The SAE Severity Index is supposed to be an approximation to tolerance limit data, but there are incongruities in its derivation which renders the formula unsupportable. The same logic on which the Severity Index appears to be based can be used to support a wide range of possible values for the exponent on the acceleration, including infinity. This inconsistency results because necessary distinctions have not been made between: the formula for a fitted approximation to the tolerance limit data, the scaling of severity as such, and the measure of the acceleration magnitude of a pulse, the "effective acceleration." It is recommended that a formula which more literally follows from the tolerance limit data be adopted. In the long run, however, it is believed that a much more appropriate measure of injury severity would result from processing head impact data in such a way as to reflect the probable degree of brain injury.