## Friday, June 20, 2014

### Did Roger Clemens Have the Best Age-Adjusted Season Ever in 2005? Part 2.

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

Did Roger Clemens Have the Best Age-Adjusted Season Ever in 2005? Part 2.

I looked at this question earlier this week. The stat I used to measure pitcher performance was RSAA, which tells us how many runs a pitcher saves above average (it is also park adjusted). But it is affected by the quality of the fielders. Now I will look at the issue by trying to create a defense independent stat to rate the pitchers, following the idea of Voros McCracken who found that pitchers have little influence over what happens on balls in play. The measure I will use won’t be as sophisticated as the one he uses, but it will give us some idea of which pitchers did better than we might have expected based on their age while removing the influence of the fielders.

First, I found all pitcher seasons with 150 or more IP from 1920-2005. Then I ran a regression with each pitcher’s ERA relative to the league average being the dependent variable and strikeouts, HRs and walks (all relative to the league average) being the independent variables (data is from the  Lee Sinins “Complete Baseball Encyclopedia,”). Here is the regression equation:

(1) Rel ERA = .658 + .279*BB + .242*HR - .201*SO

Again, these are all relative to the league average. Each pitcher’s stats can be plugged into this formula to get their defense independent relative ERA (the correct term might be fielding independent, but I’m not sure). In any case, this is their expected relative ERA based only on stats that they are responsible. Once I had this for all pitchers in the study, I cut down the total to only pitchers who had at least 10 seasons with 150+ IP. Then I found the relationship betwee this predicted relative ERA (or defense independent ERA or DIPS ERA) and age. The graph below shows the relationship.

This graph covers the ages 22-44 for pitchers who had at least 10 seasons with 150+ IP. There were a few ages younger and older than this, but not many. The relationship was actually better when only these ages was covered. The numbers in the graph are the average DIPS ERA for each age in this sub-group of pitchers.

I could have just used the average DIPS ERA for each age for all the pitchers. But we can’t simply find the average DIPS ERA for each age because its possible that a pitcher must be pretty good to be used at very young and/or very old ages. Sometimes the average for very old ages is pretty high because only good pitchers are still around. By only looking at pitchers who had at least 10 seasons with 150+ IP, we get a more realistic aging pattern since this group is likely to be pretty good and we therefore don’t have to worry about the old guys being good since all of these guys are good since they pitched so long.

The equation which shows the relationship between DIPS ERA and AGE

(2) DIPS ERA = .00052*AGESQUARED - .0322*AGE + 1.3755

But this was for the pitchers who had at least 10 seasons with 150+ IP. For all the pitchers, I assumed they had the same aging pattern, but I moved the intercept up to take into account the inferior quality as compared to the smaller group. The shift in the intercept was equal to the the difference in average DIPS ERA between the whole group of pitchers (.9466) and the smaller group (.9011). That was .0455. That got added to 1.3755, making the intercept 1.421. So the equation to predict DIPS ERA becomes

(3) DIPS ERA = .00052*AGESQUARED - .0322*AGE + 1.421

Now each pitcher’s age was plugged into equation (3) to get a predicted DIPS ERA. Then that got compared to the value from equation (1). Let’s take Dazzy Vance from 1925, example (age 34). His predicted DIPS ERA would be be .9042 based on that age (plugging an AGE of 34 into equation (3)). But his DIPS ERA from equation (1), based on his relative strikeouts, HRs and walks was .4546. So he was .4496 better than his age predicted.

The next step was to see how many runs he saved as a result of this. He pitched 265.33 innings. That makes 29.5 complete games. The league ERA that year was 4.27, so his age predicted ERA would be 3.86 (.9042*4.27).  But his predicted relative ERA (or DIPS ERA) was 1.94 (4.24*.4546). That difference is 1.92 (3.86 – 1.94). That gets multiplied by 29.5 to get 56.6 runs saved. This was the most runs saved once AGE was taken into account and I considered only the pitcher’s stats. Here are the top 25 age adjusted seasons in runs saved based solely on the pitcher’s stats.

 Pitcher YEAR AGE Runs Saved Dazzy Vance 1925 34 56.5956533 Pedro Martinez 1999 27 56.50779595 Lefty Grove 1930 30 55.3703178 Bob Feller 1940 21 49.41058275 Dazzy Vance 1924 33 49.24335387 Pedro Martinez 2000 28 46.46541235 Dazzy Vance 1928 37 43.97893864 Bob Feller 1939 20 43.40136659 Dazzy Vance 1930 39 43.13738011 Roger Clemens 1997 34 41.05611036 Bert Blyleven 1973 22 40.72525954 Dolf Luque 1923 32 40.26181751 Johnny Allen 1936 30 40.07463135 Randy Johnson 1995 31 38.66133362 Lefty Grove 1927 27 37.97919687 Pete Donohue 1925 24 37.79832039 Lefty Gomez 1937 28 37.72100203 Randy Johnson 2004 40 36.97886686 Kevin Brown 1998 33 36.85872621 Lefty Grove 1926 26 36.54630565 Lefty Grove 1931 31 36.33560254 Lefty Grove 1929 29 36.208095 Lefty Grove 1932 32 36.1143788 Cy Blanton 1935 26 36.10329252 Bob Feller 1946 27 36.05170998

These stats are not park adjusted. That is why Pet Donohue is up there. He pitched in a low-run park. Clemens of 2005 is not here. He would only be 215th.

I used one other method last week to find the best age adjusted seasons. I subtracted the normal peak age from each guy’s age and took the absolute value. That got multiplied by the number of runs saved (which was not age adjusted as in the above explanation-it was simply (IP/9)*(the difference between league ERA and the ERA predicted by equation (1)). The peak age was 29.89. I found that by finding the average age for the top 250 seasons in predicted relative ERA (using equation (1)). For example, Dazzy Vance in 1930 was aged 39. That minus 29.89 is 9.11. He saved 53.75 runs. His relative ERA predicted by equation (1) to be .6237. That times the league ERA of 4.97 is 3.10. The difference is 1.87. He pitched 258.667 innings. That divided by 9 is 28.75. That times the 1.87 difference is the 53.75 runs saved. That gets multiplied by 9.11. That gave him 489.67 “age points.” The top 25 in “age points” are listed below.

 Pitcher YEAR AGE Runs Saved Age Points Dazzy Vance 1930 39 53.75051586 489.6671995 Bob Feller 1940 21 54.8268672 487.4108494 Bob Feller 1939 20 46.90794659 463.9195918 Randy Johnson 2004 40 44.86122903 453.5470255 Dazzy Vance 1928 37 54.65467339 388.5947278 Bert Blyleven 1973 22 46.98793732 370.7348255 Dwight Gooden 1985 20 37.02470115 366.1742944 Dwight Gooden 1984 19 32.87340375 357.9913668 Jack Quinn 1928 44 24.19020867 341.3238443 Waite Hoyt 1921 21 37.74713278 335.5720104 Randy Johnson 2001 37 44.7325033 318.0480985 Vida Blue 1971 21 34.27435979 304.6990586 Babe Adams 1922 40 29.91900156 302.4811057 Dazzy Vance 1929 38 37.20115978 301.7014058 Roger Clemens 2005 42 24.7192402 299.3499988 Lefty Grove 1937 37 42.06229935 299.0629484 Nolan Ryan 1989 42 24.30933947 294.3861009 Bob Feller 1938 19 26.98090041 293.8220054 Dazzy Vance 1925 34 68.65550985 282.1741455 Frank Tanana 1975 21 31.45033843 279.5935086 Pete Donohue 1925 24 46.90945662 276.2966995 Lefty Gomez 1931 22 34.76705924 274.3120974 Dutch Leonard 1949 40 27.05088775 273.4844751 Randy Johnson 2000 36 44.15458989 269.7845442 Mark Prior 2003 22 34.1780478 269.6647972

Clemens makes this list. Notice that there are some relatively young pitchers here. By using absolute value, the farther a pitcher is from the “peak age,” the more points he would get. So this puts a guy 10 years over peak on the same footing as a guy who is 10 years under.

Here is the response to a comment

I tried a 4th order polynomial, and certainly it fits the data better. But that is a select group of pitchers. I am using it to try to estimate the "true" pattern for all pitchers. I am not sure that finding the absolute best fit for a small group of pitchers should be applied to a much larger group. The 4th order polynomial changes directions a few times. That may not happen for the whole group of pitchers (6,690). The smaller group, the guys who had 10+ seasons with 150+ IP, had about 1,900 guys. I think it is more reasonable to assume a u-shaped function and try to make the best of it.

On HRs, I tried a regression with HRs, BBs, and SOs,  per 9 IP as the independent variables and ERA (not taken relative to the league average) as the dependent variable. The values for HRs, BBs, and SOs are more like what we would expect (HRs were 1.47). Then I got a predicted value for each pitcher then divided that by the league average. Then I ranked those pitchers. The problem is that almost all of the best 25 or so seasons then come after 1990. That is not the case in the method I described above.

There might be something strange going on because those pitchers came in a high HR and perhaps high strikeout ERA. Maybe that is why the value for relative HRs came out so low in the first place.