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There are certainly off field reasons for firing the HC.  We all see a LOT of programs fire a fairly successful guy and then go through a merry-go-round of coaches either not given enough time or simply worse as HCs - Texas, Tennessee, USC, Eastern Michigan, Florida, ...  Finding the right balance is a trick when you have Deep Pocket Donors calling you at 2AM every night.

What if Ohio State had kept Fickell?  My guess is he'd be doing pretty well, maybe not as well as Day is, but 10+ wins a year.  Luke seems to be a good coach at least at a lesser program.  What if UGA had kept Richt?  My guess is they'd be averaging 10+ wins a season, probably not being a playoff team more than once, maybe.  Richt didn't do much at Miami. 

I agree with you 100%- Ohio State would be nowhere near what they are right now if they went with Fickell and let Ryan Day go get a head coaching gig somewhere else. Fickell is a really good defensive coach. Ryan Day is an ELITE offensive coach. Think you're pretty much on the money- they'd be a 10+ win competing for B1G- not the juggernaut that they currently are. Same thing with UGA. Kirby took their recruiting up a notch and he's an elite defensive coach. 

Lost back-to-back bowl games to Wisconsin. That got him fired.

Not technically. 

It, along with two bad years of offense got his son fired. And when Richt refused to can his kid, he was gone.