True Levels

         This is just a silly little thing, but it worked better than I thought it would, so I thought I would share it with you. 

         When a #1 pitcher faces another #1 pitcher, the winning percentage of each one is .500. 

         Well, it isn’t; there is the bullpen, but we don’t care about that.  Screw the bullpen.  We’re assuming that when two number ones square off, the winning percentage of each one is .500.  That means that if you have a .500 winning percentage against number ones, you are a true #1.  You are 1.0000.  If you have a winning percentage less than .500 against number ones, for your career, then you are something not quite as good as a 1.000, some number OVER 1.000, but it also means that if you have a winning percentage better than .500 against number one pitchers, then you are something BETTER than a #1.  You’re not a number one starter; you’re a number 0.72, or a number 0.85, or whatever.  If you read that paragraph again two or three times, it will make sense; I promise you.

         Bob Gibson, as we showed early in this series, had a less-than-.500 winning percentage against #1s—everybody does—but a better-than-.500 winning percentage against #2s, and against everybody worse than a 2.  That means that his "position" on the scale, for his career, is somewhere between 1.00 and 2.00.  But what is it?

         The obvious thing is to triangulate his wins against #1s, his losses against #1s, and the number itself, 1.00.  He was 44-55 against #1 pitchers, so we multiply 1.00 times 55 and divide by 44, and our first estimate of his "true level" is 1.25. 

         That was the obvious mathematical approach to the issue, but it actually wasn’t the first thing I tried, because I thought that something that simple couldn’t possibly work—but it does.   You get more or less consistent evaluations of pitchers from the top of the scale to the bottom.  

         Bob Gibson against twos was 50-43, so to estimate his "true level" when he pitches against twos, we multiply 2.00 times 43, and divide by 50.  That makes 1.72, so now we have two estimates of his true level—1.25, derived from his ability to compete head to head against ones, and 1.72, derived from his record against twos. 

         Against threes, he was 51-30, so we multiply 3.00 times 30, and divide by 51.  That’s 1.76.   3.00 to 1.76 is the same ratio as 51 to 30. 

         Against fours, he was 40-22, so we multiply 4.00 times 22, and divide by 40.  That’s 2.20.  4.00 to 2.20 is the same ratio as 40 to 22. 

         Against fives, he was 36-14, so we multiply 5.00 times 14, and divide by 36.  That’s 1.94. 

         Against sixes, he was 24-6, so we multiply 6.00 times 6, and divide by 24.  That’s 1.50.  See how easy this is?

         Then we have six estimates of his true level in a starting rotation, over the course of his career—1.25, 1.72, 1.76, 2.20, 1.94 and 1.50.   They’re all kind of in the same range, aren’t they? 

         Then we "weight" each estimate by the number of starts that it represents, or you could do the number of decisions that it represents, I don’t care, but I used starts.  For Gibson, this is

         113 X 1.25 = 141.25

                  (because he had 113 starts against #1 pitchers in his career)

         109 X 1.72 = 187.48

         89 X 1.765 = 157.06

         79 X 2.200 = 173.80

         59 X 1.944 = 105.00

         38 X 1.500 =   57.00

Then you add up the total, divide by Gibson’s total starts, and you get Gibson’s "true level", which is 1.70.   Over the course of his career, he’s not a "1" or a "2"; he’s a 1.70.   Which is really good; it’s not the greatest ever, which some people want to make Gibson, but it’s really good. 

The greatest ever. . .well, let’s not get to that.  Let’s do Kip Wells.  You remember Kip Wells?  He wasn’t too good.  In his career he made 219 starts, but was 69-103 with a 4.71 ERA. 

Wells in his career was 10-22 against #1s, which is not too good but there are a LOT of guys who have done worse, so that scores a 2.20, in 44 starts.  Against #2 starters he almost held his own, going 19-21, so that scores at 2.21 in 52 starts.  So far, so good.

Unfortunately, he was 6-18 when facing #3 starters.  That scores as 9.00, in 33 starts.  He was 6-10 when facing #4 starters, so that scores at 6.67 in 19 starts, and he was 10-5 against #5 starters, so that’s a good 2.50 score, in 23 starts.  But then he made 48 starts against sixth starters and was 12-21, so that scores as 10.50, and in 48 starts so it carries a lot of weight.  Putting it together, Kip Wells comes out with a true level of 5.46, meaning he was a career 5^th/6^th starter, which is a true statement; he was.   Unfortunately, that also makes him the worst in history, which is probably not a true statement; he was bad, but he probably wasn’t the worst ever.  I don’t know.  The only four pitchers who had 200 starts and score worse than 5.00 (a fifth starter) are Jamey Wright (5.17), Si Johnson (5.23), Brian Moehler (5.24) and Kip Wells. 

The best ever, by this method, was Lefty Grove.  Grove in his career was 41-34 against #1 starters, 41-17 against twos, 47-22 against threes, 54-14 against fours, 26-9 against fives, and 45-6 against sixes.  Those translate to true level estimates of 0.83, 0.83, 1.40, 1.04, 1.73, and 0.80.  Putting it all together, his true level estimate for his career is 1.07.  Nobody is a flat "#1" for his whole career, but Grove is pretty close. 

This is a list of the top 50 pitchers of all time, by this method:

You have to admit, that’s a pretty good list of pitchers.  Give me a starting rotation of Lefty Grove, Whitey Ford, Clayton Kershaw, Pedro Martinez and Allie Reynolds, and I’ll take my chances. 

The system works better than one would intuitively assume that it ought to, and I know a couple of things I could do to make it work better.  But I’m not going to do them, because there is a ceiling on how well you could make it work.  The system has the inherent flaws of won-lost records.  It tracks too closely against won-lost records.  It does import some new information into the discussion, but even if further refined it would always be too heavily influenced by how good the pitcher’s teams were.