Aging Patterns and Selective SamplingBy Tangotiger
This article first appeared at Fanhome 3 years ago. It predates my grasp (such that it is) of regression towards the mean. It is being reprinted here without any editing.
Selective sampling
What does management know about being able to see the skill-level of a player beyond what the numbers tell us? What if you have a regular player in one year who because of his poor performance in his second year has his playing time reduced? Is this poor performance in his second year an indication that the player's skill-level has diminished, or is it simply a player having some bad luck, and the team not having faith in his skills?
Let's first try to measure the performance of a player. I will use a simple method called Linear Weights Ratio (LWR). You assign weights to each hitting event (1.0 for a single, 1.6 for a double, 2.2 for a triple, 3.0 for a HR, and 0.7 for a walk) and divide the sum of all that by his hitting outs (AB-H). It's sort of a modified slugging average that includes walks and more properly weights each of the events. The historical average in baseball is 0.56, with a typical range of 0.4 to 0.7. Players over 1.0 have had an exceptional season.
Classifying playing time
The next thing to do is to classify players by playing time. I have chosen plate appearance (PA) boundaries of 300+ (regulars), 175+ (platooners), 85+ (bench-warmers), 0+ (September call-ups). That last category also includes if a player missed the season entirely.
Another variable is age. The farther a player is from age 28 the more his performance will change. Therefore, his age is a variable that needs to be controlled. I have chosen 6 age boundaries: 22-, 23-25, 26-28, 29-31, 32-34, 35+. I will denote them as age groups: 21, 24, 27, 30, 33, 36, respectively.
All data reflect players in year x of 1919-1998.
Age Class 27 Data
Ok, let's get to it. There are 4000 players in age class 27 who were regulars. 2500 of them were regulars for 3 consecutive years (years x,x+1,x+2). The LWR for this group of players in these 3 years was .620, .618, .612. So, you have a group of players who management considered to be good enough to be regulars in year x, and who demonstrated a certain skill level. In the following year, x+1, these players continued to demonstrate this level of play, and management continued to give them the playing time. And again in the year following that one, x+2. Since we selected players at their stable peak, we didn't expect to see much if any dropoff and that's what we got.
Let's look at the more interesting case, the one where players were regulars one year (x), then ?? the next year (x+1), and then regulars the year after that (x+2).
PAclass1/lwr1 refers to year x, etc.
So, look at what happens. No matter how much playing time these guys received in year x+1, they ALL reverted back to their first year performance. Look at the 30 guys who were regulars one year, and basically minor-leaguers the next year. They all bounced back to their previous level.
Let's look at regulars in the first year, zeros in the second year, and ?? in the third year.
Here again, players reverted back to their first year performance.
How about guys who were bench-warmers 2 years in a row? (Remember, these are guys 26-28 years old).
These bench-warmers were basically .490 hitters. Whether by talent or by playing time, we don't know. But watch what happens when some of them ARE giving playing time. The bench-warmers who become regulars all of a sudden are .586 hitters. Those who remain bench-warmers maintain their average.
The complete data for Age 27
Here is the whole set of data for the age 27 class. I invite your analysis...
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