﻿ The In-Season Aging Curve | The Hardball Times

# The In-Season Aging Curve

One metric says Adrian Beltre, almost 37, figures to have his best month in July. (via Arturo Pardavila III)

Aging is a fact of life, and a fact of baseball. After a certain age, a baseball player must expect to see his performance diminish. They may defy it for a time, but eventually, year by year, the aging curve takes its toll and brings down even the greatest players.

However, even though we measure the process year by year, it does not occur in such large and discrete increments. It is a continuous and gradual process, punctuated by injuries big and small. Theoretically, just as we measure decline from last year to this year, we should be able to measure it last month to this month, or at least beginning of the season to end of the season.

At least I’d think so. Remember, in theory there’s no difference between theory and practice, but in practice there is*. So I decided to test my assumption by measuring monthly performances of older players to find whether their performance declines in-season.

* No, I am not paid by the Yogi Berra-attributed quotation.

I also could have tested the opposite case, to see whether young players show a measurable improvement during the season. A big impediment to this is that ideas about the front end of the aging curve are currently in flux. Recent research has suggested players may no longer climb to a peak but arrive in the majors at a plateau and eventually decline from there.

If this is true, there’s no time in a player’s career in which to measure rising performance, or such a short, shallow rise that one could not glean any in-season progress from the numbers. I might return to the question some day, once we’ve stopped debating the shape of the early curve (if we ever do). For today I will stick with the late curve, whose trajectory is sadly not in dispute.

### Ground Rules

This question involves one of my favorite metrics, tOPS+, which compares a performance split to the total performance, on the standard scale where 100 is average. The split can be for anything, like handedness or home/road play, but in this case it will be for months of the year. I’ll be breaking down each player from April to September* to see how his performance changes.

* Figures for April include any games played in March; those for September include October games (not postseason, of course).

I recognize that batting is not the only measure of a position player’s performance and that, though pitching is a bigger part of the equation for hurlers, it is not the entire picture there, either.

I chose to survey players between the ages of 34 and 37. This is late enough that their decline phases should be well underway but not so old that the sample size for each age shrivels to insignificance. The survey period is from 2011 to 2015.

I considered both batting and pitching, handled separately, of course. Pitchers batting were excluded entirely from the offensive numbers, but if a position player somehow found himself on the mound for more than one game in a season, and in different months, I let it count. The effect on the overall data is microscopic, and it would have felt mean to throw them out.

What was absolutely necessary was that a player have plate appearances, or batters faced, in more than one month. If he played in just one month, I excluded him and his automatic 100 tOPS+ for that month. Leaving such players in would have resulted in dragging all the totals closer to the seasonal mean, especially those for September when so many minor leaguers get called up.

All others with two or more months of measured performance in a season are counted. Gaps at the start, end, or middle of a year, or combinations thereof, don’t keep anybody out of the mix. Players are pro-rated by plate appearances/batters faced in each month (which is why I can be generous with position players who pitch).

Also, I adjusted for league tOPS+, as the offensive environment shifts during each season. For example, run scoring rose markedly in the last two months of the 2015 season, league tOPS+ going from 95.7 in April to 104.0 in September. I took the aggregate for the ’11-15 period, pro-rated by PA, and then altered players’ splits by the necessary amounts.

Crowning the King of Baseball
Administrators of a venerable but little-known award have some work to do.

### The Six-Month Grind

Before going to the results, I will give tables of sample sizes for the ages and months involved. These are skippable if you like, but there are a couple of interesting things that emerge from the data.

PA FOR HITTERS, 2011-2015
 Age M/A May June July Aug. S/O All Mos. 34 5546 5879 5439 5117 5284 5121 32386 35 4500 4929 4525 3987 3789 3512 25242 36 3064 3060 3089 2900 2603 2499 17215 37 2418 2450 2212 2014 2338 1840 13272 All 15528 16318 15265 14018 14014 12972 88115

BF FOR PITCHERS, 2011-2015
 Age M/A May June July Aug. S/O All Mos. 34 4972 6007 5736 5475 5430 4897 32517 35 3940 4563 3917 3839 3880 3376 23515 36 3377 4097 3186 3090 3281 3086 20117 37 2216 2093 2072 1670 1728 1422 11201 All 14505 16760 14911 14074 14319 12781 87350

The totals of plate appearances/batters faced for batters and pitchers come within one percentage point of each other. There is no discernible advantage for either group lasting longer as players, at least in the 34-37 age group. There is a difference in year-by-year patterns, though. Hitters wash out of the majors more steadily, while pitchers go in fits and starts, at least in this sample. Pitching being a more volatile activity, perhaps this is what we should have expected.

The steadiness and volatility carry over to the monthly breakdowns. Hitters’ PAs trend downward more smoothly than the pitchers’, with the May spike definitely stronger for pitchers. Those spikes happen largely because there are fewer April games than May games. Also, the substantial drops in September happen for reasons other than advanced age. September call-ups bring mainly younger players into the league, who will take at-bats and innings away from the rest. This amplifies the downward trend, though I doubt it causes it entirely for the month. (Also, game numbers for August and September/October are almost equal.)

The sample size work done, we can look at the performance, starting with batters. Remember, 100 represents season average for the players, with higher numbers being better.

tOPS+ FIGURES FOR OLDER HITTERS, 2011-2015
 Age M/A May June July Aug. S/O 34 107.5 99.1 95.7 94.3 102.3 101.7 35 102.8 109.6 99.6 91.2 96.6 98.3 36 102.6 105.2 105.6 91.3 99.2 94.5 37 98.6 101.6 101.8 109.9 90.4 100.5 All 103.8 103.8 99.8 95.0 98.2 99.2

I’m glad I cast a wide net. The individual ages tend to be all over the place. The 34-year-olds have two of their better months right at the end, while the 37-year-olds follow up their clear best month in July with their clear worst in August. However, the overall sample does its work in smoothing out the rough patches, if not creating a perfect line.

A rough trendline for these numbers (not weighting for PA numbers) gives a drop of just over one and a quarter points of tOPS+ per month, with an r^2 of 0.49. This would work out to the true aging effect being five-eights of a point of OPS+ per month, or seven and a half per year. As an approximation, that sounds fairly plausible.

We can track the decline another way, by dividing the season into halves. Hitters in April through June produced a 102.5 tOPS+, which dropped to 97.4 for July onward. Taking that drop over three months, midpoint to midpoint, and assuming the same coefficient of determination, that would work out to a loss rate of about 10 OPS+ points per year. The gap is caused by the lower precision of two data points versus six.

Now let’s take a look at the numbers for pitchers. My standard is tOPS+ against, matching the hitters. In this case, a lower number is better for the pitcher, and we’re expecting numbers to rise as the year progresses.

tOPS+ FIGURES FOR OLDER PITCHERS, 2011-2015
 Age M/A May June July Aug. S/O 34 101.5 99.8 95.1 104.8 102.6 97.1 35 91.6 97.3 97.9 104.4 108.4 102.3 36 102.3 100.9 106.5 101.8 99.9 97.0 37 104.7 94.8 85.6 98.5 105.3 118.7 All 97.6 98.8 96.9 103.3 103.9 100.9

The pitchers had some wilder swings, which continues the theme of their volatility. No hitter cohort went 10 points or more from the average in a month, but it happened twice with 37-year-old pitchers, and not by small amounts. Overall deviation from the mean, though, ended up about even: 4.22 points for batters, 4.15 points for pitchers.

The tOPS+ figures get smoother with added samples, just as with the hitters. It’s visually pleasing to see all under-100 numbers in the first half of the season and all over-100 numbers in the second half, even if they’re still bouncing around. For first-half/second-half splits, the numbers are 97.8 up to June, and 102.8 from July onward.

The rough-and-ready trendline shows a shallower decline during the season than for hitters. Pitchers shed 1.1 points of OPS+ per month, with an r^2 of 0.48, meaning the actual aging effect would be closer to half a point per month, or six points per year. Using the r^2 on the half-to-half figures produces a loss rate for aging of 9.6 OPS+ points a year.

To restate: older batters lose effectiveness in-season at about 7.5 to 10 OPS points per year; older pitchers lose effectiveness in-season at six to 9.6 points per year. The data are too rough to state with certainty that older batters decline faster during the season than older pitchers, but it’s at least a working hypothesis.

In a previous discarded draft where I had pitchers declining faster than batters (I accidentally used numbers unadjusted for monthly league run environment), I explained it by the particular punishment suffered by pitchers’ arms. For the reverse case, I have no good explanation, except possibly a species of survivor’s bias. A pitcher with a hurt arm will almost surely stop pitching for a while and not put up numbers handicapped by his injury. Batters are likelier to fight through nagging injuries (which come on faster with encroaching age), with numbers that suffer accordingly. But this is only a guess.

I did want some handle on whether in-season decline is accelerated or retarded compared to overall decline. I can run a check on this for the batters, thanks to some research done by Jeff Zimmerman (who wrote the first aging curve study linked in the introduction). The scale he used for this was wRC+, not OPS+, but the two are similar enough to give a good idea of where we are.

OFFENSIVE DECLINE BY POINTS OF wRC+ LOST, 2006-2015
 Age 34 Age 35 Age 36 Age 37 34 to 37 -4.7 -2.8 -11.5 -10.0 -29.1

Across the four player ages I examined, Zimmerman’s numbers say players will shed on average 29.1 points of wRC+, or 7.275 per season. (This is for the period of 2006 to 2015, which contains all the years I looked at.) However, I need to weight the numbers for the greater number of PAs by the younger players in my samples. Doing so brings the rate down to 6.28 points of wRC+ lost per season.

Zimmerman’s year-round decline rate ends up somewhat slower than the range of in-season rates I calculated. This may be margin-of-error stuff, but it does suggest that batters decline faster from the wear of the season then recuperate enough in the winter months to slow the rate of athletic decline.

To sum up, what I looked for, I found. Older players have measurable declines in their performance as the season progresses, in degrees roughly comparable to the year-to-year rates we see. Batters appear to erode more quickly in-season than pitchers and more quickly than their year-round rates. I can make no conclusion, even a tentative one, on whether pitchers wear down faster in-season than overall.

Were this to happen, though, it would produce an intriguing and somewhat disturbing possibility: that older pitchers who work deep into October due to their teams making playoff runs will pay for it with worsened play the next season, and maybe beyond. This is surely not an original notion, but working on this small study brought it into focus for me. In the next couple of months, I hope to have something more substantive to say on the matter.

### References and Resources

• Baseball-Reference for player data.
• Jeff Zimmerman was generous and timely with his aging curve data, and he has my thanks.
• So does Craig Edwards, who reminded me of Zimmerman’s aging data in the very article I had linked. Just call me “Bonehead” Tourtellotte! (Actually, don’t. I’m a sensitive fellow.)

A writer for The Hardball Times, Shane has been writing about baseball and science fiction since 1997. His stories have been translated into French, Russian and Japanese, and he was nominated for the 2002 Hugo Award.
Guest
AaronB

Shane, nice job. I think the trends do make sense. For the most part, the players, & pitchers especially, wear down as the season progresses.

Any thoughts on doing something similar with younger players? I’m a Cards guy, so watching them last season, it was pretty clear to me that Wong & Wacha wore down as the season progressed, while Carlos Martinez actually seemed to get stronger.

Guest
Brian Cartwright

Thanks for the confirmation.

I use a target date In my Oliver projections, which is the midpoint of the range of game dates. For example, if I’m doing a pre-season projection, the target date is about july 1. If I’m doing a rest-of-season projection on Aug 1, the target date is about Sep 1, so the player has an additional 2 months of aging built into the projection. That doesn’t matter much for a player in his prime, but is noticeable for the older players you studied.

Guest
Jonathan Judge

Neat idea and execution.

Guest
Antonio Bananas

Any correlation to temperature? A few of the lines looked to dip during the hottest months.

Also, how did you control for pitcher opponents? Starters get 5-6 starts/month. If 3 of those happen to be against good or bad teams, that would seems to skew the data. Or for that matter, hitters who had a month with abnormally easy/hard schedules.

Guest

First and foremost, let me say that I have come here this morning without any malice for the beloved Chloé Marcie Bag