Do Clutch Pitchers Exist?

 

by PETE PALMER

 

(this was originally published in the spring 1985 issue of The National Pastime, published by SABR, the Society for American Baseball Research-Special thanks for Gerald Wachs for copying and sending me the article)

 

Over a career, a good pitcher wins more games than an average pitcher by allowing fewer runs than average and by receiving good batting support from his teammates. A clutch pitcher wins more games than expected-based on the number of runs scored and allowed-because he performs better in close games. That is, provided he exists.

The number of runs allowed by each pitcher is available from normal season data. Runs scored for each pitcher can be estimated by taking the runs his team scored times his innings pitched, all over nine, times the games the team played. Pitcher batting can be included by taking 80 percent of the number of runs produced compared to the average pitcher; 20 percent is assumed to be reflected already in the overall team scoring. This is done by using Linear Weights, which credit: 0.47 runs for a single; 0.31 runs for each extra base, walk, or hit by pitch; and a value for each hitless at bat which makes the league average come to zero (this value is generally -0.25 to -0.27 runs). For pitchers, the league average for runs produced is found by examining pitcher batting only.

The relationship between runs and wins was described in my previous National Pastime article ("Runs and Wins," 1982) as well as in The Hidden Game of Baseball (1984). The num ber of runs ,needed to produce an extra win over the course of a season is equal to ten times the square root of the number of runs scored per inning by both teams. Since the number of runs per inning is usually around one, the number of runs per extra win is about ten, and almost always between nine and eleven.

A pitcher would not be expected to win exactly the number of games predicted by the formula. The meas ured error can be expressed in terms of the standard deviation of the dis- tribution of differences. The standard deviation is calculated by taking the square root of the average of the squares of the differences between expected and actual wins. If the distribution is normal, two-thirds of the differences should fall within one standard deviation and 95 percent within two. The anticipated standard deviation can be compared to the value actually found, and if they are about the same, the conclusion would be that the variation between a pitcher's runs allowed and runs scored and his wins is due only to chance and that there is no such thing as a clutch pitcher .

This anticipated standard deviation is not easy to find. If all teams were evenly matched and runs scored and allowed were not known, the standard deviation could be expressed exactly based on a binomial distribution, which represents the outcomes of many coin flips-no heads out of five, one head, etc. This number is equal to the square root of the probability of success times the probability offailure times the number of trials or games. For 162 de- cisions by a .500 pitcher, this would be the square root of one-half times one-halftimes 162, or 6.36. However, if runs scored and allowed are known, the number would be smaller. Based on the minimum value found from the study cited above, this is about 4.1, or two-thirds of the original value. In the present study, though, runs scored are only estimated by overall team figures, introducing an error which will cause the anticipated standard deviation employed to be set at five-sixths of the binomial one. Previous investigations have revealed th~t the variation in run scoring due to chance is equal to the square root of twice the number of runs involved, so if a pitcher went 162 innings and expected to have 81 runs scored for him, the standard deviation due to chance alone would be equal to the square root of two times 81, or 12.7.

The data analyzed consisted of all pitchers from 1900 through 1983 who had at least 150 decisions-ofwhom there were 529. Twenty-six men would have been expected to exceed two standard deviations; only twenty were found. Of these twenty, six were modern ace relief pitchers. All six had a much lower winning percentage than expected, a fact probably due to the score situations when they entered the game. They were likely to have been brought in when the score was tied, but more likely still to have entered when their team was ahead, thus making it easier to have picked up a loss than a win.

To illustrate this, a separate study was performed, checking the lowest ratio of runs allowed to losses for all pitchers since 1900. The top eight were all modern reliefpitchers, led by Skip Lockwood, who in 1979 allowed only seven runs for the Mets yet lost five games. The data (five losses minimum) are presented in Table A.

           

 

 

 

The records of the six reliefpitchers whose won-lost records failed of prediction by more than two standard deviations are presented in Table B.

 

 

 

In a sample of 529, it would be expected that one pitcher would diverge from the norm by more than three standard deviations. Two were found, both of whom lost considerably more games than predicted. Their records are presented in Table C.

 

 

 

No other pitcher was more than 2.6 standard deviations from expected in either direction. Unfortunately, of the twelve remaining pitchers who were over two standard deviations from expected, four played in the early part of the century when runs-allowed data was incomplete and thus had to be estimated from known data on earned runs allowed, as shown in the Macmillan encyclopedia. These are indicated with asterisks. Thus more research is needed to find the exact figures. Table D presents these twelve.

 

 

 

            Looking at the top winners in history (Table E) , most come pretty close to what would be expected.

 

 

 

            The conclusion is that although good pitchers allow fewer runs than average, clutch pitchers do not exist.