What is a Normal Career Trajectory?

Since I've been writing about normal and abnormal career trajectories the last few days I'm sure several readers have wondered just what a "normal" career trajectory is.

At first that seems like a simple question to answer. Just calculate the batting average, slugging percentage, or OPS of all players who have played major league baseball at various ages and graph them. While that seems like an obvious answer, things are not so simple. If you proceed along those lines you quickly find that there a lot of players whose careers end at a young age due to poor performance and so the early ages will be biased towards lower values. This will tend to distort the picture and show more improvement with age than is really the case since only the better players will still be playing in their early thirties. This problem is even more pronounced as you get to advanced ages since only players that have been very productive make it past age 35 (Roy Hobbs excepted of course). The end result would be a curve that makes it appear that players remain at a low level into their early thirties and then suddenly improve.

What we need to do instead is perform these calculations on a subset of the player population. What I did was to select all the players whose careers started after 1900 and who appeared in games from 1901 to 1978 and who garnered over 6,000 plate appearances in their careers. By following this methodology I excluded all players who were active in 2003 (Rickey Henderson was a rookie in 1979) and selected only those who had relatively long careers equivalent to being a regular position player for around 10 years. An argument can also be made to only include players who played in 10 or 15 seasons or from ages 21 to 39 or some such span. Conveniently, this also excluded the current crop of players whose suspected chemical enhancement would skew the data – after all we’re after a baseline here. Of course, that's not to say that players in the past did not use other forms of illegal or banned substances. But the presumption is that even if so the problem was less frequent than in the lively player era. This gave me a set of 249 position players.

In order to measure the productivity of a player I chose to use Normalized OPS (NOPS or OPS+) for reasons discussed here. I calculated NOPS by taking the raw OPS and dividing it by the league OPS for each player and multiplying by 100. Values greater than 100 are therefore above the league average. These were then weighted by plate appearances (using only AB+BB since the data for sacrifice hits, hit by pitch, and sacrifices was not available extending across the entire time span). Finally, the weighted values were averaged for each age. I then graphed the NOPS by age discarding the sample sizes under 10 at ages 17,18, 43, 44 (Sam Rice), and 53 (Minnie Minoso) and came up with the following (the yellow line is a three year moving average:



As you can see players with long careers tend to begin their careers just below the league average and quickly surpass it reaching a sustained performance level about 15% greater than the league average when they are 25 to 28 years old. Their peak performance comes at the age of 26 with an NOPS of 115.8. From the age of 28 on, there is a slow descent that begins to accelerate at the age of 33. That continues through their late thirties until they reach about league average again at 40 years old. Of course, as the ages increase past age 33 the sample sizes decrease. This accounts for the slight upsurge in NOPS at age 41 and the flatter nature of the curve at the right end. For those interested in sabermetrics you'll notice that the yellow curve is very similar to one drawn by Bill James way back in the 1987 Baseball Abstract and reflects one of the sabermetric principles I covered in my article Sabermetrics 101.

"Both hitters and pitchers peak at age 27 and decline more quickly than is commonly thought. This should impact how players are scouted, developed, and paid. For example, many players by the time they reach free agency are already past their peak performance and so can be expected to decline."

When you compare this curve with the curves I've posted for Barry Bonds the differences become clear while the curve for Sammy Sosa looks similar to this one. One objection to making that comparison would of course be that the players considered in my "normal" curve did not focus on nutrition and weight lifting as today's players do. I'm certainly supportive of that argument and assume that the curve would show sustained performance at more advanced ages. What it wouldn’t show, however, is increased performance at those advanced ages.

A second objection to making the comparison is that you can't compare one individual with a group average. Once again, I'm sympathetic to the argument and another way to do it would be to compare him directly to other players who have played in as many seasons. However, doing so would only serve to highlight the different career trajectories of Bonds' with Babe Ruth, Hank Aaron, Willie Mays, and others.

And finally, a third objection is that there have been examples of power hitters having their best homerun seasons bunched late in their careers. Clay Davenport recently noted on SABR-L that Hank Aaron's best homerun season came at age 39, Darell Evans at 38, Carlton Fisk at 40, Hank Saur at 37, Andres Galarraga at 35, Harold Baines at 36 and 40, Edgar Martinez at 37, and Cal Ripken at 38. And for many of these players their higher power seasons were bunched at the end of their careers. I don't disagree and certainly believe that power lags total performance. However, in Bonds' case it's not just his power that increased but his total performance including batting average, walks, slugging percentage, and even strikeout ratio. That said, it would be interesting to look at the careers of these individuals as a group when compared to Bonds. Work for another day.