I have addressed all criticisms raised, but if you are not satisfied with my responses then feel free to continue holding your belief.”

JC said that.  You know what, I’ll say it as well.  So, that quote above, I’ll ditto it.

He is an impossible person to chat with.  To those people who think I’m difficult: I’m here, and I answer every question.  Don’t tell me I’m difficult. 

He can believe in Santa Claus, I’ll believe in that we landed on the moon.  To each his own myth.