Which ones had starting QB's returning?
So just for fun.....between 2015 and 2016 there were 27 coaching changes in D1/FBS.
Of those, 14 of the teams had a returning QB, and 13 did not*
The AVERAGE difference in wins from year to year was +.26 wins.
The MEDIAN of the difference in wins was 0
SO, on average, there was little to no impact when changing coaches regardless of record.
Returning QB
The AVERAGE difference in wins from year to year with a returning starter at QB was -.07 Wins.
The MEDIAN difference in wins from year to year with a returning starter at QB was -.5 Wins.
No Returning QB
The AVERAGE difference in wins from year to year without a returning starter at QB was +.62 Wins.
The MEDIAN difference in wins from year to year without a returning starter at QB was 0 Wins.
The teams that changed coaches were a mix of teams. If I subjectively split them into two groups: The Helmet Schools and the Non-Helmet Schools we get the following
The AVERAGE difference in wins from year to year for a helmet school was +1 Wins.
The MEDIAN difference in wins from year to year for a helmet school was +1.5 Wins.
The Min difference in wins from year to year for a helmet school was -2 (Georgia, returning QB)
The Max difference in wins from year to year for a helmet school was +3 (Va Tech, returning QB)
The AVERAGE difference in wins from year to year for a non-helmet school was +.13 Wins.
The MEDIAN difference in wins from year to year without a non-helmet school was 0 Wins.
The Min difference in wins from year to year for a non-helmet school was -6 (Bowling Green, returning QB)
The Max difference in wins from year to year for a helmet school was +6 (UCF, returning QB)
So those are the numbers, fit them into your narrative as best you will.
*To be clear, if the starter from 2015 was still on the roster but did not take the majority of the snaps, I still counted them as having the same QB on the team. I did not check to see how many of those were due to injury, although I know BYU was an injury situation.