from Amazon
Thursday, April 08, 2010
When do pitchers peak?
I took Rally’s WAR database for all pitchers born between 1926 and 1966. I summed up each pitcher’s WAR by age and each pitcher’s IP by age, and figured that age’s WAR per 9 IP. For example, pitchers aged 24 years old were an average of .070 wins per 9IP above replacement. The best rate was put up by 38 year old pitchers, as they were .095 wins per 9IP. Now, naturally, the ONLY pitchers pitching at that age are the really good ones. So, in addition to knowing the WAR of the surviving pitchers, we need to know how many survivors we’ve had.
The 24-yr olds had 90 thousand innings, while the 38-yr olds had 17 thousand innings. Had I limited my 24 year olds to the best pitchers at that age totalling 17 thousand innings, I’d have had a much better rate than .070 wins per game.
However, what if I find an age that is both higher than 90 thousand innings AND higher than .070 wins per game? Well, then in that case, it’s unambiguous: this age has the higher peak performance. Here’s the data:
Age WAR_per_Game IP
16 -0.450 20
17 -0.074 61
18 -0.038 563
19 0.034 2628
20 0.058 7471
21 0.073 20754
22 0.064 39879
23 0.070 64129
24 0.070 90850
25 0.072 115991
26 0.076 130124
27 0.076 134617
28 0.077 122329
29 0.081 111315
30 0.087 97852
31 0.085 83333
32 0.084 72144
33 0.083 60879
34 0.089 51076
35 0.085 40027
36 0.094 31697
37 0.090 23557
38 0.095 17404
39 0.089 12600
40 0.084 9878
41 0.086 6958
42 0.069 4746
43 0.065 2733
44 0.077 1879
45 0.086 1498
46 0.003 694
47 0.030 210
48 -0.026 139
The peak age in terms of innings pitched is age 27. In addition, it is symmetrical around age 27 between the ages of 24-30.
The AVERAGE age of a pitcher (that is, his age weighted by his IP) is 28.7 years old. There are as many innings thrown by 26 and younger as there is by 31 and older as there is by 27-30 year olds. That is, breaking up the IP in thirds, and the boundaries are 16-26, 27-30, 31-48.
What can we say without ambiguity, looking at this data? Well, age 23 is a higher peak than age 22 (better wins per game, and more IP). Age 24 is a higher peak than 23. Age 25 is higher than 24. Age 26 is higher than 25. Age 27 is higher than 26. The peak age is AT A MINIMUM age 27.
At age 28, the number of IP goes down, but the performance per game goes slightly up (the bad guys are discarded, causing this effect). Had the bad guys remained, what would have happened? Could we just give them a WAR of 0? If we do, then age 27 is easily the higher one, as the gross WAR is 1137 at age 27 and 1047 at age 28. But, what if we give the bad guys a WAR of .03 wins per game? In that case, we’re adding an extra 41 wins, still not enough to catch up. Indeed, you’d have to give them a WAR of +.07 per game to the bad/missing IP in order for age 28 to overtake age 27.
So, it’s clear enough: age 27 IS the peak age for pitchers. And since we see that adding in a WAR value of something above 0 still doesn’t change our conclusion, we may as well just simply go by total WAR, here are those totals:
Age totWAR
16 -1
17 -1
18 -2
19 10
20 48
21 168
22 283
23 500
24 709
25 929
26 1,097
27 1,135
28 1,047
29 1,006
30 945
31 783
32 672
33 562
34 504
35 380
36 331
37 236
38 183
39 125
40 92
41 67
42 36
43 20
44 16
45 14
46 0
47 1
48 0
The average WAR age (WAR weighted by IP) is 29.1 years old.
For those looking to show that the peak age is both 27 and 29, that’s how you do it. The actual peak of the mountain is 27. But, the average height of the mountain is 29.
In no way is the peak age of a pitcher anything less than 27.
Indeed, the total WAR pretty much matches the total IP that I think we can simply use IP as the metric to establish the peak age. It’ll at least serve as a sanity check.