Did Roger Clemens Have the Best Age-Adjusted Season Ever in 2005?

I originally posted this to Beyond the Box Score in 2006.

When a 42 year-old pitcher has a 1.87 ERA in 211 innings pitched, you can’t help wondering if he did something unusual for his age. This is a great season for someone in their prime. But how to measure this? I tried a couple of different ways.

First, I looked at every pitcher’s RSAA with 150 or more innings pitched from 1920-2005. RSAA is a stat Lee Sinins uses in his “Complete Baseball Encyclopedia.” It is “Runs saved against average. It's the amount of runs that a pitcher saved vs. what an average pitcher would have allowed.” It can be negative and is park adjusted. To adjust RSAA for age, I multiplied each of these pitcher’s RSAA times the absolute value of their age minus the typical peak age. To get peak age, I found the average age for the 250 best RSAA seasons from 1920-2005. It was 28.93. So the farther away from the peak age a pitcher was, the bigger bonus he got. Of course, the farther away from the peak age a pitcher gets, the less likely he is to have a high RSAA (I did not include pre-1920 or dead ball era seasons since there were so few HRs hit then, making the pitching environment much different).

Pitcher	YEAR	RSAA	AGE	Age Points
Roger Clemens	2005	53	42	692.77
Dazzy Vance	1930	64	39	644.55
Randy Johnson	2002	62	38	562.41
Grover C Alexander	1927	50	40	553.56
Randy Johnson	2004	50	40	553.56
Lefty Grove	1939	54	39	543.84
Dwight Gooden	1985	58	20	517.87
Lefty Grove	1936	70	36	494.98
Randy Johnson	2001	59	37	476.20
Phil Niekro	1978	46	39	463.27

Clemens had an RSAA of 53 in 2005. His age minus 28.93 is 13.07. That times 53 is 692.71 “age points (the difference is due to rounding). So by this measure, yes, Clemens had the best age adjusted season. Notice that there is a “young” pitcher here, Dwight Gooden from 1985. He had a great year but was not close to the peak age. So he had one of the best age adjusted seasons.

But by how much did Clemens exceed the expected RSAA for a 42 year-old pitcher? We can’t simply see how much each guy exceed the average RSAA for each age because its possible that a pitcher must be pretty good to be used at very young and very old ages. Table 2 shows the average RSAA for all pitchers with 150 or IP from 1920-2005 by age.

AGE	RSAA
19	8.60
20	10.89
21	3.75
22	3.47
23	4.83
24	5.70
25	5.83
26	6.59
27	5.48
28	5.47
29	6.51
30	6.82
31	6.36
32	5.96
33	7.26
34	7.32
35	8.64
36	8.92
37	8.52
38	7.64
39	10.33
40	11.25
41	3.44
42	6.25
43	0.67
44	4.29
45	2.20
46	-5.00
47	-4.00

Notice that the RSAA is much higher for ages 39 and 40 than for ages 27-30. There were only 40 pitchers aged 39 while there were 123 at age 27. So the old pitchers are not necessarily as good as the young pitchers or there would be more “old” pitchers. It seems only the good ones are allowed to keep pitching at an advanced age. To get an idea of a truer aging pattern, I looked only at pitchers who had at least 10 seasons with 150+ IP. I wanted to only include “good” pitchers since you have to be good to pitch this long. This helps reduce the problem illustrated by Table 2 and allows us to see how performance changes with age. The graph below shows this pattern.

The graph shows the average RSAA for each age from 19 to 47 for pitchers who had at least 10 seasons with 150+ IP.  Notice the equation y = -0.0556x² + 3.1648x - 30.949. It tells us the mathematical relationship between age and RSAA with y being RSAA and x being age. The R² says that 85.42% of the variation in RSAA is explained by age. This equation is a second order polynomial

Since this only applies to the select group of “good” pitchers who had at least 10 seasons with 150+ IP, I had to make an adjustment to apply it to all pitchers. All pitchers in this group had an average RSAA of 6.23 while the “good” pitchers had 12.28. The difference is 6.05. To apply the equation to all pitchers, I reduced the intercept (-30.949) in the equation by 6.05. So it became about –37. To predict any pitcher’s expected RSAA based on age, I used the equation

RSAA = -0.0556*AGE² + 3.1648*AGE – 37

This allows all pitchers to have a realistic aging pattern and it is adjusted downward to reflect the lower quality of all pitchers as opposed to the “good” pitchers who had at least 10 seasons with 150+ IP. Each pitcher had their RSAA predicted based on their age and this equation. Then their predicted RSAA was subtracted from their actual RSAA. The more they exceeded their predicted RSAA, the better their “age adjusted” performance. Table 3 below shows the top 20 seasons.

Pitcher	YEAR	AGE	RSAA	Pred	Diff
Pedro Martinez	2000	28	77	8.03	68.98
Lefty Grove	1932	32	75	7.34	67.66
Lefty Grove	1931	31	75	7.68	67.32
Lefty Grove	1936	36	70	4.88	65.12
Pedro Martinez	1999	27	71	7.92	63.08
Roger Clemens	1997	34	69	6.33	62.67
Dazzy Vance	1930	39	64	1.86	62.14
Lefty Gomez	1937	28	69	8.03	60.98
Red Faber	1921	32	68	7.34	60.66
Lefty Grove	1935	35	65	5.66	59.34
Dizzy Dean	1934	24	66	6.93	59.07
Randy Johnson	2002	38	62	2.98	59.02
Dolf Luque	1923	32	66	7.34	58.66
Pedro Martinez	1997	25	65	7.37	57.63
Lefty Grove	1930	30	64	7.91	56.10
Greg Maddux	1995	29	64	8.02	55.98
Roger Clemens	2005	42	53	-2.16	55.16
Randy Johnson	2001	37	59	3.98	55.02
Frank Sullivan	1955	25	62	7.37	54.63
Randy Johnson	1999	35	60	5.66	54.34

Clemens 2005 does well, at 17^th (out of 6,690 pitchers). But it was not the best age adjusted year ever. If you plug in 28 into the equation, you get 8.03. That is the expected RSAA for a 28 year-old pitcher. But since Pedro Martinez actually had an RSAA of 77, he exceeded his prediction by 68.98. No other pitcher beat the trend by more. Some of the pitchers are old by baseball standards, but not all of them.

One aspect of RSAA is that the fielders will have a role. The better the fielders behind the pitcher, the higher the RSAA. Next week I will do the same analysis but with a defense or fielding independent measure of pitching. This will isolate the age adjusted performance solely due to the pitcher.

Here is a response to one of the comments

Anyone close to the average peak age has no chance. My rationale was to try to reward both being good and far away from the peak age. I agree that method 1 is not perfect. So that is why I did method 2. Notice there that the best guy is Pedro Martinez at age 28, close to the peak age.

Yes, I could square the age difference. Here are the top 20 from the pitchers with 150+ IP from 1920-2005

Pitcher    YEAR    AGE    RSAA    pts
Roger Clemens    2005    42    53    9053.7197
Dazzy Vance    1930    39    64    6489.9136
Jack Quinn    1928    44    27    6131.8323
Randy Johnson    2004    40    50    6127.245
GrovC Alexander    1927    40    50    6127.245
Lefty Grove    1939    39    54    5475.8646
Randy Johnson    2002    38    62    5100.4238
Nolan Ryan    1991    44    21    4769.2029
Phil Niekro    1978    39    46    4664.6254
Roger Clemens    2004    41    32    4661.9168
Dwight Gooden    1985    20    58    4625.2042
Ted Lyons    1942    41    30    4370.547
Bob Feller    1939    20    51    4066.9899
Jack Quinn    1926    42    23    3928.9727
Phil Niekro    1984    45    15    3873.6735
Randy Johnson    2001    37    59    3842.3691
Phil Niekro    1979    40    30    3676.347
Jack Quinn    1924    40    30    3676.347
Don Drysdale    1957    20    45    3588.5205
Nolan Ryan    1989    42    21    3587.3229