THE BOOK--Playing The Percentages In Baseball

Very interesting work Tom.  I have always wondered about the interplay of age versus experience involved in the gains in performance during the mid twenties, however.  I think it is probable that the majority of the gain is not due to some inherent physical ability peaking due to the effects of age, but a honing of baseball specific skills due to additional major league experience.  You should be able to regroup the basic data from your study to test for this shouldn’t you? 
My hypothesis is that during the first several years of MLB playing time (or several thousand innings) most of the gains would be due to experience.  After 2 or 3 or 4 years of MLB playing time the gains due to experience would fall off sharply, and effects due to actual physical aging should begin to predominate

This would presume that MLB experience is somehow more relevant than minor league experience, doesn’t it?  (And in this study, with no minor league data, would make minor league experience non-existant.)

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When you try to isolate specific tools, like “speed” (triples per doubles, or SB per CS), it’s apparent that that tool ages very early in a player (early 20s).

I have no doubt that the drop in speed is balanced out against the experience in his mid20s, but that at some point, experience adds very little to nothing, and can’t counteract the diminishing effects of aging.

So, I agree with your hypothesis.  I don’t know if I’d be able to isolate experience in all this.

Great article.  I was curious where the first value for the Chain column came from though (-6 in the first table and -28 in the second one).  Thats just a derived value from the first Delta and second Chain value, right?

Those were selected so that the peak in the CHAIN would be zero.

Cool, thanks

Tango, what is the reason that the amount to regress is not apparently easy to figure out? I recall the same problem in your pitchers component aging article on the other site.

David is referring to this article:
http://www.tangotiger.net/adjacentPitching.html

For the fielders, I actually wanted to do the aging curves for all the positions, before trying to figure out the regression process.  I would also expect less selective sampling for the corner OF and 1B, since you don’t really decide to keep a player or not at those positions if their fielding stinks, unlike SS, where good performance is necessary.

Anyway, I just wanted to see all the data first, before getting too far ahead of myself.

Tango—so if I understand correctly the regression amount is still up for debate?

You would also have reverse selective sampling, no? If a player’s skills are perceived to have diminished in year 2 of any pair, he is moved to another position or does not play much or at all.

So, let’s say that there is a 5 run change in true talent from age 29 to 30. In year 1, we’ll call the combined defense of all SS, zero.  So, in year 2, it will be -5. Now, let’s say that half of the players decline in true talent by 2 runs and half by 8 runs.  And now let’s say that the ones that decline by 8 runs are moved to 2B, 3B or some other position in year 2.

What will the delta look like?  Obviously it will look like -2 runs rather than -5 runs, which it should be.  Exactly the opposite of Tango’s selective sampling, which is also valid.

Is this selective sampling any less prevalent or significant than the one that Tango is talking about?  There has to be some sort of cancelling out effect, no?

My UZR aging curve, assuming no selective sampling, and thus no adjusting or regressing any numbers, shows a gradual decline from age 22 to age 32 or so, and then a precipitous decline after that.  I don’t have the individual positions handy, but IIRC, it is a similar curve for the SS, only the magnitude of the drops is different.

For all UZR, from age 22 to 32, there is only a -10 run drop (per 150).  I think for SS it is twice that or around -2 per year.

So with no regression at all, I am getting a much, much smaller drop than Tango.

Given my results using UZR differ so much from Tango’s, using WOWY, and given that there are at least 2 selective sampling issues to content with, I have abolutely zero confidence in the results, I am afraid.

Even so, I do love the WOWY, as long as there are large samples of players and/or data.  As I have always said, given large enough samples, coarse data is ALMOST ALWAYS better than granular data because there is less chance of error when using coarse data, not to mention the “simplicty and transparency” that some people (not me) love.  I don’t love it because I am more interested in accuracy than anything else (like making it believeable or credible or what have you).

Let’s expand on your illustration.  We take for granted that the true talent drops by 5 runs from age 29 to age 30.  At age 29, the runs of all SS is zero.  At age 30, if all those SS had played at SS, they’d be -5, half of which would be -2 and half of which would be -8. But, you don’t know which half would be -2 and which would be -8.

Let’s go back to the age 29, where all the SS are zero on average.  Of that group, 10 performed at +6 (with true talent of +4), 10 performend and are true talent zero, and 10 performed at -6 (with true talent of -4). 

Come age 30, 9 of the performing +6 are still at SS, 7 of the performing 0 are at SS, and 5 of the performing -6 are at SS.

Now, since we stated as a given that the true talent drop is 5 runs between age 29 and age 30, the performing +6 (true talent +4) of age 29 would be -1 at age 30.  The second group would be -5, and the third group would be -9.

So, let’s add it up:
count, PerformAge29, PerformAge30, group
9, +6, -1, top
7, +0, -5, middle
5, -6, -9, bottom
21, +1.14, -4.24, weighted average

If we knew the true talent level of the 21 surviving SS at age 29, the chart would look like this:
count, TruetalentAge29, PerformAge30, group
9, +4, -1, top
7, +0, -5, middle
5, -4, -9, bottom
21, +0.76, -4.24, weighted average

So, if we see a performance level of our SS that survive into age 30 of +1.14, that needs to be regressed down to +0.76 (33% regression toward the mean in this illustration) in order to estimate their true talent level.

BUT, we don’t have to worry about their age 30, if and only if their being a SS at age 30 was not dependent on how well they played at age 30.  As long as they survived on Apr 1 at age 30 in being a SS, and they weren’t moved off SS in the middle of the year at age 30, their performance at age 30 *is* (as a group) their true talent level.

Now, clearly this doesn’t happen all the time.  So, you do have it going both ways.  But, it’s much more a year 1 function than a year 2 function, I would think.

Here it is for CF:
http://spreadsheets.google.com/pub?key=pkimQBCeCjbinEQ-SULkibQ&gid=1

I broke it up based on whether the pitcher was in his 20s or 30s.  Be careful with the data at the bottom, where the sample size is very tiny.

The chain looks similar to the SS one.

Remember, this is not doing WOWY.  It is doing simply using the same combination of:
- centerfielder
- pitcher
- park
- batterhandedness
in consecutive years, and looking to see of all balls in play, how many did the CF convert into an out.

The average age of the pitcher in the first year and the second year will be roughly the same for each age of the shortstop.  I didn’t look, but say for the pitchers_in_20s sheet, the age of the average age of the pitcher was 26 the first year and 27 the second, and in the pitchers_in_30s sheet, the average age of the pitcher was 32 the first year and 33 the second.  Remember, it doesn’t matter, since for each centerfielder’s age, the age of the pitcher is virtually identical.

It DOES matter in terms of regression, in that the pitchers_in_30s sheet more likely has pitchers in their decline, so the “aging” includes not only the aging of the centerfielder, but an extra oomph of the pitcher aging.

Have fun with it…

Tango brought this up in the mailbag, so I thought I’d come back to this and see what people think. This is based on STATS, Inc. ZR data compiled by SG over at Replacement Level Yankees Weblog. I took a look at players who played a position in both years. A players chances in both seasons was capped at the smaller number.

http://www.editgrid.com/user/cwyers/zr_age_curve_second_pass

Colin,

I don’t have MS Access on my home computer and can’t open SG’s .mdb file for 1987-2007, but when I had looked at his older csv file 1987-2006 there were some data quality issues. [I don’t mean SG’s work, I mean the actual data.] 1) STATS’ ZR for 2000 for outfield did not use the same methodology as other years - popups fielded by outfielders were counted, so the OF ZRs are roughly 10 points higher for that year. The last I knew, prior years appear to have been restated at various web sites according to the current methodology but not that year. 2) prior to 2002 (the first year for which direct statement of opportunities was still available on any public web site), SG was reporting estimates of zone opportunities using the “Dial method” and the “Rally method.” Exact opportunities for many players for 1997-2001 can be found (or reconstructed from) printed sources, and I found that for infielders the Dial/Rally estimates could be off by as much as 100 opportunities in one season. I’ve never corresponded with SG so don’t know if his 2007 database improves on the 2006 version.

At one time I put some work into making my own version of a ZR database (aside from printed sources, you can very often reverse engineer opportunities from plays made as derived from retrosheet event files, then dividing by ZR; the difficulty being that lack of perfect agreement between retrosheet batted ball types and stats batted ball types introduces some ambiguity about whether STATS would have counted it as a play made). However, I put that on hold and pursued less tedious projects.

Additionally, you still have to contend with the selective sampling concerns discussed by Mickey and Tango in comments 9 and 10.

Bottom line: it would be great to look at ZR as a check on aging curves because there’s so much data, covering complete careers, and its flaws are not fatal, but I think to do the necessary aggregation for your study, SG’s work needs to be extended to make opportunities more accurate for older seasons. I think part of the reason I found it tedious was that I had not yet created the necessary cross references for mapping IDs (see links in comment 13 in that topic).

Email me if you want to explore improving his database ...

Colin: can you verify your 3B numbers?  They seem to show the opposite pattern of all the other positions.

To confirm, you did:
PM1 = sum(minCH*ZR1)
PM2 = sum(minCH*ZR2)

where minCH is the minimum of CH1 and CH2

That’s the good way to do it.

Based on your data, every position (except 3B) peaks in his early 20s.

Joe - SG’s IDs were often wrong, using the same ID code for both Ken Griffeys, for example. So I had to go through and remap a lot of the IDs. I have full mappings for RetrosheetIDs in my version now, in addition to the Lahman IDs. I’ll shoot you an e-mail.

Tom: No, but I think I ended up with the same results. I did:

SUM(PM / ActualChances * MinChance)

Which I think gets you to the same thing, it’s just more awkward. I’ll look at the 3B numbers in just a minute.

The aging “curve” for third basemen, just eyeballing it, looks like it has three peaks - one at age 22, one at age 33, and the last at age 42. I think past age 39 there’s really not enough data to do anything with - we’re dealing with one guy that got about four chances a year. The other two humps, though - that’s disconcerting to say the least. The age 22 peak seems to agree with the other data, at least. Where age 33 is coming from, I have no idea. I’ll rewrite the query to show me individual players and look at that.

Spreadsheet updated. There was a bug in the code, so that it was matching a player’s year one with EVERY position he played in year two. That’s fixed now. The 3B aging curve looks a lot better. I haven’t looked at all of them in depth yet.

Same caveats still apply as before - the Dial/Rally method is used to estimate chances prior to 2002, and no regression is used. I’m working on getting better estimates of chances from the Retrosheet data, but my numbers seem wildly off so far. (They correlate extremely well, I’m just severely undercounting outs somehow. I think its missing batted ball data but need to actually confirm that.)

http://camdendepot.com/analysis_infield_age_curves.html

Love to see this stufff…