THE BOOK--Playing The Percentages In Baseball

Thanks for posting that, Tango.

The only thing that the delta method really tells us is what we can expect from one age to the next if all we know is that a player is X years old.

And all that JC’s results tell us is the average trajectory for a player who has already met his requirements, after the fact - and even then, it might not apply to players of different ages. For example, if we have a player who is 30 and has played for 10 years with 5000 PA, like an Andruw Jones, our expectation for his age 31 year is NOT necessarily going to be commensurate with JC’s curve.

If JC were to split his sample up into players who started very young and players who did not, he might get different results, etc.

Getting back to the delta method, even though we can safely use the numbers for each age interval if all we know about a player is his age, when we “piece” those intervals together to form a trajectory, as I do several times in my article/study, it is not real clear what that curve even represents.

The way I look at it, the delta method and then using a “composite” curve, like the ones in my article, has limited use.  JC’s results have limited use as well.

Again, what we really want to do is to construct aging curves for various class of players and then apply those to particular players for projection purposes.

MGL,

This is good.  One-year differences are going to have much less of a problem than selecting on people with longer careers.  You’re never going to fully account for selection bias this way so I would suggest looking into selection models. 

Basically, you can estimate each player’s Pr(playing next year).  I am not a selection model expert (hoping someone else jumps in here), but my idea is that you want to find people who are “exogenously” (something unrelated to their performance) more likely to play next year.  Say you have 2 .220 players, but one is more likely to play next year than the other.  Selection models use this information to account for the selection bias by controlling separately for Pr(selected).  I would think you could use position scarcity - maybe 1992 was a bad year for 3Bs so a bad offensive 3B is more likely to play in 1993 than in 2003 when 3B was more stacked. 

The intuition is this...pretend for a large group of players you knew that there was a 100% chance they’d play next year for reasons unrelated to their performance (eg. they have compromising pics of the owners).  Then, the problem is solved - you would just look at this group.  You’ll never get to 100% obviously, but you don’t need to.  You can control separately for Pr(play next year) which tells you “how selected” that player is. 

The steps I’m proposing are:
1) Estimate Pr(play next year) using all info including some factor unrelated to performance.
2) Regress change in performance on age, controlling for the predicted probability found in (1).

I think this gets you the right answer. Again, I’m hoping someone adds on to this idea here…

Even if you solve the selection bias issues, you are still stuck with the notion that there are probably many aging curves that correspond to players who only play part-time, full-time, are good players, bad players, etc.

IOW, I think that the selection bias issues are the least of the problem.  The principal problem is defining what it is you are trying to determine when you look at ALL players.

I’ll grant JC something.  At least he defined his group of players such that we can say with some level of certainty that his resulting aging trajectory is the average aging trajectory of players who fit the profile in his sample.  How useful that is on a practical level is another story.

To me, the more interesting thing was seeing the differences in the two eras - pre and post-1980.  As I show in the article, it appears that the post-peak decline is significantly different in the modern era than it was many years ago, and to do any kind of age adjustments in our projections using models based on data more than 20 years old is problematic.

What was also interesting was seeing the drastic differences between the curves generated when we use the delta method on all players and players with long and fruitful careers only.  This suggests that when we do age adjustments for players who already have lots of years and PA under their belts, we also want to be careful not to use the models that are generated from data on all players.  That is probably where JC’s trajectories (and the ones I came up with for these kinds of players) become useful.

It’s late, so forgive me if I’m just seeing things, but I think your graphs on pages 12-14 are all the same. It looks like, based on where the “with non-survivor” line is that it’s the 1980-2008 data graphed all three times.

Excellent work, MGL!

One little thing I noticed, the survivor bias adjustment for younger players. I am looking at Table 5, for example the age 24/25 line. The composite player has 41 PA in his age 24 year and 94 career PA up to that point. His career LWTS is -25 runs/500 PA. He also has a -25 LWTS in his age 24 year, so he has shown no improvement. Then he doesn’t play at all the following season (no surprise).

The projection would have him at -10 LWTS in his age 25 season, if he were given the chance to play. That seems too aggressive to me. The year 2 projections for over-30 players look a lot more reasonable to the naked eye.

Judging from the charts, the selection bias adjustment makes a much bigger difference in the post-peak years anyway. So my complaint is pretty minor.

--

Depot, I like your idea. One possibility is that an almost washed-up player on a bad team may get more playing time. Or, how about players on expensive contracts. We have to be very careful, though, since often when a guy doesn’t play as much as he “should” there is a very good reason.

dcj,

The hypothetical experiment I am suggesting is....take 2 randomly-selected groups.  In group A, everyone has to play next year.  You would just study that group.  That guy in group B who doesn’t play - you observe “him” in group A.  What I’m suggesting is a way to essentially replicate this experiment.  Find someone that doesn’t play (group B) and then find that same guy who randomly has a 20% chance of playing.  This actually solves the problem you’re suggesting...as long as our “shock” to playing time is unrelated to performance. 

MGL, I think it’s important to get the right methodology (and your study was a very useful step, a point which I hope is not lost in my suggestions).  Selecting the sample by player-type or year is the easy part.

"The projection would have him at -10 LWTS in his age 25 season, if he were given the chance to play. That seems too aggressive to me. The year 2 projections for over-30 players look a lot more reasonable to the naked eye.”

yes, -10 does seem to high.  But, as you said, even we force it to another number, it probably won’t change things much.

“It’s late, so forgive me if I’m just seeing things, but I think your graphs on pages 12-14 are all the same. It looks like, based on where the “with non-survivor” line is that it’s the 1980-2008 data graphed all three times.”

Yes, it does look like I screwed up the graphs.  Thanks.  I’ll redo and re-post.

Sean, I just removed those graphs. They were not important. Thanks again.  Nice to know that someone actually looks at these things closely!  Good catch!

Also, if any of you have not read Tango’s stuff on the survivor bias problem, he tries to regress the Year I numbers for the players who got a little lucky and played in Year II.  I think that is a difficult way to do it, as it is hard to know how to do the regressions and how much to regress just that one year. I think my way is better, but I am not sure.  Either way should work.  Theoretically, adjusting the Year I stats for the players who go on to play in Year II is the better way to do it, but again, I think in practice it is next to impossible to know how to do that properly.

To me, the more interesting thing was seeing the differences in the two eras - pre and post-1980.  As I show in the article, it appears that the post-peak decline is significantly different in the modern era than it was many years ago, and to do any kind of age adjustments in our projections using models based on data more than 20 years old is problematic.

If you read the THT 2010 annual, you will see that I note a similar thing regarding starters born since 1962.  They have a long career as well (in terms of years, not batters faced).

I agree with MGL that we need to be careful to rely on players in the far past to determine an aging trajectory.

MGL’s file has been updated.

MGL—What are the % of total PA for the 5000PA group and the 1000 PA group.  I looked in the Doc and couldn’t find the information.  Thanks.

Excellent!

What are your conclusions on how much we should regress players WAR based on age?

Do certain skills age better or worse than others?  Could we use this to identify groups of players that would age well or poorly?  This would be very useful for projections and valuation of longer term deals.

The 10/5000 players had 47% of the total PA from 1950-2008.  They were 28% of the players.

For the 1000 PA group, they had 93% of the PA and they were 75% of the players.

“What are your conclusions on how much we should regress players WAR based on age?”

Not sure what you mean.

“Do certain skills age better or worse than others?”

Yes, of course.  If we did the same plots for each offensive event or skill, we would get very different peaks and trajectories.  Tango shows us these on his web site.

“Could we use this to identify groups of players that would age well or poorly?  This would be very useful for projections and valuation of longer term deals.”

Not sure what you mean by that either.  But we do find that certain body types age differently as well as the fact that speed seems to be correlated with aging curve, although that may just be because of body type.

You’d be getting pretty close to doing similarity profiles ala ZIPS and PECOTA doing that.

Also, as you pointed out w/ the Speed/Body type issue, is causing multicollinearity by using highly correlated inputs to generate the curve. 

That said, it would be really interesting to see the results by projected speed score put into separate buckets (Slow, Average, Fast).  That one comes up a lot on blog comments, some saying slow players age worse, others saying the opposite. 

Other interesting buckets would be time on the DL (as a proxy of injury history) and Position.  I’m guessing catchers fair worse than Left fielders, for example.

Boy, I’m not actually asking you to do all this stuff, but it’s fascinating, just thinking out loud.  What about for fielding, and pitching.  I know pitching is problematic before including projections for the players who fallout, but I’m wondering if that would actually help with getting the aging patterns.

I’m guessing noise would be a problem with those, but it’d still be interesting.  Or using the overall projected quality of the player as a bucket (scrub, average, star).  I bet the list could go on, but also the reliability of the buckets might become problematic.  I didn’t actually catch that you did not include it, but using MLE’s for players who moved to non-ML leagues might help mitigate the survivor bias some. 

Any way, interesting reading.  I like how it finds a halfway point between JC’s 5000 PA group and the delta method.  Makes a lot of sense.

I like how it finds a halfway point between JC’s 5000 PA group and the delta method.  Makes a lot of sense.

That sounded dumb.  Of course it would be halfway. 

How did you handle the aging component on the projections?  You say conservative projection, but wouldn’t that include some kind of assumed aging?

Depot, now I see what you mean. Problem is, how do we make sure the shock is unrelated to performance? Are there players right now who we think are going to have more or fewer PA next year than they “deserve”?

This is the same issue we run into with MLEs. In that situation, there’s a group of players who will probably stay in the minors as long as the major league starter at their position stays healthy, but if the guy gets injured the minor leaguer gets called up. I’m not aware of anyone who has created MLEs based on this idea, but it seems like a good approach to me.

Is there a similar trick we can use for aging? Not clear to me what can be done.

Thinking about pitching, I’m reminded of JC’s distinction between injury and “ordinary aging.” What happens when we do a long-term projection for a 24-year-old starting pitcher? He could follow a standard career path. He could blow out his arm and be finished at age 25. He could get injured but come back anyway at reduced effectiveness, like Frank Tanana. He could lose his mechanics like Dontrelle Willis or Barry Zito. He could find his niche in the bullpen. He could learn a new pitch and take a big leap forward like Cliff Lee.

I guess what I’m saying is, there is a huge range of possible trajectories for any player at any time. For single-year projections we can get away with just taking the average, but for multi-year projections I don’t think it is as useful.

Expanding on my last point, check out Raul Ibañez.

Age / OPS+
33 / 115
34 / 125
35 / 121
36 / 123

This is when the Phillies signed him to a 3/$30 deal. The ZiPS projection for the next three years was:

37 / 109
38 / 102
39 / 92

To be worth his contract, Ibañez would have to stay at about 120 OPS+. If you project him to drop this steeply, it looks like a terrible deal. As we all know, in his actual age 37 season Ibañez put up a 131 OPS+.

I am not defending the Phillies here, because no one would (or should) have projected zero age-related decline. But I think the sabermetric community, myself included, underestimated the chance that he would roughly maintain his production.

Interestingly, ZiPS now projects Ibañez for a 125 OPS+ next year (age 38). That seems high to me, but what do I know?

Very nice analysis by MGL.  It certainly confirms that JC’s results were largely a function of sample choice, not some new insight into player aging (and JC’s requirement actually created more bias: players needed 5000 PA between ages 24 to 35).

MGL, can you clarify how much impact the non-survivors had?  When I compare Table 1 to Table VI, it appears to have a very small impact—e.g., at age 36 the difference is -25.8 vs. -22.8.  But Chart III suggests a difference of about 15 runs at that age.  Which is right?  (I’m guessing it’s the tables.)

The 1980-2008 post-peak curve looks much flatter than seems plausible to me, even assuming a PED effect, though my intuition could certainly be wrong.  I can see three possible factors at work:

* Using the average PA approach may create a significant bias from the mid-30s on, because a declining player will lose PAs more quickly than one maintaining his production (the 600/575 couplets will show a much smaller decline than the 600/325 couplets). 

* The year II projections for older players may not be conservative enough.  These are guys who often have a long track record of performance, and if they and/or MLB teams decide it’s the end of the road it’s likely the year 1 decline was more real than bad luck.  (And how about a footnote for me on the idea of using forecasts for the non-survivors, suggested in this thread:  http://www.insidethebook.com/ee/index.php/site/comments/the_ten_year_aging_curve/. :>)

* A reverse form of survivor bias at later ages, because the players in these couplets are disproportionately players with a flatter than average age curve.  The guys who fell off a cliff at ages 32-33 aren’t in your 34-35, 35-36, etc. samples.  (On the other hand, we don’t actually know that players who decline quickly in their early 30s would continue to decline raplidly in the mid- and late-30s—but seems plausible.)

But none of these factors would seems to explain the pre- and post-1980 difference, which I assume is real.

*

I would also note that using rate stats, while certainly a legitimate choice, does understate the rate of decline in player’s offensive value.  PT drops fairly quickly, so the change in RAR is more rapid.  And then of course there are substantial defensive and baserunning declines as well.  If our ultimate goal is forecasting future value of players at different ages, I think looking at RAR and WAR is ultimately more relevant.

Great comments and questions. I’ll try and respond to some of them later tonight or tomorrow.

My graphs are all screwed up in the article.  Every time I cut and paste one graph into my Word document from Excel, it changes another one.

I’ll have to figure out how to correct that problem.  I thought I was going crazy.  As soon as I fixed one graph another one would be messed up.

dcj,

Yeah, I’ve made that exact suggestion (using injuries as “shocks” to getting called up) before for MLEs.  Someone should do it. 

For this topic, I was suggesting just using some stats on other players at the same position as predictors of whether someone plays the next year.  The idea is that a lousy 3b is more likely to stick around an extra year if the 3b crop is generally bad.  Or maybe use some information about the positions of the top players in the minor leagues (i.e. the potential replacements).  It would be a lot of work, but this is definitely the avenue to get the right answer.

Hopefully, I fixed all the problems in the article and Tango will post the new one.

File has been updated…

I have to agree that the most interesting thing would be the significant change in the decline period for players in the later era.

Just a clarification on the following:

“JC Bradbury, a self-proclaimed “enonometrician” (economist and sabermetrician combined)”

An econometrician in general isn’t associate with sabermetrics, they’re just statistically oriented economists.

I think you make a good point about ‘what question we’re asking’ toward the end as well.  I think some people may be interested in seeing:

“if player X was allowed to play a full 15 year career no matter what his production, how would his performance look?”

That’s what Bradbury is trying to do here, and that’s the general question researchers in aging studies are most likely to ask.  I disagree that this is that “nebulous”, though.  With little prior information about a player early in a career, we want this to guess how his performance is projected to evolve.  Once they’ve played for a little bit, we can adjust it based on the information we have.  First estimating this is an important aspect of narrowing things down though, then we can get on to the more detailed versions.  Of course, the best way to estimate it is freeze rosters in MLB for 15 years and see what happens.  Obviously, that’s not going to happen.

I think there’s plenty to be done in this area.

Depot/2,

I think you’re definitely on the right track here.  Essentially using their survival probabilities and combining this with a matching scheme may be a great way to go forward with the aging studies.  One problem is finding something (other than a single performance metric) that predicts their probability of survival and then combining that with their performance trajectory to match them.  But using the matching scheme we produce aging curves for similar players by players that DID survive, despite having similar types of talent levels as those that didnt’, for whatever reason.  That way we create a counterfactual world in which each player has a “10 year career”.

What the corrected Table 3 shows is that the problem of survivor bias in the delta method isn’t really that big a deal.  The curves are roughly the same whether you adjust for it or not.  It’s really only a factor after age 35 or so, and at that point our ability to accurately project the non-survivors is probably pretty limited. 

In fact, if we just limited our analysis to players who meet some reasonable career minimum (2000 PA?), we can probably just use the delta method without worrying about survivor bias as all.  That will remove the cup-of-coffee players we don’t really care about.  And I’m willing to assume that players whose careers end after that much PT haven’t been that unlucky in their final season (especially when you consider the fact that they got demoted to AAA and had further opportunities to prove they belong back in the big leagues).

This is good news, because it means we can study aging without using the quadratic approach that requires a biased sample of long-career players.

Small thing:  I think the two curves in table 3 are labeled incorrectly.

MGL:  How sensitive is your finding about the post-1980 change in aging curves to the performance of Bonds and other likely PED users?  For example, if you remove Bonds, McGwire, and Sosa, does the difference persist?  Just Bonds?

It certainly seems plausible that there’s been a shift.  Players in their 30s have a MUCH bigger financial incentive today to try to play as many seasons as possible.  Still, the shift you find is surprisingly large (to me).

Guy, good question about Bonds et. al.  However, I am not sure it would make sense to remove players who were “known” (or even suspected) steroid users when there are probably 100 more who also used but are not “known.” And of course, one of the reasons for getting a different aging curve in the modern era is probably PED use.  I suppose if we remove all known and suspected PED users, any residual differences could be attributed to things OTHER than PED use.  But again, we are still probably left with lots of PED users. Plus a lot of suspected users are because of weird aging trajectories and that would not be a good reason to remove them from our sample (we would want our suspicions to be independent of their trajectories).

"“if player X was allowed to play a full 15 year career no matter what his production, how would his performance look?””

That is sort of what a “generic” curve generated using the delta method for all players tries to do.

But, that still is not a very practical question.  The question that is most practical when dealing with actual players, is, “Given this player’s age, years in the majors, etc. (trajectory so far), what can we expect in terms of aging, for the next few years?”

And that can only be answered by looking at the trajectories of similar players in history.  Which is why all of these “after the fact” and “generic” curves generated by JC and me and Tango have limited practical value and meaning.

And even when we are dealing with specific players, the answer should be something like:

“Well, he has a 10% chance of not playing at all next year, a 15% chance of next year being his last year, but if he does play next year, his likely increase/decrease due to aging is X, and if he does go on to play for the next 2 years, his likely increase/decrease in Year III is Y. etc.”

When I mention ‘Player X’, I actually mean his trajectory based on his player type and all the information we have and matching that to similar players that were allowed to play throughout a long career.  So I think we’re on the same page here.

The thing is, from a ‘practical’ point of view, we’d be thinking as a general manager.  In my experience of sitting around building my fantasy team, it’s more curiosity, and the probability of survival is more important to me because I am not the one making the decision to bias the sample.

As the GM, you have the power to decide his fate to continue playing.  So if you were to project a career trajectory based on giving the full opportunity, you could give the player that opportunity, rather than make the decision based on a bad luck year (which sounds like what you’re implying toward the end there).  This is why it’s important to understand the full question about ‘aging’, and not convolute it with other factors.  I think everyone here wants to step in that direction, and I enjoyed reading your write up.

Without using a full career trajectory (and we can match them based on previous players that are very similar), we’re using a lot of other informational tidbits that very likely have nothing to do with biological or mental ‘aging’ in baseball.  They very well could be predictive of survival and performance, but they aren’t aging in the sense that a medical/biomedical/biomechanical person would define.  That’s okay, but like I said, I think you make a great point at how we are going to define what we’re looking for.

We don’t have to stick to the generic curve, but I think it’s an important step in finding heterogeneous curves among players.  Once it gets conditional on the player type (and its matches), the curve used can even be updated each year based on updated events in the most recent season.  I think we’re agreeing on a lot here, I just feel like there is still value on the generic curves for players, given the disparity in defining what ‘aging’ is.  This is a really interesting question, and there can be some real dynamic work done here.

Would someone be able to help me out and point me to some of the previous aging studyies that have been done? Specifically, those that include defensive contribution in some manner, and also those that look at player type and their different aging patterns.

I would be grateful for any help.

Oh, I suppose I should mention that I know of and have read the studies that Tango has done on tangotiger.net. I was really interested about other people’s work posted elsewhere on the net.

Thanks again for any help.

I did a study for the “2009 Hardball Times” book.  It’s a bit like mgl’s, but I didn’t try to actually try to figure out what the correction for the bias should be, and I tried regression to the mean for the guys who played instead of trying to figure out projections for the guys who didn’t.

My study is at http://www.philbirnbaum.com/aging2.pdf .  Thanks to Dave Studenmund for permission to post it.

Here’s what I did:

For every age from 26 to 39, I only looked at players who had played at least 5 years with at least 1000 total career PA.  Then I looked at the average change from that year to the next, weighted by the average of the two PA, and including the non-survivors, using their Year II projection, as in my article.

These numbers are more “practical” for players we are projecting.

For example, here is the first age interval:

26-27 508 .8 1.8%

What this means is that from 1950 to 2008 there were 508 players who by the time they were age 26 had played in at least 5 seasons (including their age 26 season) and accumulated at least 1000 PA.

1.8% did not play the next year in their age 27 season (they may have come back after that).

The average change from their age 26 to their age 27 season was .8 runs per 500 PA, including those 1.8% (9 players) who did not play in their age 27 season (I gave them a Year II performance equal to their projection for Year II).

This is the kind of thing you want to know if you are projecting a player after his age 26 season, and he has already played for several years.

Here is the rest of the data:

26-27 508 .8 2%
27/28 779 -.6 3%
28/29 1061 -2.2 3%
29/30 1224 -1.6 6%
30/31 1257 -2.1 9%
31/32 1204 -2.2 11%
32/33 1111 -2.5 14%
33/34 981 -4.0 17%
34/35 831 -4.5 22%
35/36 663 -4.6 25%
36/37 485 -5.0 26%
37/38 357 -4.4 31%
38/39 253 -7.5 36%
39/40 161 -4.6 39%

You can see that even for players with at least 5 years and 1000 PA, the model that JC comes up with and the curve that I came up with for the 10/5000 players after the fact, is not a good one in terms of projecting their future trajectory, or at least the difference between their most recent season and the next season.

In fact, those numbers look more like your typical “delta method” curve for all players or for all players with at least 1000 PA (basically the same thing).  Peak at 27 or 28, a slow decline (2 runs per year) until age 33 and then a a large decline (4-5 runs per year) after that.

When I chain the above numbers and plot the resulting curve next to that in Chart III, which is the aging curve for all players, after adjusting for survivor bias, they are almost exactly the same.  IOW, players who play a few years here and there, come up for a cup of coffee, etc., at various ages, do not have much of an effect on the overall aging curve, as generated from the delta method.

In fact, I am pretty comfortable using the curve in Chart II for most players when doing projections.  Obviously once we get into the 10/5000 realm for players in their thirties, we have to start using a different curve, more like the one in Chart VII or presumably the one that JC came up with.

I am still concerned about the fact that the deltas, even when we include the non-survivors, include “real” aging changes plus regression.  If that is true and we do a projection, which includes regression of course, then we would be adjusting for age too much (downward).

Tango’s method attempts to get around this problem by regressing the Year I numbers.  That is a good approach, but as he indicates on his web site, it is not clear how much to regress the numbers.

I think the trick might be to do a Marcel projection for everyone based on the Year I and prior numbers, including an age adjustment and then compare that to the actual Year II numbers.  Of course you don’t know what the age adjustment is yet.  So you play around with that until the projection and the actual Year II numbers are equal or are minimized for all players.

Of course the age adjustment you end up will depend on how much regression you do in your projection.  The more regression you do, the more the increase (or the less the decrease) at each age interval will appear to be.

It also concerns me that the players with the best Year I numbers and therefore the most PA (since PA and performance in any one season are correlated), and hence the players that are going to be regressed the most, get the most weight, which also increases the negative differences we see in each age interval when using the “delta method.”

I have to do some more research in this.  I still think there are a lot of problems.

MGL: you will find that if you focus on pitchers, rather than batters, you will get more insight.

Of course, pitchers present two additional problems:
- starter/reliever (where the basic rule of 1 run per 9IP holds since at least the mid-50s)

- DH

"I am still concerned about the fact that the deltas, even when we include the non-survivors, include “real” aging changes plus regression.”

MGL:  If you are adjusting for the non-survivors, why will there be any regression needed?  The only reason we have to regress is the problem of non-survivors, right? So once you deal with them, any other change has to be age related.

BTW, all of these methods are actually capturing a 3rd element as well, which is improvement in league quality.  Each year, our players are competing against a slightly better pool of opponents.  This isn’t a criticism—it’s just a component of what we call aging decline in baseball.

It’s like if you did an aging curve for Olympic-calibre swimmers, measuring the increase in expected times (worse performance) for various events by age.  Then, you did a second curve estimating the probability of these swimmers winning a championship or an Olympic medal in these event.  The rate of decline would be sharper in the second model, because it would also capture the improved times of competitors.

Guy, that’s why in one test I did, I only looked at the exact same hitter/pitcher pairs in back-to-back seasons (say Raines/Gooden in 1985 and 1986).  Easily my favorite of all these studies.

Guy, that’s why in one test I did, I only looked at the exact same hitter/pitcher pairs in back-to-back seasons (say Raines/Gooden in 1985 and 1986).  Easily my favorite of all these studies.

I am not sure why that would be an improvement, Tango.  All of these studies are based on an assumption that the quality of the opposition remains basically the same.  Guy is questioning that assumption by asserting that the league is gradually getting better.  By eliminating both the new opposition players that enter the league in year 2 and the old opposition players from year 1 that retire in year 2, the same pair opposition players are not actually the same, they are a year older too.  How close they are to being similar opposition to year 1 in aggregate depends on where those opposition players are in their own aging curves, i.e. whether they are young and getting better, or old and getting worse.  Any imbalance in the young/old ratio creates a bias that can be just as bad as if all opposition players had been left in, perhaps worse because you are working with a smaller N.

Peter: you are correct to a point.

The argument is that you have alot of hitters in their 20s facing pitchers in their 30s (or, hitters on the upswing facing pitchers on the downswing).  So, if you have a disproportionate such number, then that would be a reason you have hitters getting better numbers: not because of age improvement, but because the pitchers were on the downswing.

To argue that however, you have to show a disproportionate number of hitters or pitchers on the upswing or downswing in the last 50 years.  Sure, in one year, it could happen.

But, given that the number of players by age for batters and pitchers is pretty much in balance historically, that’s a hard sell.

So, yes, you have a point technically.  In actual practice, it becomes a non-issue.

I don’t get it ... what would looking at pairs of exactly the same batter/pitcher get you?  If Raines/Gooden was .280 in 1985, but .290 in 1986, what does that tell you?

Maybe I’m missing the point ...

Phil: see if this helps

http://www.hardballtimes.com/main/article/fielding-aging-curves/

Peter raises an interesting issue.  I’m inclined to agree with Tango that the net effect would be minimal. But I suppose declining players might outnumber improving players somewhat, since most players just don’t have that many pre-peak IP/PA.

But to me, it’s not important to separate aging and quality of opposition except when you’re specifically trying to measure league improvement.  Otherwise, the increasing quality of opponents is just a constant, and we can treat it at part of the aging curve. 

*

I’d like to hear MGL talk about what differences he sees in his data between using the average-PA approach and the all-players-weighted equally approach, specifically for the post-peak aging curve.  My concern is that the average PA approach will understate the rate of decline, because declining players get fewer PA.  (And the reverse might be true for pre-peak players).  I took a look at the 37-to-38 transition for players since 1980.  If I weight by average PA, I get an OPS decline of .057.* But if I weight all players equally, the decline is about 50% larger: .076.  That’s a big difference, and consistent with my concern/expectation.  I haven’t checked, but I think weighting by the lesser of the two PA would serve to further reduce the measured decline, as that method heavily weights the players who had two good seasons.

* OPS is not an ideal choice here because it doesn’t adjust for parks or changes in league offense.  But since I was only interested in comparing the different methods of weighting players, I think it does the job.

Tango/46: the link you sent was your study using matched pairs to figure aging trajectories for fielding.  That’s a bit different, because you can assume that a pitcher’s results on BIP probably don’t vary much with age.  So if you look at Yount/Augustine two consecutive years, you’re really looking at just Yount’s change, because you can ignore that Augustine is older too.

But for pitchers/hitters ... Gooden is aging at the same time Raines is.  So if Raines goes .280 to .290, you don’t know if Raines is getting better, or Gooden is getting worse.

But I suppose declining players might outnumber improving players somewhat, since most players just don’t have that many pre-peak IP/PA.

Ah, but it’s not the number of pre-peak to post-peak among batters.  It’s that number of pre-peak batters to pre-peak pitchers and post-peak batters to post-peak pitchers are the same.

Guy, the problem with the weight everyone equally approach is that there are a lot of fringe players with few PA per season, and if you give them equal weighting, you are coming up with an aging curve that does not represent the “average player” weighted by playing time.  What if you have a league where 10% of the players get 90% of the playing time, but the fringe players have different aging curves than the regulars?  If you weight everyone equally, your resultant aging curve is not going to be very useful or representative of the “league.”

But I agree that there are problems (biases) associated with weighting by the average or the lesser of the two PA, which was the concern I stated in my last post.  Basically that the number of PA in both years is related to performance, which is problematic.  I think it (the number of PA per season) is also related to perceived quality by the team, which is also a problem.  IOW, if a player has 100 PA in a season and is -10 and another players has 500 PA in a season and is -10, I think the latter player is probably a better player and his mean that we regress toward is probably higher.  That is going to cause problems with the aging curves when using the delta method including the non-survivors, I think.

As far as the league getting better, if you are using lwts, forced to zero each year, it is not the opposition that is causing a problem.  You don’t care about the quality of the opposition.  You care about the quality of the other batters (if you are analyzing batters).  Right?

If you are using anything other than a league normalized stat, not only do you have to worry about quality of opposition, you also have to worry about park changes, weather changes, ball changes, strike zone changes, etc.

MGL:  Yes, I didn’t mean to suggest that everyone-equal was “right.” Just saying that the choice of approach can have big impact on the result, and it’s hard to know which approach is better.  On the other hand, there are no “cup of coffee” players who play at age 37 and 38.  I didn’t set a career minimum, but I’m sure all these guys have at least 2000 PAs, and most far more.  So even if you study only players who meet some reasonable standard of career playing time, the correlation between PT and production poses a serious problem. 

Totally agree with you that using lwts (or OPS+ or wRC+) takes care of the issue of changing league talent.  I think we should consider that part of the aging process.  I just thought it was worth noting that we were implicitly doing that.

*

Going back to your concern about “double regressing” (comment 39):  If you include projections for non-repeaters, haven’t you removed the need for any regression?  I don’t see a problem here.

Phil: but if you look at all guys as old as Raines (aged 26 to 27), then you WILL know the change in performance, because the pitchers they faced will be an average of say 28 years old.  And you know you have identical pitchers in both groups.

You can weight all players equally without worry if you look at the SD of performance from the mean - the SD at 50 PA is going to be larger than the SD at performance at 250, etc.

Tango/52: I still don’t get it.  If I look at Raines this year against a bunch of pitchers who are 28 years old, then next year I’m looking at Raines against a bunch of pitchers who are 29 years old. 

How do I know the change is because of Raines, and not because the pitchers got older?

Guy, I don’t think that using a league neutral stat takes care of the league getting better problem. It only shifts the focus from the pitcher (for batters) to other batters.

If I am zero lwts this year and next year my true talent stays the same, but batters and pitchers get better, I will be less than zero lwts.

“Going back to your concern about “double regressing” (comment 39):  If you include projections for non-repeaters, haven’t you removed the need for any regression?  I don’t see a problem here.”

I don’t think that including the non-survivors takes care of the problem when you are weighting unequally.  It only addresses players who do not play at all. It does not address players who get fewer PA because they were unlucky/bad in Year I.

Using SD of performance is essentially the same thing as weighting by PA.  Weighting by PA is not a problem.  The problem is with the bias caused by correlations between performance and playing time, both in the same and the following year.  Plus there is the problem of what to use for the weightings when you have PA from Year I and Year II.  This is not a simple issue. There are no easy answers or solutions. I have thought about it for many years.

MGL:  I don’t think we need to “take care of” the league improvement problem.  What we want to know is how a player’s ability to help us win changes as he ages.  And that depends entirely on how much better/worse he is than those he plays against, so a context-neutral stat like lwts is perfect for that. In your example, the player’s lwts should decline because his ability to generate wins is diminished, even though his skills are exactly the same. 

I’m not saying you couldn’t try to separate the two factors if you wanted to, but you don’t need to in order to calculate valid performance projections.

Guy we are on the same page. I have never thought that you needed to separate the two things (league changes in quality and “aging").

Anyway…

I decided to generate a new aging curve using the same methods as I have been using (delta including non-survivors), but this time I used a “true talent” estimate for Year I.  I did this exactly like we would do a projection, but leaving out the last step, which is the age adjustment for projecting Year II.

So basically rather than using the actual Year I stats in the “deltas”, I took the last 3 years including Year I, and got a weighted average of them (3/4/5) and then added in 1200 PA of league average lwts, where the league average I used was the 1950-2008 MLB averages for that age.

Now, before I did the weighted average of the last 3 years, I converted the lwts for the 2 years before Year I into what they would be if the player were already at their age in Year I.  For example, if the player’s lwts at age 24 were -5 and then at age 25 it was -1 and then at age 26 it was +3, I would convert the -5 at age 24 to what it would be at age 26, and I converted the -1 at age 25 to what it would be at age 26. Then I would get the weighted average of all 3 years of “age converted” lwts.  After regressing that towards the league average 26 years old, I get the “true talent” lwts for that player at age 26.  That is what I used for the Year I lwts in the deltas, rather than their actual Year I lwts.

When I did this and compared it to my regular delta method aging curve (including non-survivors, they are almost exactly the same from age 27 to 35 and the peaks are around the same.  But before age 27 the curves are completely different, as they are after age 35.  Before age 27, the curve using the true talent numbers for Year I is much more shallow and after age 35 it is much more steep.

What is happening is that there are lots of young players who are having bad years in Year I and the much better years in Year II, forming a steep aging curve at the younger ages.  When we use “true talent” or regressed values for Year I, those bad years are being heavily regressed and is flattening out the curve.

The same thing is happening at the older ages.  There are lots of players who are having bad years in Year I and then even worse years in Year II (but not that much worse).  When we use true talent or regressed numbers in Year I, those bad years are not looking as bad, so when they do even worse in Year II, it looks like more of a dropoff.

Unfortunately, I don’t know if the regressions/true talent numbers or the actual numbers in Year I are correct to use for the aging curves. I do know that if we use the true talent algorithm above to do the projections AND we use the aging adjustments generated from using the actual Year I numbers, or projections will be too good for the young players (less than 27) and too poor for the older (>35) players.  So you either have to use this new aging curve (the one generated from the regressed Year I numbers) when you do your age adjustments in your projections, or you have to change the way you do your regressions in your projection algorithm for young and old players.

As I keep saying, this stuff is really, really tricky and dicey!

Reading some of the links that take me to some of the aging component studies that Tango did, I have the following question as to properly do a component based age adjustment.

Tango lists age adjustments for the following components (that I am interested in).

Hits, XBH, BB, SO, Triples and HRs.

My question becomes how do I properly adjust for doubles and singles and in what order do I apply the age adjustments?

My first inclination is to adjust the HRs, Triples and Hits, as those adjustments are listed.  Then how do I adjust for doubles?  Do I assume the XBH is for doubles?  XBH should refer to doubles, triples AND HRs, right?  After correctly adjusting the doubles tally, I would assume to find the new adjustment for singles you would just (Singles = H-2B-3B-HR).  But I am not sure on how to properly do the age adjustment on doubles.

What is the proper methodology for doing a component based age adjustment given a player projection with the adjustment factors listed above?

vr, Xei

XBH = 2B+3b

And when I do these things, I turn them into “binary” components, and are independent.

See the legend at the bottom of this page for one such way to do these things:
http://www.tangotiger.net/agepatterns.txt

xei,

start with PA
1. calculate HP, BB and SO as pct of PA, the rest are balls contacted
2. calc HR as pct of BC, the rest are BIP
3. calc BH (SI+DO+TR) as pct of BIP
4. calc XBH as pct of BH, then SI=BH-XBH
5. calc TR as pct of XBH, then DO=XBH-DO

59/60. Took a lot of algebra, but I think I got it now.  Thanks!
vr, Xei

Now on hardball times:

http://www.hardballtimes.com/main/article/how-do-baseball-players-age-part-1/

I wish THT would post the “lastest comments” like I do.  How do we know if someone posted on an older article unless we check it ourselves?  Studes, if you need the template, I can send it to you.(*)

MGL posted:

Andrew, I agree with all of that.  As I reiterate throughout the two parts, there really is no one-size fits all aging curve.  And in practice, you are better off addressing each player on a case-by-case basis.

For example, if you have a 31 year-old FA that you are thinking about signing, you would want, at the very least, to look at the aging curves of similar players during the modern era - for example, full-time, 30-32 yo players who have played for X years already.

None of the generic curves I discuss, or JC’s, or anyone else’s, will be much help. You have to look at specific aging patterns for similar-type players, including such things as body-type, speed, injury history, etc.

In addition, a player’s own historical trajectory might give you some idea as to his future trajectory.

Really, the only 3 things you want to take away from this article, including the second part a-coming, is:

One, if you look at players who have already played for 10 seasons and many IP, as JC did, of course you get a very different aging curve than you would expect from any player before the fact, even in the middle of their careers.  To extrapolate that to all players, most players, or even the “generic” player, sans the very part-time ones or the ones with very short careers, is ridiculous, as Tango, Phil B., and many others have already stated.

Two, the modern era appears to have a significantly different aging curve, probably for all players.  i arbitrarily defined the modern era as post-1979, but it could be anything really.

And three, if you absolutely have to answer the question, “What does the average aging curve look like for MLB players, including those who do not have long and/or illustrious careers (and many of these part-time players DO reach their peaks), and what is their peak age,” the answer probably looks something like my last curve, at least in the modern era, although the one in the next installment after I adjust for survivor bias is probably more appropriate.

And that curve (for the “average” MLB player) is not unlike what we have thought all along - a fairly steep ascent until a peak of 27 or 28, and then a gradual decline which gets a little steeper if and when a player gets into his thirties and beyond.  There is simply no way that we can expect a player (not knowing anything else about him, such as body type) who has not already finished a long career (or come close to finishing) to peak at 29 or 30, as JC suggests.

Of course it makes no real practical sense to talk about a player’s peak age and his trajectory after he has already finished his career.

(*) The irony is not lost on me that I now expect Studes to be scouring my comments section to find my post

Part 2:

http://www.hardballtimes.com/main/article/how-do-baseball-players-age-part-2/

I have to say that I find MGL’s article so particularly balanced, that a reader can see why he makes the choices he makes.  And his conclusions are fairly timid enough that he acknowledges a level of uncertainty related to whatever the question being asked.

MGL presents his research as a scientist would.