Touching BasesJune 03, 2010
WAR Aging Curves
By Jeremy Greenhouse

WAR, short for Wins Above Replacement, is an all-encompassing metric of a player's value. It incorporates hitting, defense, baserunning, durability, and spits out one number. Using Sean Smith's invaluable WAR database, I studied positional player aging.

We know that speed and defense peak early and that power and walks peak late. With WAR, we can throw everything together. Overall player value was originally posited to peak between ages 28-32, but the subject has been revisited and peak age revised to somewhere around 26-30. Here's my basic aging curve.

To develop this curve, I found all examples of players playing in two consecutive seasons, excluding the first and last year's of a player's career, since those tend to be somewhat fluky. I then computed the average difference in WAR between such seasons.

While players between 30 and 35 years old are often the best in the Majors, they are likely in decline. In general, I find that players improve at a decreasing rate until they're 27 or so and then decline at an increasing rate. I'm not trying to toss my hat into the J.C. Bradbury vs. MGL debate, but I'm using that as my benchmark for further aging curves.

My intention is to find how players, given a certain set of characteristics, age as compared to others. Height and weight are fairly consistent attributes, but unfortunately, height and weight data are unreliable for baseball players. Nevertheless, it would make sense that players with different body types would age their own separate ways, so I used body mass index to differentiate between big and small players.

Bigger is better, although the aging curves move along more or less parallel lines. You might say that bigger players age less gracefully than smaller players, but that could be just because they are better and therefore have more room to collapse. Regression to the mean works more heavily on players farther from the mean.

Next, I separated players by career defensive ability, as defined by the sum of the positional and total zone components of WAR.

Bad defenders are good hitters, otherwise they wouldn't play. I would imagine that during a bad defender's peak, he is a passable fielder. But as he ages and his defense deteriorates at a pace that outstrips the offensive decline of good defenders, the good defenders become better all-around players than the bad ones.

Separating by career hitting value,

Bad hitters peak two years earlier than good hitters. My guess is that good hitters use their power, which peaks late, while bad hitters get by with their speed, which peaks early.

Bill James once submitted that "young players with old player's skills...tend to peak early and fade away earlier than other players." Old player skills consist of striking out, walking, hitting for power, and being slow. Separating players by career baserunning value yielded no trend. I also looked at strikeout and walk rates. To do so, I had to limit my sample to years after 1954.

This evidence indicates that high-strikeout players do indeed peak a year earlier than low-strikeout players, but they also have a smoother aging curve than their counterparts. If they fade away faster, it's only because they weren't as good in the first place

By walk rate,

High-walk players actually peak a year later than low-walk players, but fade faster.

There are some lessons on regression to the mean in here. Better players appear to decline quickly because there's more room for them to collapse in case of an injury. I'm not making any conclusions about aging curves for types of players with old player skills or any such subset, since the more specifically I drill down a type of player, the smaller the sample becomes. Even so, big or small, old player skills or no, the Ryan Howard contract was a mistake.


What's the difference between a 'bad' hitter and a 'good' hitter on these charts?

Jeremy, by starting the plot at 0 for both at age 19, you are inadvertenly making it seem like some types of players peak higher than others.

There's two things that you should do:
1. Figure out the actual average WAR peak in wins, and set THAT as the peak point for each curve, and let the starting point float

2. Make both lines intersect at the peak points.

I'll guarantee you that someone is going to interpret your charts incorrectly.

Thank you for these, such information is extremely helpful in thinking about player aging. Not surprised high walk rate players peak later, since learning the ML zone is likely a more lengthy process than we realize. I'll be interested if you do make tangotiger's changes.

I'm puzzled. What's the y axis? What do the lines represent? "[T]he average difference in WAR" makes it sound like the curves represent a first derivative, but the rest of the text makes it sound like they're levels.

Instead of using career ability, should you instead look at their skills at various ages (22, 24, 26, etc...) then compare the sets of curves? There's a lot of issues with the method (it's messy, sample size reduction, added measurement error) - but I'd think using career values is a bit much of an apples-to-oranges thing (one guy might play 15 years, another 7; players of equivalent initial defensive ability can end in different 'buckets' if the better hitting one has a long career and, hence, a longer decline phase; and so on...).

I would be curious to know the distribution of the data. Offhand I would SUSPECT that the standard deviation of WAR is (positively) correlated with age--that the two are not independent. That is, among 37-year-olds you have, say, an Andy Pettite, still a top-flight player, on one end, and washed-up part-time DHs on the other.

Might there also be some sampling bias in that more good players will play longer--the bad ones wash out of the majors at younger ages--which would tend to overstate the relative amount of decline in better players.

Shthar, above 0 vs. below zero hitting runs, according to Rally.

Tango, my bad. Will make points intersect at the peak if I do another aging curve.

Der-K, part of what I liked about what I did was that I was able to compare apples to oranges. Your idea would be great if not for sample size problems.

Ethan, standard deviation of talent by age is interesting. And there's certainly sampling, but I'm not sure what you're getting at.

There is an incredible amount of work to be done along these lines. And I would say that this may be the most valuable information a GM could have. Time and again we see teams award huge long-term contracts to good 30-35 year-old players, and then in a year or 2 or 3, they owe 10s of millions to an unproductive player

I am trying to find someone locally that can tell me if the Dodgers Ball I have from the 1950's with 25 names on it is authentic. The ball was given to my sister by a young man that tried out for the Dodgers, he gave her the ball and she gave it to me and I saved it all these years.
I would br interested in knowing if it is worth anything--then maybe I would put it up for sale.
Thank you for any help you can give me.

P.S. we lived in the mont pleasant area of Schenectady.

Thank you Buck