** The Problem With “Total Clutch” Hitting Statistics **

by Cyril Morong

Click here to see my sabermetric blog called Cybermetrics

A recent article (late 2003) appeared in *BusinessWeek* magazine called
“Ball Park Figures You Can Bet On” which described a “new statistic” developed
by Benjamin Polak and Brian Lonergan of Yale University which measures “wins
contributed” by major league hitters. (another article on their work appeared in Nov. 2004 in the NY Times-see sources below) From the online
version:

“Here's how their method works: Let's say the home team is down by two runs in the bottom of the fifth inning, with no outs and a runner on second base. At that moment, the home team has a 39% chance (or 0.39 probability) that it will win. If the batter grounds out, and the runner at second fails to advance, the team's chance of winning falls to 33%. The difference between the two, -0.06, is assigned to the batter who just grounded out.”

Now they add this up for the whole season, every plate appearance and get wins contributed for each player (see link in sources).

The problem with this approach is that it is not new and that it really tells us nothing about what a ball player is worth since in the long run this “total clutch” stat is highly correlated with normal hitting statistics, as I will demonstrate(my critique is not new-See the book "The Hidden Game of Baseball" by John Thorn and Pete Palmer. They discuss what Dick Cramer had to say about the Mills brothers) By “total clutch” stat, I mean one that takes into account every plate appearance and each one is weighted by its importance according to the score and inning. Hits when the game is late and close will count for more than hits when the game is early and the score is lopsided.

This is definitely not a new stat. It goes back at least as far as 1970 when Eldon G. and Harlan D.
Mills published their book *Player Win Averages*. Polak and Lonergan’s “wins contributed” stat
is similar. So is the “Player Game Percentage” in the book *Curve Ball* by
Jim Albert and Jay Bennett. So is the
“Game State Victories (or Wins) found at the Rhoids Sports Analysis website
(see sources). So is “player's win
value” by Ed Oswalt (his link is also in sources). So what Lonergan and Polak have done is definitely not new.

Let’s start with the Ed Oswalt’s measure “player’s win value” (or PWV) since he uses thirty years of data, covering the years 1972-2002. The best hitters on his list will not surprise you and his stat divided by plate appearances (or PA) is highly correlated with stats like on-base percentage (OBP) and slugging percentage (SLG) as well as OPS (OBP + SLG).

First, I looked at the top 100 players in plate appearances from 1972-2002. I then correlated relative OPS (relative to the league average for each player) with Oswalt’s PWV/PA. The correlation was 0.948. This is very close to a one-to-one relationship. If you square this (called r-squared), you get 0.898, meaning that 89.8% of the variation across hitters in PWV/PA is explained by relative OPS. This is important because it shows that a very simple, non-clutch, non-situational, non-context stat like OPS pretty much explains a much more complex context dependent stat that is supposed to tell us the value of hitters.

In the figure below, you can see the relationship where PWV/PA is a function of relative OPS.

In the table below, you can see each player’s PWV/PA and his relative OPS. Bonds, for example has 137, which means his OPS was 37% higher than the league average for the 1972-2002 period. The top ten or twenty hitters will not surprise you.

Rank |
Player |
PWV/PA |
Relative OPS |

1 |
Barry
Bonds |
0.0080 |
137 |

2 |
Mark
McGwire |
0.0068 |
131 |

3 |
Jeff
Bagwell |
0.0060 |
127 |

4 |
Will
Clark |
0.0050 |
118 |

5 |
Mike
Schmidt |
0.0049 |
126 |

6 |
Ken
Griffey Jr. |
0.0048 |
124 |

7 |
George
Brett |
0.0045 |
119 |

8 |
Rod Carew |
0.0045 |
118 |

9 |
Tony
Gwynn |
0.0042 |
115 |

10 |
Jack
Clark |
0.0041 |
118 |

11 |
Reggie
Jackson |
0.0040 |
118 |

12 |
John
Olerud |
0.0040 |
116 |

13 |
Fred
McGriff |
0.0040 |
119 |

14 |
Rafael
Palmeiro |
0.0039 |
119 |

15 |
Kirby
Puckett |
0.0038 |
114 |

16 |
Mark
Grace |
0.0038 |
111 |

17 |
Rickey
Henderson |
0.0038 |
114 |

18 |
Eddie
Murray |
0.0037 |
114 |

19 |
Dwight
Evans |
0.0037 |
117 |

20 |
Wade
Boggs |
0.0036 |
116 |

21 |
Ken
Singleton |
0.0036 |
111 |

22 |
Keith
Hernandez |
0.0036 |
110 |

23 |
Fred Lynn |
0.0035 |
117 |

24 |
Darrell
Evans |
0.0033 |
110 |

25 |
Jose
Canseco |
0.0033 |
115 |

26 |
Jim Rice |
0.0032 |
118 |

27 |
Dave
Parker |
0.0031 |
112 |

28 |
Harold
Baines |
0.0031 |
111 |

29 |
Ken
Griffey Sr. |
0.0031 |
109 |

30 |
Don
Mattingly |
0.0030 |
113 |

31 |
Toby
Harrah |
0.0030 |
108 |

32 |
Ellis
Burks |
0.0030 |
117 |

33 |
Andres
Galarraga |
0.0029 |
113 |

34 |
Tim
Raines |
0.0028 |
111 |

35 |
Lou
Whitaker |
0.0027 |
108 |

36 |
Dave
Winfield |
0.0027 |
114 |

37 |
Cecil
Cooper |
0.0026 |
111 |

38 |
Pete Rose |
0.0026 |
107 |

39 |
Paul
Molitor |
0.0025 |
110 |

40 |
Gary
Matthews |
0.0025 |
108 |

41 |
Ted
Simmons |
0.0025 |
110 |

42 |
Dale
Murphy |
0.0024 |
114 |

43 |
Al Oliver |
0.0024 |
112 |

44 |
Roberto
Alomar |
0.0024 |
110 |

45 |
Brian
Downing |
0.0024 |
110 |

46 |
Jose Cruz |
0.0024 |
107 |

47 |
Craig
Biggio |
0.0023 |
110 |

48 |
Dusty
Baker |
0.0023 |
109 |

49 |
Sammy
Sosa |
0.0023 |
118 |

50 |
Wally
Joyner |
0.0023 |
111 |

51 |
Paul
O'Neill |
0.0022 |
111 |

52 |
Barry
Larkin |
0.0022 |
110 |

53 |
Bobby
Grich |
0.0021 |
112 |

54 |
Steve
Garvey |
0.0020 |
109 |

55 |
Bobby
Bonilla |
0.0020 |
115 |

56 |
Ron Cey |
0.0019 |
111 |

57 |
Tony
Phillips |
0.0019 |
101 |

58 |
Carlton
Fisk |
0.0019 |
111 |

59 |
Ryne
Sandberg |
0.0019 |
110 |

60 |
Robin
Ventura |
0.0018 |
107 |

61 |
Andre
Dawson |
0.0018 |
111 |

62 |
Chili
Davis |
0.0018 |
108 |

63 |
Alan
Trammell |
0.0016 |
105 |

64 |
Chris
Chambliss |
0.0014 |
105 |

65 |
Robin
Yount |
0.0014 |
107 |

66 |
Cal
Ripken |
0.0014 |
106 |

67 |
Julio
Franco |
0.0013 |
106 |

68 |
Graig
Nettles |
0.0013 |
105 |

69 |
George
Hendrick |
0.0012 |
108 |

70 |
Brett
Butler |
0.0011 |
104 |

71 |
Don
Baylor |
0.0011 |
108 |

72 |
Chet
Lemon |
0.0009 |
110 |

73 |
Gary Carter |
0.0008 |
107 |

74 |
Brady
Anderson |
0.0008 |
104 |

75 |
Bill
Buckner |
0.0007 |
101 |

76 |
Ruben
Sierra |
0.0007 |
104 |

77 |
Carney
Lansford |
0.0007 |
104 |

78 |
Buddy
Bell |
0.0004 |
104 |

79 |
Joe
Carter |
0.0004 |
104 |

80 |
Willie Randolph |
0.0004 |
100 |

81 |
Tony
Fernandez |
0.0004 |
101 |

82 |
Todd
Zeile |
0.0003 |
103 |

83 |
B.J.
Surhoff |
0.0001 |
99 |

84 |
Jay Bell |
0.0001 |
102 |

85 |
Steve
Finley |
0.0000 |
103 |

86 |
Willie
McGee |
0.0000 |
100 |

87 |
Gary
Gaetti |
-0.0003 |
100 |

88 |
Tim
Wallach |
-0.0005 |
101 |

89 |
Terry
Pendleton |
-0.0005 |
97 |

90 |
Dave
Concepcion |
-0.0006 |
96 |

91 |
Devon
White |
-0.0007 |
99 |

92 |
Steve Sax |
-0.0009 |
96 |

93 |
Lance
Parrish |
-0.0009 |
103 |

94 |
Omar
Vizquel |
-0.0012 |
92 |

95 |
Willie
Wilson |
-0.0013 |
96 |

96 |
Ozzie
Smith |
-0.0015 |
92 |

97 |
Garry
Templeton |
-0.0016 |
93 |

98 |
Frank
White |
-0.0018 |
93 |

99 |
Bob Boone |
-0.0025 |
91 |

100 |
Larry
Bowa |
-0.0035 |
87 |

I then ran a linear regression in which PWV/PA was the dependent variable and relative OBP and SLG were the independent variables. It used all 284 players with 5000 or more plate appearances from 1972-2002. The regression equation was

PWV/PA = -.0246 + .000149*OBP + .000097*SLG

The r-squared was .935, meaning that 93.5% of the variation in PWV/PA is explained by the model. The standard error is .00056 or about .39 wins for a 700 PA season. The correlation between OBP and SLG is about .52. Each of those has a correlation of over .8 with Wins/PA. So again, two very simple stats explain what is going on with the much more complex, clutch stat.

To see how each player did compared to what the above equation predicted, go to the following link. You can also see which hitters exceeded their predicted PWV/PA the most.

Now another stat, the Game State Victories (GSV) from the Rhoids Sports Analysis website, shows the same tendencies.

I have a data set with 191 players who have 900 or more at bats over the years 2001-2003. (this is not all of them-I'll explain later). So I ran a regression in which each hitter's GSV for the three seasons was the dependent variable and their cumulative totals for various other stats were the independent variables. The r-squared I got was .91, meaning that 91% of the variation in GSV across hitters is explained by regular counting stats that are not at all context dependent (well, not quite, again I will explain later-it concerns SACs). That is, these independent variables have nothing to do with the score or the inning. Yet they explain almost all of the variation in the context dependent variable.

Here are the coefficient estimates

SAC = -.021

SF = -.049

GIDP = -.1098

CS = -.059

SB = .0299

BB = .053

HR = .106

3B = .099

2B = .0877

1B = .0603

OUTS = -.01537

Intercept = -1.47

Outs means outs not counting the GIDP. BB includes hit by pitch. The only variables not statistically significant (T-value less than 1.96) are SAC, SF and CS. That is a surprise for CS. I believe that GSV or anything like it is a clutch stat. Yet non-clutch data does a very good job of explaining the variation in GSV. It is possible that the unexplained variation is due to chance and not any kind of clutch hitting ability.

Now the data. I chose 900 at-bats because the data given that I was able to download from the Rhoids website, listed other stats, but not walks. So I wanted a convenient cutoff for which players to count and I chose 300 for individual years, figuring anyone who gets 400 plate appearances probably has at least 300 at bats. And over three years that is 900. I also used the data from Doug Steele's website to get walks, GIDP, etc.

The data problems. In some years, players who obviously did very well had zero for their GSV. Very often they were rookies who also had a zero listed for their salary and the Rhoids people wanted to do something with runs per dollar. Maybe that is why a zero is given, since you cannot divide by zero. Also some players simply had an "NA" listed. Others clearly had the wrong number, like Juan Sosa getting the same GSV as Sammy Sosa one year. Some other players were just not listed. I did not see Edgar Martinez in the "data dump" for this year. I could not always tell which Alex Gonzalez I was looking at or if I did they were not listed for all years. Some player names were not spelled the same way each year (I went through and made the necessary corrections to allow for doing subtotals in excel). So I did not have all of the players with 900 or more at bats from this period. I think about 30 got left out.

The correlation between GSV per plate appearance for players with 300 or more at bats in both 2001 and 2002 was .5. But the correlation between OPS in 2001 and GSV per PA in 2002 was actually higher, at .519. So if you wanted to predict a player's GSV per PA in 2002, his OPS in 2001 would do a slightly better job than his GSV per PA in 2001.

I also calculated a predicted GSV per PA for these players in both 2001 and 2002 using the coefficient values from the regression which used 1Bs, 2Bs, 3Bs, HRs, BBs, SBs, CSs, Outs and GIDPs. Then I calculated the difference between the actual GSV per PA in each year and the predicted GSV per PA in each year. Then I found the correlation between the differences or residuals for the two years and it was .081. That seems very low. I think this means that players who were especially good in the clutch in 2001 (who had a higher GSV per PA than predicted) were not likely to again, in 2002, have a higher GSV per PA than predicted in 2002 (I think this is the kind of analysis that Dick Cramer performed on the Player Win Average of the Mills brothers).

"Ballpark Figures to Bet On," Nov. 21, UPFRONT
section *BusinessWeek* magazine. Author was Brian Hindo.

“What's a Ball Player Worth?” can be found at:

http://www.businessweek.com/print/bwdaily/dnflash/nov2003/nf2003115_2313_db016.htm?db

*Player Win Averages* by Eldon G. and Harlan D.
Mills. 1970. A.S. Barnes, publisher.

*Curve Ball: Baseball, Statistics, and the Role of Chance
in the Game* by Jim Albert and Jay Bennett. Revised 2003. Copernicus Books.

Rhoids Sports Analysis: http://www.rhoids.com/

Ed Oswalt’s site is at: http://www.livewild.org/bb/playervalues/index.html

The Nov. 7, 2004 NY Times article is at

But you will probably have to pay to read all of it.

Other sites where you might find it are

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