Maddux, for example, gave up 49% fewer HRs than the league average (what the 1.49 means in the graph below) while walking 86% fewer batters. My HRBB rating multiplies these two numbers together. The table below shows the top 25 among pitchers with 2000+ IP from 1946-2009. Maddux has a pretty clear edge over the competition.
But then I realized that Maddux was not a great strikeout pitcher. He was not preventing batters from hitting HRs by overpowering them. I decided to then multiply each pitcher's HR rate, BB rate and SO rate. But first, I inverted the rate of strikeouts. Maddux struck out 94% as many batters as the average pitcher. Being below average in strikeouts increases the difficulty in achieving a high HRBB rate because there is a positive correlation between not allowing HRs and striking batters out (about .15). So for Maddux, 1/.94 = 1.06, indicating that he was 6% worse at striking out batters than average. So his HRBBSO rating would be 1.49*1.86*1.06 = 2.95.
But notice in the table that he finishes 2nd behind Lew Burdette, who somehow managed to give up 7 fewer HRs than average and walk 76% fewer batters while striking out 61% fewer batters. Pitching the bulk of his career for the Braves in County stadium may have helped. The simple average of the HR park factors from 1952-1962 (which includes the last year the Braves played in Boston) has Burdette with a 75. So he pitched in parks that only allowed about 75% as many HRs as average. For Maddux, from 1987-2003, his parks allowed about 109% of the league average (HR park factors from various Bill James books).
I tried to adjust for this (for these two guys). Assuming that a pitcher pitches half his innings at home, and that he allowed 7% fewer HRs than average (for a rate of 1.07) and that his park has a 75 rating, I thought it best to multiply the 1.07 by .875 (which is half way between 1 and .75). That left Burdette with a HR rate of .936 (which now means he allowed 6.4% more HRs than average). For Maddux, I multipled his 1.49 by 1.045 (half way between 1 and 1.09). That gives him an adjusted HR rate of 1.56. Then recalculating the HRBBSO rate, Burdette ends up with 2.66 while Maddux ends up with 3.09.
You don't use these words but, using your first two sentences as a guide, you purport to measure something like how good a pitcher is at preventing home runs while throwing strikes. That explains the oddity of increasing a pitcher's rating based on how poor a strikeout pitcher he was.
ReplyDeleteA pitcher who avoids walks faces fewer batters in an inning. Same goes for a pitcher who avoids baserunners of all kinds. The opposite is true for a pitcher who is successful at inducing double plays. You ignore these additional factors -- the first of the three is actually just a subset of the second -- giving the statistic questionable value as a meaningful metric. You also don't explain the essentially random decision to give each of your three factors equal weight by simply multiplying them, nor why multiplication is superior to addition in achieving a meaningful result. I don't think this statistic measures anything magical.
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ReplyDeleteThanks for dropping by and commenting.
ReplyDeleteIt would be better to include the ability to induce DPs. But how many DPs each pitcher induced divided by the number of opportunities is not so easy to put together, especially in a nice ranking relative to the league average.
The reason I multiply the two #s toghether can best be seen, I think, in another example. Suppose you wanted to measure the joint ability to hit HRs and steal bases. Player A has 20 of each while Player B has 0 HRs and 50 SBs. Adding them together would rank player B higher even though he has no HR ability.
As for giving them an equal weight, I think that is appropriate here since all I wanted to do was measure this joint ability, not value it. To place values on these things, we might as well use FIP ERA, which gives an appropriate weight to HRs, BBs and SOs. I have used that in the past in other studies where I was more interested in measuring a pitcher's value than a particularly narrow skill.
"It would be better to include the ability to induce DPs."
ReplyDeleteAbility to induce DPs is secondary to baserunners allowed, which you have conveniently ignored. In any case, the fact that ANY factor is "not so easy to put together, especially in a nice ranking relative to the league average" has nothing to do with how important that factor that is.
It reminds me of the old joke about the physicist, the chemist, and the economist who are lost on a desert island with no tools and nothing to eat but canned food. It ends with the economist opining, "Assume a can opener ..."
"The reason I multiply the two #s toghether can best be seen, I think, in another example. Suppose you wanted to measure the joint ability to hit HRs and steal bases. Player A has 20 of each while Player B has 0 HRs and 50 SBs. Adding them together would rank player B higher even though he has no HR ability."
Yes, and multiplying them would produce the absurdity that Player B would earn a score of 0. Please don't argue that the numbers should be compared to league averages. I am using your example in exactly the fashion that you did.
Let's try another one. Player A has 45 HR and 5 SB, reasonable numbers for a top-tier power hitter. Player B has 10 HR and 40 SBs, a reasonable approximation of Ichiro Suzuki's production. Multiplication would result in Player B having a ranking 8 times that of Player A. Addition would produce equity. The former is absurd. As for the latter, who knows? This goes to my criticism that you weighted the factors equally without justifying that decision.
"I have used [FIP ERA] in the past in other studies where I was more interested in measuring a pitcher's value than a particularly narrow skill." And what particularly narrow skill is that, and how accurate is your metric in assessing it? You are begging the question.
"Multiplication would result in Player B having a ranking 8 times that of Player A."
ReplyDeleteOops! I fell asleep at the wheel at that one, adding Player A's numbers instead of multiplying them. Make that a ranking nearly twice that of Player A (400/225 = 1.78). Still a result that strains credulity and makes my point, but not nearly as deliciously.