Comments on ``Measuring Parity''

From historical odds Cain and Haddock assign the probability of a tie at 25% and offer functional forms for the standard deviation of a league with equal chances of a win for each team under different point assignment schemes. They then track the ratio of actual to these idealized standard deviations and argue against using an approximation that assigns half a win to both teams in a tie game or match. Their article contains some confusing use of nomenclature and there are some important lapses in scholarship. But perhaps more important, they ignore the fact (after acknowledging it) that if one uses percentages rather than absolute points, their measures of competitive balance are invariant to the point system actually used. Although their point is well-taken for competitive balance questions where absolute points might prove informative, for other competitive balance questions their point is not.