13.51 Hall of Fame induction Baseball’s highest honor is election to the Hall of Fame. The history of the election process, however, has been filled with controversy and accusations of favoritism. Most recently, there is also the discussion about players who used performance enhancement drugs. The Hall of Fame has failed to define what the criteria for entry should be. Several statistical models have attempted to describe the probability of a player being offered entry into the Hall of Fame. How does hitting 400 or 500 home runs affect a player’s chances of being enshrined?

What about having a .300 average or 1500 RBI? One factor, the number of home runs, is examined by using logistic regression as the probability of being elected:

a. Compare the probability of election for two players who are 10 home runs apart—say, 369 home runs versus 359 home runs.

b. Compare the probability of election for a player with 475 home runs versus the probability for a player with 465 home runs. (These happen to be the figures for Willie Stargell and Dave Winfield.)

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P(HOF) = e-6.7 +0.0175HR 1 + e 6.7 +0.0175 HR