September 22, 2005

Lies, Damned Lies

A New Look at Aging

by Nate Silver

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This week’s column was originally supposed to be a break from the usual LDL routine, inspired by Tuesday night’s fantastic white Sox/Indians game, which I got to take in with New York Sun buddy Tim Marchman. Tim and I have some mysterious, voodoo-like power when we go to Sox games together. Earlier this year, Carl Everett, baseball’s best-known proponent of intelligent design theory, came to the plate in a game against the Twins, and Tim, who might or might not have joined me in enjoying a couple of beers, screamed “Hit One For Jesus!” Everett promptly smacked a two-run homer on the next Kyle Lohse pitch.

This time around, our powers worked in reverse: Joe Crede was up against Jake Westbrook in the bottom of the third, and we were having a lively conversation about what was wrong with Crede’s game, and how he had failed to live up to expectations. My famous last words were: “it’s making hitters like Joe Crede look stupid that keeps pitchers like Jake Westbrook in the game." Next pitch? Boom, two-run homer. Crede followed suit with his walk-off job in the tenth, a home run that bore some eerie resemblance to the Aaron Fricking Boone shot: underachieving third baseman, first pitch of the inning against a junkballing reliever, healthy shot to left field. Boone, incidentally, also hit a home run in the game, as did Casey Blake--the two Indians I had taken special care to dis in a column earlier this season. Sadly for White Sox fans, neither positive (“hey, Mitch Williams was fun!”) nor negative thoughts (“maybe Guillen really is insane”) could get Bobby Jenks to throw strikes, which would apparently take Eric Gregg’s being nominated to Sandra Day O’Conner’s vacant seat.

In any event, it was one of those games that really reinforced the notion that, as smart as we analysts might think we can be, our science can’t entirely do justice to the drama, art, and utter randomness that a September pennant race game can provide. Joe Sheehan riffed eloquently on this exact theme, which is why we’ll be moving on to a regular LDL full of graphs and charts and database searches in a moment. But I’ll conclude this detour by noting that poker theorists such as David Sklansky and Mason Malmuth have commented that poker (particularly Texas Hold ‘Em) represents a perfect balance of luck and skill: enough skill to reward correct strategy over the long run, but enough luck to allow the fish to have their days, and generally keep things interesting. Pretty much the same thing can be said about baseball.

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Today’s topic, then, is going to be on the differences in aging patterns by position. You’ll sometimes hear one of us say things like “middle infielders don’t age very well,” and while I’m sure there have been studies on this subject, we haven’t usually bothered to cite one of them. This article is intended to provide some simple benchmarks on the subject.

The method that I’ll apply is to compare the number of Equivalent Runs (EqR) produced by players at a given position and a given age over consecutive seasons. For example, if the cohort of shortstops produces an average of 70 EqR when they’re 23, but an average of 77 EqR the next year when they’ve turned 24, we can say that the average improvement by a 24-year-old shortstop is 10%. All the numbers here were pulled out of the PECOTA major-league database, which means that everything is park- and league- adjusted, and that only post-WWII players are included. Players are classified by their primary defensive position in the first of the two consecutive seasons: for example, while Alex Rodriguez became a third baseman at age 28, the study classifies him as a shortstop for that season since that’s where he played in his age-27 year.

The only real tricky part here is to figure out what to do about playing time. After some trial and error, I settled on a method that Clay Davenport employs in his league translation work, which is to weight the EqR based on the minimum number of plate appearances between the consecutive seasons. Another approach would have been to use a rate statistic like EqA and apply some minimum threshold of plate appearances. This didn’t feel appropriate because it neglects the impact of a player losing playing time due to injuries or being benched because of an inability to perform substantially above replacement level, which become key concerns as a player ages. On the other hand, using a counting stat but not weighting it at all could put too much emphasis on playing time. If a rookie gets called up during August of his age-22 season, and then spends the whole year in the big leagues at age 23, his EqR total is almost certainly going to improve, even if his underlying performance really hasn’t. This player remains in the study under my method, but his weighting will be dinged because he played only a partial season at age 22, so he won’t figure very prominently.

Here is the typical career track for a center fielder:

Age        Change      EqR Track
21          --           50.0
22       +19.0%          59.5
23       +10.3%          65.6
24        +6.9%          70.1
25        +2.2%          71.6
26        +6.3%          76.1
27        -3.2%          73.7
28        -5.0%          70.0
29        -4.7%          66.7
30        -4.5%          63.7
31        -6.3%          59.7
32       -11.0%          53.1
33        -6.5%          49.7
34       -14.4%          42.5
35        -8.6%          38.9
36        -8.9%          35.5

“Change” is the average year-over-year difference in EqR I described earlier. Note that the pattern is basically what we’d anticipate: rapid improvement through the early twenties, a peak at 26 or 27, a plateau period where the player loses just a handful of value each season, and finally some more serious deceleration after a player enters his thirties. The numbers bounce around some, particularly for the very oldest and very youngest players, which attests to the fact that we’re dealing with somewhat limited sample sizes.

The “change” numbers can be extrapolated into a typical career path, which I’m calling "EqR Track." For example, we assume that the player starts off by putting up 50 EqR in his rookie season at age 21, improves on that figure by the 19% number given by our model to 59.5 at age 22, tacks on another 10% improvement at age 23, and so forth. Add in some exponential smoothing, courtesy of Microsoft Excel, and you wind up with a nice looking graph. Note that I’m classifying everything by percentage of peak value, which I’ve defined here as the average of a player’s EqR Track between his age-26 and age-27 seasons (it turns out under this method that player performance is essentially unchanged between ages 26 and 27, which suggests that the typical peak comes somewhere between those ages).

 

This graph isn’t very useful, of course, without a comparison to players at other positions:

 

So center fielders, for example, have a rather typical looking career path, with the exception that they peak just a tiny bit earlier than players at other positions. This result came as a slight surprise; I associate center fielders with athletic, multitalented players like Jim Edmonds, Andruw Jones and Carlos Beltran, and those types of players tend to age very well. But center field is also home to lots of guys in the Willy Taveras mold--players whose games are pretty much entirely dependant on their speed. Once the speed goes--and speed evaporates more quickly than any other baseball skill--those guys become useless very quickly: they won’t have the range they once did, can’t do as much damage on the basepaths, and will see their batting averages drop as they can’t leg out as many base hits. Center field, like shortstop, is a position that is often home to the best player on the field, and is also often home to the worst one.

Next, we’ll turn to corner outfielders. I know that left field and right field are separate positions that require slightly different defensive skills, but lots of guys can play them interchangeably, and if lumping them together is good enough for Scoresheet Baseball, it’s good enough for me.

 

The peak comes at about the right place for the corner outfielders; for most of these guys, the primary skill is power, and power continues to develop relatively late into the twenties. On the other hand, the decline occurs somewhat quicker, probably indicating an underlying lack of athleticism, and having no place on the diamond to go if defense lapses to Glenallen Hill levels. In addition, the very young (21- and 22-year old) corner outfielders that come into the league tend to be relatively major-league ready, which perhaps reflects the fact that teams don’t tend to fool around with projects at these positions.

First basemen check in as pretty much par for the course:

 

You might detect just a very slightly elongated plateau phase in the late 20s, which is mitigated by an especially sharp 12% drop between 31 and 32. I might have expected the first basemen to replicate the corner outfield pattern a little bit more completely. It’s worth remembering, however, that first base represents the sort of alter ego of the Peter Principle at work: a player descends through the defensive spectrum until he arrives at first, a position that almost everyone can play with some bare minimum of competence. All players are subject to this erosion in defensive skill, and so it makes some sense that the aging patterns for first basemen tend to look much like the group average.

Moving violently from the right side of the defensive spectrum to the left:

 

Catchers are one of two positions--we’ll get to the other in a moment--at which the divergence from normal aging patterns is unmistakable. There is no good news here; these guys take a long time to get ready and decline very quickly once they do. Some of the slow ascent may be due to their team's reluctance to give playing time to young catchers whom pitchers aren’t quite comfortable working with, but the fact remains that catcher is a unique position that demands different skills and rewards a different, less athletic body type than anywhere else on the diamond. Couple that with the wear and tear that the playing the position entails, and things like the Ivan Rodriguez deal begin to look very silly.

But the funkiest career track of all belongs to second basemen:

 

You can perhaps ignore the weird blip in the graph between ages 21 and 22--we’re dealing with some small sample sizes there. But you can’t ignore the fact that second basemen display very sluggish improvement between 23 and 26. The typical second baseman has already achieved 95% of his peak value by age 23--versus just 84% for the league as a whole. These guys just don’t improve their games as much as players at other positions. And making matters worse, second basemen decline somewhat faster than normal in their thirties.

This point has been made before, but second base is something of a bastard position--it’s where you wind up if you aren’t athletic enough to play shortstop, but don’t have the bat (or the arm) for third. Almost no players are selected as second basemen in the amateur draft, and it’s rare to see a second baseman on a top prospect list. That is, second base is the one position where players are selected out for their lack of a skill, rather than their possession of one; it should be no surprise that they don’t tend to age well. There have been a couple of second basemen like Joe Gordon and Jeff Kent that have peaked notably late, but those guys go against type.

Analysts sometimes classify shortstops with second basemen, but the aging patterns aren’t quite the same:

 

Like second basemen, shortstops come into the league with a higher-than-usual percentage of their peak value intact. I suspect this is because, with a few obvious exceptions, shortstops are speedy, slap-hitting types, and speed and contact hitting are skills that come early. On the other hand, shortstops do tend to be good athletes, and they age perfectly well, at least up through age 32 or so.

We’ll complete the cycle by turning to the hot corner.

 

Third base is the one position with a definitively late peak--the only position, for example, where a player is on average more valuable at age 29 than he is at 25. The minor trade-off is that third basemen do tend to collapse quickly at 35 or so once their nerves and reflexes are gone; that is also about the age at which many professional golfers cease to be competitive. Although third base is arguably a hard defensive position to learn--these guys don’t field as many balls as players elsewhere on the field--I suspect the late peak has more to do with a typical third baseman’s offensive profile. Generally, third basemen are slow and need to be bulky enough to generate arm strength, which holds down their batting averages; since 1946, third base rates as having the third-worst BA on the field, ahead of only shortstop and catcher. But third basemen are expected to make some offensive contribution, and they tend to provide it with good secondary averages. Walk rate and power peak late, and so do third basemen.

Someone like Mike Lowell or Robin Ventura fits the pattern almost perfectly. So, at least to some extent, does Joe Crede. Perhaps, just perhaps, we should have seen Tuesday night coming after all.

Nate Silver is an author of Baseball Prospectus. 
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