BASEBALL STATISTICS “SHOULD COME WITH A MATHEMATICAL EXPRESSION OF THEIR PRECISION….” Sheldon Hirsch in this essay on baseball statistics asks questions that journalists do not usually ask about statistics. Hirsch asks how we can tell “which statistics to emphasize and which to downplay?” Hirsch uses the example of the popular statistic “WAR”—Wins Above Replacement.
Hirsch says that his first criterion for a statistic is that “statistics should come with a mathematical expression of their precision (or lack of it) — confidence intervals, standard errors or other measures of variability.” Does a difference between WAR for two players reflect a difference between the players’ skills or random fluctuation?
Hirsch suggests that sabermatricians do not provide information about variability because they perhaps believe that the general public would dislike it.
As I argued here, I think that the public would get along just fine in dealing with measures of variability with respect to all kinds of statistics, just as they have gotten used to weather forecasts which give probability estimates for rain or snow.