The Cat's Cradle

"No wonder kids grow up crazy. A cat's cradle is nothing but a bunch of X's between somebody's hands, and little kids look and look and look at all those X's . . . No damn cat, no damn cradle." -- Kurt Vonnegut

Wednesday, February 07, 2007

Does winning matter for Hall of Fame Induction (part 2)?

(see intro in previous post)

Below I present results for three probit models. The first table shows compares goodness-of-fit measures. The row designated “P > .5” shows the correlation coefficient between HOF induction and whether the predicted probability is over .5. The second table lists predicted probabilities for selected players.

Model 1 is based on Professor Bradbury’s specification. The differences in his predictions and model 1 are likely the result of differences in the way certain variables were calculated. Offensive production is measured using career linear weights, adjusted for ballpark factor and league run environment. Additionally I use the number of gold glove awards and the number MVP awards, as well as a dummy indicating whether the individual retired before 1960 (the first gold gloves were awarded in 1957). Finally the regression includes the number of years played and a dummy variable indicating the position at which the player played the most games (all outfielders are grouped together).

Model 2 replaces linear weights with career hits, runs, home runs and stolen bases. Additionally it includes controls for ballpark factor and run environment. I was personally surprised at how poorly it performed relative to the original model. This suggests that even though voters may not understand linear weights they look at more than just a few statistical categories.

Model 3 adds to model 1 the average winning percentage of a players teams as well as a dummy variable indicating whether he won a world series. I also experimented with variables that captured whether a player played in a major market, but these seemed unimportant. This specification might perform somewhat better, but the difference is likely small.

Model 1 Model 2 Model 3
Pseudo-R2 0.7657 0.7684 0.7989
Log-Likelihood -152.42 -150.31 -130.82
P > .5 0.7033 0.5102 0.7556
P > .05 0.6064 0.5313 0.6430
P > .01 0.5279 0.4686 0.5623

Prob. Of Induction
Name startyr endyr position Model 1 Model 2 Model 3
Pete Rose 1963 1986 OF 100.0% 100.0% 100.0%
Bill Dahlen 1891 1911 SS 95.0% 93.0% 98.0%
Joe Torre 1960 1977 C 78.5% 69.4% 73.7%
George Van Haltren 1887 1903 OF 76.5% 76.9% 63.0%
Sherry Magee 1904 1919 OF 73.1% 42.7% 70.5%
Bob Elliott 1939 1953 3B 71.1% 61.4% 57.5%
Larry Doyle 1907 1920 2B 70.7% 55.4% 75.5%
Stan Hack 1932 1947 3B 70.2% 47.5% 74.0%
Dwight Evans 1972 1991 OF 66.1% 64.9% 69.7%
Rusty Staub 1963 1985 OF 65.4% 33.5% 39.3%
Jimmy Ryan 1885 1903 OF 63.5% 81.5% 49.0%
Bob Johnson 1933 1945 OF 63.3% 72.2% 21.8%
Dick Bartell 1927 1946 SS 57.6% 58.5% 43.5%
Dale Murphy 1976 1993 OF 55.7% 57.7% 14.1%
Keith Hernandez 1974 1990 1B 55.2% 21.3% 47.5%
Phil Cavarretta 1934 1955 1B 54.9% 38.9% 38.8%
Ted Simmons 1968 1988 C 52.9% 60.9% 41.2%
Vern Stephens 1941 1955 SS 46.8% 62.8% 35.8%
Dave Parker 1973 1991 OF 45.4% 65.2% 41.0%
George Burns 1911 1925 OF 42.5% 37.4% 76.3%
Joe Gordon 1938 1950 2B 39.8% 55.2% 74.8%
Joe Jackson 1908 1920 OF 27.1% 8.3% 28.7%
Jim Rice 1974 1989 OF 25.1% 45.1% 23.8%
Steve Garvey 1969 1987 1B 24.4% 45.0% 40.4%

The real difference between models 1 and 3 shows up when comparing players. Model 3 was particularly harsh on Professor Bradbury’s favorite player, Dale Murphy. According to it, Murphy’s chances were hurt by his lack of a World Series ring and the .443 winning percentage of the teams he played on.

I surprised by how well Joe Torre scored and also by how poorly Jim Rice scored. I should note that though predictions were generated for them, Pete Rose and Joe Jackson were not included in the initial regressions.

Next time I’ll look at the players who are enshrined with the lowest predicted probabilities.

2/9/07 Update: while working on the next parts I discovered a couple of minor mistakes in my code. The results did not change much, but the tables have been updated.


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