I proceed from the postulate that horse-race reaction time predictions are equivalent to the functions of the minimum time statistic of some parallel processing model. From this vantage point several aspects of horse-race models, including some that are based on later stages of processing, are broached and attempts made to derive results about their implications. These aspects are: 1. The ability of an infinite class of limited capacity parallel models to predict straight line reaction time functions as the number of items to be processed varies. 2. A demonstration that the variance of the maximum of two symmetric independent, identically distributed random variables is less than that of either singly. 3. A method of assessing whether the average intercompletion time (i.e., average spacing) in parallel processing increases or decreases (or neither) and an example. 4. A discussion of conditions and process questions relating to whether representations of general joint probability distributions as within-stage independent parallel models yield proper probability distributions.