EDITED FOR TYPO...SORRY
I took a look at the Coaching Carousel in 2021 and 2022 to see how coaches who resigned to take other opportunities' replacements fared. I only chose those who left the school by leaving on their own for another coaching opportunity or those who retired on their own under no pressure (i.e. Frank) I chose those years because the transfer portal was intact and it would give time to see how the successors have fared:
Thanks to OU alum Bill Bender of the Sporting News for a nice resource to explain how the coaches moved on.

* = higher winning percentage by replacement

2021
Hired from within:
School Outgoing (record)/Incoming (record)
Louisiana Napier (40-12)/Desomareaux (23-17)
Notre Dame Kelly (92-39)/Freeman (30-9)*
Oklahoma Riley (55-10)/Venables (22-16)
Ohio Frank Solich (115-82)/Albin (33-19)



Hired from outside with no previous coaching at school:
NONE

Hired from outside with previous coaching at school:
Fresno DeBoer (12-6)/Tedford (19-8) RETIRED*
Nevada Norvell (33-26)/Ken Wilson (4-20) FIRED
SMU Dykes (30-18)/Lashee (29-11)*


2022
Hired from within:
School Outgoing (record)/Incoming (record)
None

Hired from outside with no previous coaching at school:
UAB Bill Clark (43-20)/Dilfer (8-16)
UC Fickell (57-18)/Satterfield (8-16)
Liberty Freeze (34-15)/Chadwell (21-4)*
Cstl CarolinaChadwell (39-22)/Beck (14-11)
Kent Sean Lewis (24-31)/Kenni Burns (1-23)
Purdue Brohm (36-34)/Ryan Walters (5-19) FIRED

Hired from outside with previous coaching at school:
Louisville Satterfield (25-24)/Brohm (18-8)*



Interesting stuff. Kind of amazing one year there were no hires from within and a concurrent year with no hires from the outside! If I get a chance to do a few prior years, I will.

I'm also kind of amazed that AD's hired from the current staff only 23% of the time in these situations during this time period.

I resorted your data, and computed the difference in winning percentages:

Hired from within:
+.067(+): 2021 Notre Dame Kelly (92-39)/Freeman (30-9)
+.051(+): 2021 Ohio Frank Solich (115-82)/Albin (33-19)
-.056(RTM): 2020 Memphis Mike Norvell (38-15)/Silverfield (41-21)
-.194(RTM): 2021 Louisiana Napier (40-12)/Desomareaux (23-17)
-.267(RTM): 2021 Oklahoma Riley (55-10)/Venables (22-16)
-.298(RTM): 2020 App State Drinkiwitz (12-1)/Clark (40-24) FIRED

Hired from outside with no previous coaching at school:
+.146(+): 2022 Liberty Freeze (34-15)/Chadwell (21-4)
+.067(+): 2020 Baylor Rhule (19-20)/Aranda (36-29)
+.017(+): 2020 Fresno Tedford (26/14)/DeBoer (12/6)*
-.079(RTM): 2022 Cstl CarolinaChadwell (39-22)/Beck (14-11)
-.085(-): 2020 Wash. St. Leach (55-47)/Rolovich (5-6) FIRED NON-FOOTBALL REASONS
-.157(-): 2022 Purdue Brohm (36-34)/Ryan Walters (5-19) FIRED
-.212(-): 2020 FAU Lane Kiffin (26-13)/Taggart (15-18) FIRED
-.349(-): 2022 UAB Bill Clark (43-20)/Dilfer (8-16)
-.395(-): 2022 Kent Sean Lewis (24-31)/Kenni Burns (1-23)
-.418(-): 2020 Hawaii Rolovich(28/27)/Graham (1-10) FIRED
-.427(-): 2022 UC Fickell (57-18)/Satterfield (8-16)

Hired from outside with previous coaching at school:
+.182(+): 2022 Louisville Satterfield (25-24)/Brohm (18-8)*
+.100(+): 2021 SMU Dykes (30-18)/Lashee (29-11)*
+.037(+): 2021 Fresno DeBoer (12-6)/Tedford (19-8) RETIRED*
-.069(-): 2020 Colorado Tucker (5-7)/Dorrell (8-15) FIRED
-.125(RTM): 2020 SDSU Long (81-38)/Hoke (40-32)
-.141(RTM): 2020 Washington Petersen (55-26)/Jimmy Lake (7-6) FIRED
-.144(RTM): 2020 Michigan State Dantonio (114-57)/Tucker (23-21) FIRED
-.393(-): 2021 Nevada Norvell (33-26)/Ken Wilson (4-20) FIRED

Interesting that one person accounts for the two most extreme data points, and they were at different schools: the biggest drop when he was hired, and the biggest gain when he was replaced.

Edit - I added Albin, and one more data bit, after the percentage change in winning percentage:
+ means that a winning program improved, or a losing became winning
RTM means regression to mean, such as a winning program wins less, or losing loses less
- means a winning program became losing, or a losing program lost more

I only reformatted it. I haven't had time to look at it. Without looking, my expectation would be a certain amount of regression to the mean in all three groups.

Lots of interesting stuff here, Mike. I will look more closely when I have time. One peculiarity that I notice is that the programs that got better all have one thing in common: all were already winning, except Baylor, which was near .500. No program that was losing got better with a new coaching hire. The second thing I noticed is that the vast majority of these coaching changes involve outgoing coaches with a winning record. Does that mean that coaches with a winning record are more likely to be fired that coaches with a losing record?

Does this mean Spence Nowinsky is our man?

I think if it does come from the outside, it better be a can't miss winner like Chadwell. Mike Jacobs looks like he fits that bill.

The real myth is a hotshot assistant coming in from the outside and taking over a program. Doesn't really happen anymore except maybe losing programs.

This sample doesn't include many teams with losing records, and those that are included didn't do all that well with a new hire. Since they aren't relevant to Ohio, I look only at teams with a winning record.

For teams who hired from within, they started with an average win percentage of .689, and with the new coach, had .641a, a drop of .048.

For teams who hired someone formerly at the school, they started a bit lower, at .642, and ended a bit lower, at .569, a drop of .073.

For teams who hired someone from the outside, they started lower still, at .621, and ended even lower, at .456.

The better a team was before the change, the more apt they were to hire an insider, and that worked the best. If the teams weren't quite as good, they turned to a former coach, and the results weren't bad. The worse a team was, the more apt they were to turn to an outsider, and the outside hires were riskier. Some worked well, but often they did not. For Fresno and Liberty, it worked well. For Coastal Carolina, Washington State, Purdue, and FAU, it didn't work as well. For UAB, Hawaii, and UC it was much worse. That's also true, obviously, of Kent State, who started with a losing record and got much, much worse.

Exactly. Satterfield is in the data twice. At UC the winning percentage dropped .427 when he arrived, more than any other coaching change on the list. UC went from a solid, winning program, to a losing program. At Louisville, when he left, the winning percentage rose .182, the most of any coaching change. It went from a mediocre program under him, to a winning program after he left.

You are correct. Most of the really strong winning programs go with inside hires, especially programs with a win percentage over .700. While Ohio isn't that high overall with Albin, if you look at the last 3 years, Ohio is 3750. If we limit the discussion to teams with a winning percentage at least as high as Solich, and don't worry about what the teams with worse records did, you find:
Inside hires: 189-106 .641. 6 examples. All 6 continued to win.
Former Staff hires: 118-78 .602. 5 examples. All 5 continued to win.
Outside hires: 78-71 .523 6 examples. 3 continued to win. 3 had losing records.