THE BOOK--Playing The Percentages In Baseball

Methodology seems very familiar to me for some reason.
http://www.insidethebook.com/ee/index.php/site/comments/basic_aging_curve_for_hitters_1957_2006/#comments

See my comment #6 and following.

One potential problem I see is that at the younger ages, you aren’t screening for talent as effectively.  Getting playing time at age 20 or 21 is only partially a function of talent—it also depends a lot on luck and the player’s own aging curve (players who happen to mature/peak very early will make these groups).  So I’m guessing the career talent level for those first couple of groups is less than the 27 and 28 cohorts.

One test:  what happens to the age 25 cohort at ages 26, 27, 28, 29?  Or the age 26 cohort at 27, 28, 29?  Do both groups continue to improve through age 27-29?  I’m guessing they don’t.....

Don’t you have a regression to the mean issue when you only look at the top 100? Isn’t that like taking the top so many in a year and see how they do the following year?

Your numbers get offset because as a group they are getting better as they age, but they are regressing to the mean. Also, aren’t injuries an issue, because almost everyone in a top 100 group probably missed virtually no time?

What’s the distribution like for these delta’s? Are there a lot of guys that collapse and a lot that keep last year’s production? Or is the movement gradual for the majority of players?

dq: since I am looking at the top 100 for each age group, that bias should cancel out, right?

I’m not looking to see how aging works for one age in isolation (in which case you would be correct).  I am looking at each age group and comparing to each other.

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Guy: don’t forget I am looking at WAR, not WAR/PA.  So, it’s possible to improve on the rates, and lose it on the quantity.

Peter, I think your idea in the other thread provided a source of inspiration here.

I don’t get it. Instead of comparing the best age 21-24 players’ age 25-27 years to their age 26-28 years, in which case they decline (I checked), you’re comparing them to how an age 22-25 group does at age 26-28, in which case that group is composed of better players.

Tango:  Wouldn’t it make more sense to create these cohorts, and then track their WAR/Game at subsequent ages?  Then you control for the talent differences among cohorts.  Why do you think it’s better to look at WAR?

Instead of comparing the best age 21-24 players’ age 25-27 years to their age 26-28 years

Jeremy, in that case, since age 26 and 27 are the same, you are comparing whether the age 21-24 players have a higher WAR at age 25 or age 28.

It’s obvious it will be higher at age 25, no?  The PA attrition will be enormous by the time they hit age 28.

You’d be asking this: given that you have 100 players that just finished their age 24 season, would you rather have, today, their age 25 season, or their age 28 season?

I’m not sure how far back I can go where you’ll get a different answer.  Maybe a group of players that ended their age 21 season, they’d have a higher WAR at age 25 than 22?  Maybe?

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you’re comparing them to how an age 22-25 group does at age 26-28, in which case that group is composed of better players

Yes, that’s the point!  Do I need an aging curve to tell me that players perform better at age 19 than age 18?  All I need to do is make the best 19 yr olds play the best 18 year olds.

So, that’s what I’m doing: I’m making the best 25 year olds play the best 26 year olds, and so on.

Guy, I wouldn’t say WAR is better than WAR/PA.  My problem is that I hadn’t already been tracking future PA, just future WAR.  I need to update that.  Until then, WAR is what I got.

In any case, future PA is also part of aging.

Here’s another way to put it.  Back in my old company softball league, we’d have the over-30s play the under-30s.  The idea is that there’d be an even talent level at that line that you’ll get a competitive game.  Had we made it the under-25s against the over-25s, it would not be fair.  Nor if we had it at the 35 year old line.

So,that’s another way to do it: select the best under, say 28 and over 28 in a given year and see how they do.  And repeat.

By the time good players are 25, they are already in MLB.  You might miss out on some Wade Boggs or Chase Utley season.  But for the most part, it should work well.  Very slight bias.

Tango - Id be interested in seeing how the aging curve for the 2nd 100 differs from the top 100 by this method.

"By the time good players are 25, they are already in MLB.”

True, but you’re selecting based on age 20-22 for many cohorts.  So your younger groups will be less talented players. 

“So, that’s what I’m doing: I’m making the best 25 year olds play the best 26 year olds, and so on.”

That would be interesting to see.  Can you show us best WAR for 24-26, 25-27, etc.?

What you are doing is taking 25 year olds who were good at 21-24, and making them play 26 yr olds who were good at 22-25.  Not quite the same thing.

What you are doing is taking 25 year olds who were good at 21-24, and making them play 26 yr olds who were good at 22-25.  Not quite the same thing.

It’s better. I can’t just look at the WAR of the 21-24 guys and compare it to the WAR of the 22-25 guys.  There’s little WAR accumulated at age 21 and lots at age 25, so the answer will be self-evident.

What I’m doing is saying this: “I want the best 25 year olds in MLB, and I want them to play the best 26 year olds in MLB.”

So, how do I figure out who are the best 25 year olds (BEFORE they actually play at age 25)?  Well, figure out who performed best at age 21-24.  That’ll give me what I want (for the most part).  Like I said, I may miss out on some (a few) great 25 year olds that had a late start.

And how do I figure out who are the best 26 year olds?  Again, whoever performed the best from age 22-25.

Basically, I’m doing a simple Marcel to figure out who are the best 25 and 26 year olds.  And then I’m simply seeing who accumulates the most WAR: the 25 year olds or the 26 year olds?

(I agree, I should do WAR/PA, in addition to PA, and I’ll do that today if I get the chance.)

Rinse, repeat for all other ages.

Peter: the difference between the way you proposed it in the other link, and how I am doing it here is that I’m looking at the out-of-sample data.

Basically, I’m creating a simple Marcel, selecting an equal number of players at each age, and then looking at their out-of-sample results.

I took the top 100 from ages 21-24, and threw out Evan Longoria and Troy Tulowitzki,

and computed an average pa per year.

Only 24 of those players got more average pas in ages 25-27 than in years 21-24. Five are WWII guys, so call it 24 out of 93.

You are taking the best of the group and seeing how they did in the future.

39 of the 93 got worse;

You are doing an aging study where 42% of your 26 year olds got worse.

"I can’t just look at the WAR of the 21-24 guys and compare it to the WAR of the 22-25 guys.  There’s little WAR accumulated at age 21 and lots at age 25, so the answer will be self-evident.”

Agreed.  Which is why I didn’t ask for that.  I asked to see 24-26, 25-27, 26-28, 27-29.  If you’re correct, we should see performance improve at each step, right?  I don’t think you will, at least for latter 3 cohorts.

*

“Basically, I’m doing a simple Marcel to figure out who are the best 25 and 26 year olds.”

But you aren’t.  Total 4-year WAR will be a reasonable approximation of a Marcel for your 28 and 29 yr olds.  But it won’t be for your 26 year olds, because so many factors other than talent determine total age 21-24 WAR.  Your choice of metric will become a more accurate talent measure for each successive cohort, undermining your analysis.  I’m 99% confident that the career WAR/game for your age 28 cohort will prove to be higher than that of the younger cohorts.

You are doing an aging study where 42% of your 26 year olds got worse.

They didn’t “got worse”.  We OBSERVED a worse performance.  As you know, we can know someone’s true talent exactly, and half the time, we will observe a worse performance than expected, just by luck.

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I asked to see 24-26, 25-27, 26-28, 27-29.

What you are asking for is total WAR at ages 24-26 for the top 100 players at ages 24-26?  Is that correct?

Yes, that’s correct.

I don’t have 3-years but I have 4-years:

Age1 Age2 WAR PA WAR/PA
20 23 8.8 1,570 0.0056
21 24 16.2 2,131 0.0076
22 25 20.1 2,348 0.0086
23 26 23.2 2,477 0.0094

24 27 24.7 2,503 0.0099
25 28 24.9 2,523 0.0099
26 29 25.0 2,519 0.0099
27 30 24.5 2,513 0.0098

28 31 24.3 2,531 0.0096
29 32 23.6 2,521 0.0094
30 33 22.8 2,504 0.0091
31 34 21.8 2,486 0.0087
32 35 20.1 2,420 0.0083
33 36 17.3 2,351 0.0074
34 37 14.3 2,251 0.0063
35 38 10.0 2,166 0.0046

That sets the peak at somewhere between 24-30 (average of 27).

***

This doesn’t answer my specific question though.

Here is my question: given that I have identified the 100 best 23 year olds and the 100 best 26 year olds, which group will perform the best in the next 3 years?

Am I going to get more production in the 24-26 age years or in the 27-29 age years?

But it’s the wrong question, I think.  What we want to know for both players, the 23 year old and the 26 year old, is which ages would you rather have that player for:  age 24-26 or age 27-29?  My sense is that it doesn’t matter:  the players will be equally good in both cases.  And if so, I don’t think it makes sense to talk about an “average” peak of 27.  What the data is telling us is that players are about the same from age 24-29 (roughly), and then decline.  And even the 23-26 group might be just as good as the later cohorts, if some players weren’t being denied playing time at ages 23-24.

But it’s the wrong question, I think.  What we want to know for both players, the 23 year old and the 26 year old, is which ages would you rather have that player for:  age 24-26 or age 27-29?

I didn’t know you can have a wrong question!

Anyway, the question as you put it is identical to the question as I put it.  I don’t see the difference in what you said, and what I said.  You said which I’d rather have, and I said which would perform better.

Guess I wasn’t clear.  I’m asking:
For the great 23 year olds:  better at 24-26 or at 27-29?
For the great 26 year olds:  better at 24-26 or at 27-29? [Except you selected on age 26, so that’s a problem. Let’s take great 27 yr olds, and compare their 24-26 to their 28-30.]

You keep wanting to compare the 23 yr olds to the 26 year olds, without accounting for the possible talent difference between them.  I don’t see how that can tell us anything....

You are basing this study on a group of 21-24 year olds who got less plate appearances per year at ages 25-27 then they did at ages 21-24.

Whem most major leaguers get more pas in those brackets.

For the great 23 year olds:  better at 24-26 or at 27-29?

It’s obvious they will have a higher WAR at age 24-26, no?  This is the same issue Jeremy brought up.  Attrition is huge because of the time gap.

Now, if you are focusing only on WAR/PA, that’s a different story.  But then we get back to survivor bias.  The only players playing at age 27-29 are those that are good enough to play.  The great player at age 23 who is no longer playing at age 27 is out of the sample.

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You keep wanting to compare the 23 yr olds to the 26 year olds, without accounting for the possible talent difference between them.  I don’t see how that can tell us anything....

That’s the whole point!  Just like I would ask: would you rather have a soccer team made up of U14 or a soccer team made up of U17, what are you going to choose?  The reason you want the U17 is BECAUSE of the talent difference.

Would you rather have a baseball team made up of the best 24 year olds in the world, or a baseball team made up of the best 29 year olds in the world? 

Selecting the 100 players at each age group based on how much WAR they accumulated in their previous 4 seasons, this is how many WAR they averaged:
24 3.6
25 5.0
26 5.2
27 5.5
28 5.3
29 5.3
30 4.7
31 5.1
32 4.6
33 4.5
34 3.9
35 3.3
36 2.8
37 2.5
38 1.6
39 1.2

So, the 100 best 27 year olds (selected based on their 23-26 age performance) averaged 5.5 WAR at age 27.  And that’s the best of all the ages.

How is it that it doesn’t tell us something?  It tells us that if you want the best players, and you can only select by age, select those that are 27 years old.

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Now, you can point to a sampling issue with the age 24 players, since I based it on performance from age 20-23.  And, there’s plenty of great players that only make it to MLB at age 23, and therefore, won’t be part of the pool of 100 greats.

I could change the selection criteria to only look at the previous 2 years, or do a weighted average, say a 4/3/2/1 weighting for the 4 years.

"Would you rather have a baseball team made up of the best 24 year olds in the world, or a baseball team made up of the best 29 year olds in the world?”

My guess is it’s a wash, but the 24 yr olds might be a smidge better.  But that’s if you KNOW who the best 24 year olds are.  We don’t, because we don’t have 4 good years of data on all 24 yr olds (while we do have that for all 29 yr olds). 

“The reason you want the U17 is BECAUSE of the talent difference.”

I’m talking about CAREER talent level (or age 25-29 talent level, however you want to approximate it).  You are comparing two groups of players who don’t have equal talent.  I bet the % of HOF players in your age 21-24 group is MUCH lower than in your age 25-29 group. 

“So, the 100 best 27 year olds (selected based on their 23-26 age performance) averaged 5.5 WAR at age 27.  And that’s the best of all the ages.”

No, you’ve only shown that age 23-26 data is the best predictor of true talent.  It’s quite clear from your own data in #20 that 25 year olds are just as good as 27 yr olds.  If you told me I could build a team of players at any age, I’d pick 25. 

“I could change the selection criteria to only look at the previous 2 years, or do a weighted average, say a 4/3/2/1 weighting for the 4 years.”

Yes, much better.  Or even better: 3 seasons at 4/3/2.  That will better approximate the 100 best players at that age (but still be problematic at the youngest cohorts).

And what if you take the best performers at ages 27-28, which you think is “peak.” How do these players perform at 29-30, and how did they perform at 25-26?  Are they just as good at 29-30?
My guess is they were a bit better at 25-26....

But that’s if you KNOW who the best 24 year olds are.  We don’t, because we don’t have 4 good years of data on all 24 yr olds (while we do have that for all 29 yr olds). ... Yes, much better.  Or even better: 3 seasons at 4/3/2.  That will better approximate the 100 best players at that age (but still be problematic at the youngest cohorts).

Well, then to be fair, I should just use the prior season.  This won’t tell us who the 100 best players are at a particular age, but it WILL tell us that with the same level of uncertainty.

That is, for 24 year olds, I’m looking at data from 20-23 years of age, and, for some players, that’s 2500 PA, and for others it’s only 500 PA.  Hardly a fair way to select the players.

For 29 year olds, I’m looking at 25-28 years of age data, and therefore, I won’t miss any players.  All the great players will have at least 2000 PA.

So, in order to make sure my uncertainty level in selecting the 100 best players at each age is not biased toward one age or the other, I should change the selection criteria such thatI only look at the previous season.  Yes, I’ll end up including lucky prior seasons and missing out on unlucky prior ones, but at least this problem will exist for all age groups.

Are they just as good at 29-30?
My guess is they were a bit better at 25-26

Because of the way I selected them (based on age 25-26 in part), it’s a given they were better then.  You have to look at out-of-sample data.

Right.  I meant look at the best age 27-28 players, as determined by their age 27-28 performance.  Would we rather have their next two seasons, or their two prior seasons?

I don’t know if using single season data is the answer.  Yes, luck will be equal at each age.  But there are many more 27 yr olds than 22 yr olds.  So the best 100 27-yr-olds will still be better players (age-neutral talent) than the 100 best 22-yr-olds.

Tom, the main issue I have with this method is the semi-arbitrary 100 player mark, because the top 100 at the lower and higher extremes are selected from a smaller overall sample. I just want to make sure that the selectivity is not affecting the overall result.

Is there a way to standardize on the top 1% of players or something, rather than a flat 100 best WAR totals? So that way you’re looking at the same proportional fraction of players in each bin.

Right.  I meant look at the best age 27-28 players, as determined by their age 27-28 performance.  Would we rather have their next two seasons, or their two prior seasons?

It would have to be prior.  Heck, even the best age 24-25 players might have a better 23-24 than 26-27.  First off, if they were great at 24-25 then they were probably pretty good at 23-24.  That’s how they got to get their PA.  And at age 26-27, they might not even have played.  So, you’ll have that selection bias issue.  And if you focus on WAR/PA, you’ll still have some survivorship issue.

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But there are many more 27 yr olds than 22 yr olds.  So the best 100 27-yr-olds will still be better players (age-neutral talent) than the 100 best 22-yr-olds.

Actually, there are pretty much an equal number of 22yr olds as 27yr olds as 48yr olds, with early death being a main difference. 

You are saying that there are many more 27yr olds in MLB than 22 yr olds.  But, does it matter that some Joe Schmoe was in MLB at age 27 but not age 22?

Remember, I am taking the 100 best players of an age group of players born since 1895. That means the best 1 or 2 players every year at each age group.  Now, your Ryan Howards and Chase Utleys who didn’t get a chance to come up at the young age, yes, that’s a problem.  IF of course, they actually would have otherwise been among the 100 best of all time at age 22, if not for the Phillies calmness.  If they were legitimate late bloomers, then it’s ok.  They wouldn’t have made the cut in that case.

Tom, the main issue I have with this method is the semi-arbitrary 100 player mark, because the top 100 at the lower and higher extremes are selected from a smaller overall sample. I just want to make sure that the selectivity is not affecting the overall result.

It’s a fair enough concern.  I can lower the threshhold to 50, which means I’d be selecting less than 1 player per season.

Is there a way to standardize on the top 1% of players or something, rather than a flat 100 best WAR totals? So that way you’re looking at the same proportional fraction of players in each bin.

I can’t do that.  Like I said, the 20yr olds would have almost no Joe Schmoes, but the 26yr olds would be replete with them.  Why would I select a percentage of players in those pools?

The question on the table is if you would rather have a team of 21yr olds or a team of 31yr olds.  And the very best 21yr olds are (presumably) in MLB.  And the very best 31yr olds are (presumably) in MLB.  The average 21yr olds are in the minor leagues, and would not have made the cut anyway.  The average 31yr olds are in MLB, minors, or hurt, or cut.  They would not have made the cut anyway.

I cannot use percentages.  That’s a non-starter.  I need to use an equal count.

Like I said, the issue is the selection criteria, and how that can bias the players selected by age.

If I focus on one year, and start at say age 24, then that pretty much removes the issue.

"And at age 26-27, they might not even have played”

I took the top 100 21-24 year olds who didnt play in 2009. One only played to 28 and one to 29; they were both born before 1900.

The average is they played for 12.5 more years.

They are still real good players; but they are ones who reached their peak earlier.

Terrific stuff, Tango.  A strange way of looking at things, but it makes sense.

Intuitively I would have leaned towards wOBA or linear weights with this methodology, though it’s probably fairer to use WAR.  These guys are all good enough that they would surely be in the lineup even in a slump.  So, unless they were hit by a bus, future PAs should be accounted for.

And while the chance of future injury certainly does depend on a player’s history, it’s also true that older guys always take longer to recover, and this will capture that. 

Plus I suppose that it makes sense that an aging guy who moves from catcher to DH/1st, SS to 3rd, CF to RF etc. ... they should be nicked a bit for that.  So WAR makes sense to me.

No model is ever going to capture every little bit of nuance.  The best models never attempt that.  Granted I have a bent towards predictive value.

The obvious question is “How does this compare to aging curves determined by season-to-season analyses?”.  The difference between the two is, of course, our survival/censorship bias element.

Put another way; in a parallel universe where there is no censorship bias and all players age in precisely the same way ... the universe would require that some players had convex shaped career arcs.  This by chance alone.  In that universe it would be easy to pick guys who were going to come cheap and outperform their contracts.  In this universe though ... it would be a hell of a trick.

Selecting only on the previous year, the (*) line says this:

For all nonpitchers age 27, there were 435 of them with at least 2 WAR at age 26 (the prior year).  I selected the 100 best performing of them.  Their WAR in the prior year was 6.8, with 646 PA the prior year.  At age 27, they got 5.1 WAR.

WAR_next is what you want to focus on.

As we can see, for the elite-of-the-elite, it’s fairly flat from age 25 to 33, with a peak at somewhere from age 27 to 29.

It follows the pattern that I’ve talked about in the past, that the better you are,the later you peak, with the ultimate peak age of 29 for the elites, and age 18 for the typical human being. Depending on your talent level, you will peak somewhere in between, (for the most part).

So, when we talk about “peak age”, it’s entirely dependent on the the talent level in your population.

Can we agree on this last point?

"So, when we talk about “peak age”, it’s entirely dependent on the the talent level in your population.

Can we agree on this last point?”

I’m not sure whether you’re being facetious or not.  If you are serious, what physiological reasons do you think would make some baseball players unique from all other athletes in this regard?

I never said they are unique. 

Everyone has their own peak age, and talent level is one variable in the equation.

If you know nothing else about a player, other than his talent level, then that would be the determining factor.

Tom, I see what you mean about the percentage of players not working..

Interesting how the top 100 players at each age regress so much the following year, as much as 2.4 WAR as a group!

It strikes me that it might interesting to compare the age-WAR curve for the top 50 vs the next 50 vs the next 50, to see if we can observe the peak age decreasing for the lesser players or not.

I really like this sort of out-of-the box thinking for how to look at aging. Any chance of getting WAR components, so we see how hitting ages versus fielding? And even positional, so we can observe changing roles with age.