I have no way (and probably no one on here) has any semblance of knowing this is true. If I, however, was going to design an analysis to mathematically define it and provide an actual result this is what I would do (rather than ranting and raving though there are some nice points here):
-Define the problem in modern times, or the 21st century. Among, cfb coaches with a hire date of January 1, 2000 or afterwards (to get a solid sample size) up to December 31 of this year.
-Treat race (white/Black African American) as my main exposure variable.
-Measure time of exposure as time from that hire date to time of firing (not time of getting a promotion). The outcomes would be constrained by coaches who were fired only.
-I would test the hypothesis that the time to firing among whites is equal to that among blacks as a crude estimate in a proportional hazard model
-I would then adjust for (in a separate proportional hazard model) baseline winning percentage (or winning percentage as a head coach prior to being hired. Or maybe an indicator for any prior HC experience), 10-year (or some measure for historical record) program winning percentage prior to being hired, distribution of African Americans at given university, geographic region, and any other covariates (can't think of on top of head).
-probably incorporate a weight into the model accounting for any covariate imbalance (by race) in the effect of race on time to fire date to reduce bias
-That, in a decent way is a solid way of how to see if there is in fact a racial bias for time to fire date, both crudely and with more societal context.
All of us (including Luke) yelling and gesticulating doesn't really do anything. Though its fun to discuss and see people's inherent ideological leanings
