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Understanding the relationship between demographics and hate crime rates has been at the core of much scholarly debate. Congruent with group threat theory, some research reported that a large or growing minority group has a positive effect on hate crime rates (Stacey et al., 2011). Other research, however, revealed a negative effect of minority population size, with the minority population included as the offset (Disha et al., 2011). In two recent studies, Hipp et al. (2009; 2011) caution that the selection of the appropriate denominator in computing the rate of intra- and inter-group interactions is crucial because the computation of rates entails a mathematically built-in relationship with the composition of a given group. This in turn yields conflicting findings. The present study builds on this body of work by examining whether the relationship between hate crime rates and the relative size of the minority population is a function of the structural opportunities for interaction. Using negative binomial regression analysis, we go beyond prior work by computing three distinctive measures of anti-black, anti-Hispanic, anti-Asian, and anti-Muslim/Arab hate crime rates across U.S. counties, with the following measures included as the offset: total population, group size population, and random probability of interaction.