At one time, the Dance Card had a P12 factor to account for some strange decisions made by the selection committee. They discussed this briefly in the paper they published (linked in my Dance Card entry). Previously, they had concluded that the selection committee was biased against mid-majors.
But they say in the current paper that they didn’t find statiscal support for conference bias since ~2012. But I’m pretty sure UCLA got in just a couple of years ago for no obvious reasons.