Scott Sumner just wrote up a thoughtful analysis of Tyler Cowen’s reply to Nate Silver’s counter-factual thought-experiment about baseball. But we here at prior probability are not so much interested in the original question of Nate Silver’s post (“If Hank Aaron had never hit a home run, would he still be a hall of famer?”). Nor do we wish to challenge Tyler Cowen’s point about strategic behavior (we agree with Tyler) or rehash Scott Sumner’s critique that Mr Silver is simply assuming strategic behavior away in his analysis. What we do wish to discuss here is an intriguing question that Scott poses at the end of his post:
Which of the following should cause us to “think less” of a player’s career:
1. A pitcher throws lots of spitballs, which the umps fail to notice.
2. A lineman in football is cleverly able to disguise the fact that he holds defensive players, and doesn’t get called.
3. A player uses a banned performance enhancing drug that some other players also use.
4. A player is the only person in baseball to use a certain legal performance enhancing drug (because other players are unaware of it.)
In our view, scenarios #1 and #2 are equivalent (in both cases, the players are cheating but are not getting caught), and we would not “think less” of such players since it takes skill not to get caught cheating. By contrast, the player in scenario #3 is stuck in an arms race with his fellow players (i.e. he has no choice but to use banned drugs in order to compete effectively), so we wouldn’t think any less of him either (indeed, we agree with Scott Sumner that Barry Bonds is the best batter in baseball history). This leaves #4 … we would “think less” of the player in scenario #4 because his success on the field is simply the result of luck and timing.