Should a chi-squared test be performed to determine if the observed occurrence is significantly varied outside the projected likelihood of occurrence?
Just for fun, I might do that, some time this weekend...but I'm pretty sure I already know the answer. Just tinkering with the 2008-2011 schedules (so far), I found that in a given season about half the teams (on average) had at least one opponent with a bye in the week immediately before they played. If you take as your null hypothesis the idea that these byes are randomly distributed, then the probability that it would happen to a team
every year for a decade straight would be (1/2)^10 = 1 in 1024. That is, the
p-value for that event is 0.00098--which is usually extreme enough to reject the null hypothesis.
Of course, that doesn't mean that the byes are distributed "with malice", just that they are very probably not distributed
randomly. (I'm not even sure we want it "random"--we want it to be
fair.) It could be that the ACC's scheduling algorithm is introducing these artifacts because it is not sufficiently robust to deal with things like Thursday games, or non-conference rivalry games on set dates (GT, Clempson, FSU, and Louisville all have this issue).
Maybe they need to search around for a school with a top-flight Systems Engineering program, no optimize their scheduling process...