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 ResearchSpecial 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 expectedbased on the number of runs scored and allowedbecause 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, twothirds 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 flipsno 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 onehalf times onehalftimes 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 twothirds 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 fivesixths 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 decisionsofwhom there were 529. Twentysix 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.










TABLE A 



Player 
Club 
Lg 
Year 
Runs 
Losses 
Runs/Loss 
Skip
Lockwood 
NY 
N 
1979 
7 
5 
1.40 
Diomedes
Olivo 
Stl 
N 
1963 
9 
5 
1.80 
Steve
Howe 
LA 
N 
1983 
15 
7 
2.14 
Jim
Brewer 
LA 
N 
1972 
16 
7 
2.29 
Lee Smith 
Chi 
N 
1983 
23 
10 
2.30 
Rollie
Fingers 
SD 
N 
1978 
33 
13 
2.54 
Darold
Knowles 
Was 
A 
1970 
36 
14 
2.57 
Al
Worthingtion 
Min 
A 
1964 
18 
7 
2.57 
The records of the six reliefpitchers whose wonlost records failed of prediction by more than two standard deviations are presented in Table B.


TABLE B 




Runs 
WL 
WL 

No. of 
Player 
foragst 
actual 
expected 
Diff. 
std. dev. 
Skip
Lockwood 
512539 
5797 
7480 
17 
3.30 
Rollie
Fingers 
762569 
112110 
13290 
20 
3.24 
Mike
Marshall 
647548 
97112 
11594 
18 
3.02 
Stu
Miller 
846697 
105103 
12088 
15 
2.44 
Hoyt Wilhelm 
1007773 
143122 
159106 
16 
2.33 
Goose
Gossage 
581440 
8173 
9361 
12 
2.23 
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.


TABLE C 




Runs 
WL 
WL 

No. of 
Player 
foragst 
actual 
expected 
Diff. 
std. dev. 
Bert
Blyleven 
14991191 
176160 
202134 
26.00 
3.34 
Red
Ruffmg 
26882117 
273225 
303195 
30.00 
3.24 
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 runsallowed 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.


TABLE D 




Runs 
WL 
WL 

No. of 
Player 
foragst 
actual 
expected 
Diff. 
std. dev. 
Tom
Seaton 
621614 
9365 
8078 
13 
2.52 
Joe
Coleman, Jr. 
10821202 
142135 
126151 
16 
2.34 
Togie
Pittinger 
869982 
115112 
101126 
14 
2.22 
Casey
Patten 
8221069 
105128 
91142 
14 
2.18 
Wes
Ferrell 
15651382 
193128 
178143 
15 
2.05 
Mike
Torrez 
14581469 
184155 
168171 
16 
2.05 
Dave
Koslo 
820740 
92107 
10792 
15 
2.60 
Harry
Howell 
11861103 
131145 
147129 
16 
2.48 
Eddie
Smith 
752816 
73113 
8799 
14 
2.39 
Dizzy Trout 
13851166 
170161 
188143 
18 
2.38 
Denny
Lemaster 
835778 
90105 
10392 
13 
2.32 
Otto Hess 
660644 
7090 
8278 
12 
2.20 
Looking at the top winners in history (Table E) , most come pretty close to what would be expected.


TABLE E 




Runs 
WL 
WL 

No. of 
Player 
foragst 
actual 
expected 
Diff. 
std. dev. 
Walter
Johnson 
26631902 
417279 
435261 
18 
1.66 
Pete
Alexander 
25341851 
373208 
365216 
8 
0.79 
Christy
Mathewson 
23571613 
372189 
366195 
6 
0.64 
Warren
Spahn 
26842016 
363245 
375233 
12 
1.16 
Eddie
Plank 
22071570 
326193 
328191 
2 
0.21 
Gaylord
Perry 
24342128 
314265 
323256 
9 
0.86 
Lefty
Grove 
23961594 
300141 
301140 
1 
0.11 
Steve
Carlton 
21881733 
300200 
299201 
1 
0.10 
Early
Wynn 
22852037 
300244 
298246 
2 
0.24 
Robin
Roberts 
21921962 
286245 
290241 
4 
0.41 
Fergie
Jenkins 
21861853 
284226 
290220 
6 
0.66 
The conclusion is that although good pitchers allow fewer runs than average, clutch pitchers do not exist.