An aside in a recent Unfiltered entry on Bernie Williams’ JAWS outlook—the part where I dismissed the idea of calculating the positional standards by using the median score instead of a modified mean where the lowest score is dropped –prompted an email from reader BD:
From a statistical prospective, the validity of using the mean to represent the central tendency of a population is a mistake when the population is not normally distributed, and also a mistake when having small populations to look at (and I think you probably know this already).
By dropping the lowest point, you are trimming the distribution of an least one outlier (though not the upper-end outliers such as the Babe or Willie Mays), allowing one or two super-duper-stars to dictate the Hall more than, perhaps, they should.
Arguably, you still increase the standard of the Hall by switching your standard to the median, since you’d only be allowing in those who are at least as good as half of the people in the Hall at his position.
BD is correct in noting that the population of Hall of Famers used to calculate the standards is small and not normally distributed, and that upper-end outliers skew the scores. It’s worth remembering that the entire population of major-league ballplayers isn’t normally distributed either. It’s the far right end of a bell curve of ability where the peak is probably around “Able to catch up to Dad’s whiffle ball junk by age nine,” with “Able to put on pants one leg at a time,” and “Competent enough to be invited to join company softball team” as the first standard deviation in either direction; “Replacement Level DH” is a few stops up the line. As Bill James noted in his “Breaking the Wand” valedictory, “For every player who is 10 percent above the average player, there are probably twenty players who are 10 pecent below average.”
As we look at the VC voting this week, that worth remembering. Take first base, where the true HOF mean JAWS score (as opposed to the standard where the lowest score is dropped) is 82.5, and the standard deviation of HOF first-sackers is 19.1. There are six first basemen who are at least one standard deviation above that score, but nobody who is two above. Eleven more are within one standard deviation above the mean. Meanwhile, there are 24 first basemen within one standard deviation below the mean, and 45 within two. For every superficially half-decent candidate like Gil Hodges (75.7), you’ve got Don Mattingly (76.9), Mark Grace (75.7) and Norm Cash (74.5) crowding the picture, and guys like Will Clark (87.4) and Keith Hernandez (89.5) who actually qualify by JAWS standards but aren’t on any ballot this year.
Getting back to the mean/median distinction, the deciding factor comes down to a pragmatic decision that better models the voting process. Using the modified mean, JAWS identified eight candidates on the 2007 Hall of Fame ballot as worthy of a vote: Bert Blyleven, Rich Gossage, Lee Smith, Mark McGwire, Cal Ripken, Alan Trammell, Tony Gwynn and Albert Belle (at least if we base the decision on the latter on the superiority of his peak score relative to the small margin by which his career score falls short). Had I used the median, which lowers the standards by anywhere from 2.1 JAWS points at catcher to a whopping 10.1 in centerfield and 13.5 points in rightfield (and actually raises them 2.6 points at third base), Dave Concepcion, Andre Dawson and Dale Murphy would have also made the cut, for a total of 11 “worthies” on a ballot limited to ten names.
Within the wide, wide range of opinions held by actual voters and interested observers, I don’t think you could find a single credible analysis that concluded that there were more candidates on the ballot who are worthy of election than there were spots to vote for them. Given that receiving at least 50 percent of the vote is a strong indicator of the electorate’s future intent to induct (only Hodges has been double-crossed thus far), the BBWAA consensus—a simple majority of the voters, rather than the supermajority needed to actually gain election—appears to be that five or six players on this year’s ballot were “worthies”: the elected Tony Gwynn and Cal Ripken, plus the “50+” group: Gossage, Jim Rice, Andre Dawson and Bert Blyleven, the latter of whom backslid from 53.3 percent in 2006 to 47.7 percent this year.
As for the VC, I advocated three candidates in today’s piece; switching to the median adds Bobby Bonds to the pile, but we’ll be lucky if the senility set grants Ron Santo entry, and expecting more than one player to be elected is like hoping that Juan Pierre will add 100 points of OBP in Dodger blue. Ain’t. Gonna. Happen.
Ultimately I feel strongly that JAWS should at least have one foot based in reality, so I’m forced to reject the idea that the raw positional median should be the bar that the system uses. The BBWAA and VC may not always have the “right” candidates flagged for Cooperstown, but at least they’re not overcrowding the dais, and a credible system needs to respect that.