That a domain were confirmation bias, small sample size, etc... will really alter our result, many team will have a new coach one season, one of them will improve, 3 will not and we will still remember the one that improved and the importance of coaching.
It is apparently quite hard math/stat wise to see an significant coaching impact in basketball (outside Popovich) and hockey team result:
Do NBA Coaches Actually Make an Impact?
Do NBA Coaches Matter?
How Much Difference Do NHL Coaches Make? - NHL Numbers
All told, there were 41 total coaching transitions in the six seasons covered by my analysis. Five teams experienced no coaching turnover in this analysis, while fourteen had two or more coaching changes that met the criteria above.
In aggregate, the change in coaches
had no clear impact on teams’ performance.
The Data Science of Firing Your Hockey Coach
Show a significant while not crazy impact on winning rate if you change coach mid season, but previous NHL success and experience has no positive impact on it (even better not to have experience or previously won a cup)
It is a bit hard because you never have the chance to compare the same team coached by different coach and that even thought terrible coaching would probably have terrible result versus good coaching, how many bad coach would you have in the best paid league in the world with only 31 teams.
Has an Habs fan, we had really good season with some of the worst coach ever like Carbonneau, it was not easy to see where Therrien success come from either and Julien had a much worst season.