Aging Curve

February 27, 2010

In order to make decisions about players, we need to know how good they are presently and how those skills will improve or decline in the future. Even if you don’t subscribe to the notion of statistical projection, you certainly agree with the concept of estimating how good a player is going to be. If you need a second baseman and Ben Zobrist asks for $56 million, you have to decide if you think he will be worth that to you over the four years. You can use whatever method you want to arrive at that estimate of value, but you have to have an estimate of value to make a judgement about the deal.

Let’s say we’re talking about a 3 WAR player who is slightly above average on defense and nicely above average at the plate. It’s our best guess about how good the player is at the moment. It could be a wrong guess, but it’s the best we have. Next we have to decide how good the player will be in years 2, 3, and 4 of the deal. After we develop an estimate of his Year 1 talent, how do we estimate his Year 2-4 talent despite no new information from Year 1 (because it hasn’t happened yet)?

We have to apply an aging curve. Simply put, an aging curve represents the average improvement or decline expected based on the player’s age. Human beings generally can’t run as fast at 36 as they can at 26. They get injured and tired more easily. Sometimes their vision or hand-eye coordination diminishes. No two players bodies age in exactly the same way, but overall there are consistent trends.

For example, players are typically much better overall at 27 then they are at 37. Pitchers lose velocity as they age. Base running ability peaks early. There’s no single rule that says a player gains 0.020 wOBA from 26 to 27, but the patterns we can observe from the rest of the MLB population can help us forecast what will happen to a player in the future given what we know about them in the present.

There are two dimensions to this. One is skill-based and one is playing time-based. As you get older, you’re more likely to get hurt and you’re more likely to perform worse when you are healthy. Both need to be applied to players as they age.

Additionally, aging curves can vary based on era and player type. Sluggers in the 1990s probably age differently than defense-first players of the 2010s. This isn’t to say that the age completely differently, just that they the precise shape might look a little different. A recent aging curve study by Jeff Zimmerman gives us this:

And here’s one from Mitchel Litchman’s 2009 piece at The Hardball Times (Part 1 and Part 2):

There is plenty more research on the subject, too. A sampling:

The basic idea is that given skills and player types age a certain way on average. We can project individual player talent at a given point in time, but if we want to decide how good they will be in two years, we have to take their current ability and forecast how they will age. Using aging curves is a simple way to do that.

Keep in mind that aging curves are averages and that some players will do better or worse for lots of reasons. They are guides, not rules. Some of the main beliefs about aging are that defense and running peak early, hitters start to decline around 30, and that pitchers lose velocity pretty much from the day they make the majors. To that end, a basic rule of thumb is that once a player gets to 30, you sort of expect them to lose about 0.5 WAR per year of value due to aging. Some players will age better or worse, but that’s an average estimate.

So if you have a 3 WAR player and expect him to age normally, your four year values are: 3, 2.5, 2, and 1.5. That totals 9 WAR over 4 seasons. At this point, you have to decide how much one win is worth to your team to decide if the contract was smart, but our understanding is that the average cost of one win on the free agent market is about $8M/WAR in 2016. Teams may have incentives to follow a different number, but that’s outside the scope here.

Aging is based on the premise that players skills and health will change over time and aging curves are developed by comparing players across many years. There is some disagreement about whether hitters improve until they peak around 27-28 or if it’s more of a flat line from 22 until 28 when they start to decline. The jury is still out because a lot of our original premises were based on some data from the Steroid Era.

The simple truth is that players age in somewhat predictable manners and if you want to evaluate a player into the future, applying an aging factor to their present value is a good way to go. There are all sorts of little complexities in calculating the right curve, but the idea that we should look at past player aging to make decisions about the future of current players is easy to follow.

-Neil Weinberg