I previously looked at some UZR aging curves for each position here at Beyond the Box Score. I decided to take that study one step further and do a comparison of the individual components of UZR (Arm, Range, Double Play, Error and Total UZR) as players age. For this article, I looked only at the outfield positions and will look at the infield positions next time .
Simple explanation of calculations
I took players that played the same outfield position two years in a row and compared how their UZR components -- Range, Arm, Errors and Total UZR (there's no double play calculations for outfielders) -- changed as a player aged.
A teaser graph is below. Position-specific graphs, methodology details, and discussion are after the jump.
Complex explanation of calculations (Feel free to skip to the results then come back to this part. Seriously.)
I downloaded all the players available from Fangraphs that have UZR numbers, which are player-seaons from 2002 to 2008. I created matched pairs using players who played the same outfield position for at least 20 innings two years in a row.
Then I found the harmonic mean of the two inning totals (HMI) (discussion on it at from #11 to #18 on The Book Blog) so I could weight the importance of each matched pair appropriately. Matched pairs with more innings are more meaningful, and we need a way to weight the two innings totals within a pair.
Harmonic mean = 2 / [(1/number of innings in one season)+(1/number of innings in next season)]
200 innings at age 25
100 innings at age 26
Harmonic Mean Innings between 25 and 26 = 2/((1/200)+(1/100)) = 133.3 innings
Once I had the HMIs calculated, I pro-rated the component UZR values each season from the actual innings played to the HMI. Let's look at the same player and assume he had the following stats (remember all the component values will add up to the UZR value.):
Range, Error and Arm = 1
UZR = 3
Innings = 200
Range, Error and Arm = 1
UZR = 3
Innings = 100
Age 25 Adj
Range, Error and Arm = 1 * (133.33/200) = .67
UZR [Range+Error+Arm] = 3 * (133.33/200) = 2
Age 26 Adj
Range, Error and Arm = 1 * (133.33/100) = 1.3
UZR UZR [Range+Error+Arm] = 3 * (133.33/100) = 4
Next, I subtracted the younger age values from the older age values for each component to find the change in defensive value. I will continue on with the previous example:
Age 26 - Age 25
Range, Error and Arm = 1.333 - 0.667 = 0.666
UZR = 4 - 2 = 2
The preceding calculations were done for all the matched pairs. Then the changes in defensive value and HMIs of all matched pairs were grouped together by age of the second year. The components of each pair were added up along with the HMI to get a total for that age. Finally, the totals were pro-rated to 1350 HMI, which is 150 nine inning games, or about one nearly-full season.
Age 25 to Age 26
Range = 6
Error = 5
Arm = 4
UZR = 15
HMI = 5000, note that 5000/1350 = 3.704
Range = 6/3.704 = 1.620
Error = 5/3.704 = 1.350
Arm = 4/3.704 = 1.080
UZR = 15/3.704 = 4.050
The number of complete seasons are small for the early 20's and late 30's age brackets. Here is a graph of the number of complete matched pair season for each age.
Because of a lack of data, I didn't use numbers for 22 or younger pairs or 36 and older pairs for my final results.
Once these numbers were calculated, I graphed them for each position. After adjusting for the number of innings played, finally I took all the outfield positions and combined and graphed their numbers. Now that you are completely lost on the background calculations, let's look at the results...
Here are the graphs for change in component UZR values for the three outfield positions and all positions combined. I assumed the player had an average value for all attributes at age 22, and then plotted how his numbers would change as he aged:
- All three positions trend generally the same.
- UZR trends down at -2 UZR from ages 24 to 30. After that point it remains relatively steady.
- The main contributor for the declining UZR is the decline in Range.
- Arm values also decrease from age 24 to age 30 by about 1 run per year, but then actually begin to increase at 0.5 per year. The reason for this trend isn't readily apparent, but I have two possible explanations, neither backed by any facts:
1. Players are continuing to add muscle mass as they get older.
2. This increase might be a direct result of their range decreasing. Since the old guy on the field doesn't get to as many balls at the fence, he doesn't get his arm tested as much.
- Error rate is fairly constant across all ages.
There they are, your UZR component aging curves. I know you can all now sleep at night, unless you are one of the hardcore few that just can't wait for the infielder curves, which should be coming soon. As always, I am open to suggestions and comments.