The best pitchers allow fewer runs than other pitchers. Of course, the lower the better. But since some pitchers got to work in low-run parks or in low-run eras, some adjustment has to be made to make any comparison fair. A guy who pitched in a high-run park or high-run era should get some kind of bonus. Pitchers who logged a lot innings and/or had longevity should also get some positive adjustment. Even if they gave up slightly more than the average number of runs, piling up innings will have value. All of these factors were taken into account here.
The first step was to use RSAA or "Runs saved against average" from the Lee Sinins Complete Baseball Encyclopedia.". The exact definition is: "It's the amount of runs that a pitcher saved vs. what an average pitcher would have allowed." It is park adjusted, so if a pitcher saves 50 runs but in a very pitcher friendly environment, his RSAA will be less than 50. Notice also that it is compared to the league average, so it could be negative.
To see how this works, let's take Cy Young, for example. His career RSAA was 813. But his actual number of runs allowed was 3,167, while the average would have allowed 4,221. So it appears that he saved 1,054 runs, more than what the RSAA shows, meaning Young must have been helped by pitching in relatively low-run parks. That is why the park adjustment is important, to remove such distortions. But I also want to compare Young's runs per game to the league average to predict or estimate his winning percentage. So what is the league average? I could add 813 to 3,167 to get a league average of 3,980. Or I could keep the league average of 4,221 and raise Young's runs allowed by the difference between 1,054 and 813. That is 241, or the amount by which his RSAA had to be adjusted becaues of his low-runs parks. That would give Young 3,408 runs allowed.
So I could have Young with 3,408 runs allowed while the average pitcher would have allowed 4,221. Or Young allows 3,167 with the average being 3,980. I decided to used the average of both possibilities for Young's runs allowed and the possibilities for the average runs allowed. That gives Young 3,287.5 runs allowed and makes the average runs allowed of 4,100.5. The difference is still 813. Then I found Young's runs per game and the runs per game for the average pitcher. Young pitched 7,356 innings. Dividing that by 9, we get 813.333 games. Then Young has 4.02 runs per game while the average was 5.02.
Now what winning percentage should we expect? I used a formula called "Pythagenpat," which is a variation on Bill James's "Pythagorean Formula." Pythagenpat estimates winning percentage by
- Finding the total runs per game and raising that to the .287 power (an exponent of .287). You add runs scored (RS) and runs allowed (RA), then divide by the number of games. Call the result X.
- Then find
For Young, the total runs per game is 9.04. That raised to the .287 power is 1.88. So, in Young's case, X in step 2 is 1.88. Using RS = 5.02 (the average runs allowed during Young's time) and RA of 4.02, we get a winning percentage of .602. Multiplying that by 813.333 gives Young 492 wins. But how do we get to "Wins Above the Replacement Level Pitcher" or WARP?"
First, let's recall that RSAA compares the pitcher to the league average, not a hypothetical replacement pitcher. A guy could have a negative RSAA (that is, be a little below average) and still have some value since they are better than the replacement level pitcher. A season with, say, a .490 winning percentage would normally hurt a guy's career value since that is below average. But the replacement level pitcher, might only be good enough to have a .400 percentage or one even lower. So having a pitcher who can get a .490 winning percentage, especially if he has a high IP total, can still be valuable.
The next step was to find how many games a .400 pitcher would have won in the same number of games as any given pitcher. In Young's case, the replacement pitcher would win about 326 games, or about 165 fewer than Young. That gives Young a WARP of about 165. The table below has the rankings.The pitchers included in the study were the top 900 through 2005 in RSAA and any others who had at least 2,000 career IP. That was 1,021 guys and they are the ones ranked below. I also show each pitcher's WARP based on a .333 winning percentage for the replacement pitcher. It looks like the highest ranked pitcher who is not in the Hall of Fame and is also eligible is Bert Blyleven. There are many, many Hall of Fame pitchers who rank below him.The pitchers near the top are probably not very surprising.
