Justin Wolfers presents this graph that he (along with Eric Bradlow, Shane Jensen, and Adi Wyner) made comparing the career trajectory of Roger Clemens to other comparable pitchers:
The point is that Clemens did unexpectedly well in the later part of his career (better earned run average, allowed fewer walks+hits) compared to other pitchers with long careers. This in turn suggests that maybe performance-enhancing drugs made a difference. Justin writes:
To be clear, we don’t know whether Roger Clemens took steroids or not. But to argue that somehow the statistical record proves that he didn’t is simply dishonest, incompetent, or both. If anything, the very same data presented in the report — if analyzed properly — tends to suggest an unusual reversal of fortune for Clemens at around age 36 or 37, which is when the Mitchell Report suggests that, well, something funny was going on.
I can’t comment on the steroids thing at all, but I will say that I’d like more information than are in the graphs. For one thing, Clemens is clearly not a typical pitcher and never has been. At the very least, you’d like to see the comparison of his trajectory with all the other individual trajectories, not simply the average. For another, the graphs above seem to be relying way too much on the quadratic fit. At least for the average of all the other pitchers, why not show the actual averages. Far be it from me to criticize this analysis (especially since I am friends with all four of the people who did it!)–this is just a recreational activity, and I’m sure these guys have better things to do than correct ERA’s for A.L./N.L. effects, etc.–but I think you do want to have some comparisons of the entire distribution, as well as a sense of how much the “unusal reversal around ages 36 or 37” is an artifact of the fitted model.
P.S. to Justin, Eric, Shane, and Adi: Now youall have permission to be picky about my analyses in return. . . .
P.P.S. Nathan made this plot showing data from the 16 most recent Hall of Fame pitchers.