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).

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.

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*AGE^{2} + 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.

Clemens 2005 does well, at 17th (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.

## Connect with Beyond the Box Score