Do longer playoff series (in first to x formats) lead to worse outcomes in subsequent rounds?

In the NHL, it’s generally accepted wisdom that if two teams face each other in a playoff round, and one team has played fewer games in the playoffs due to having fewer losses in previous rounds, they’re at an advantage due to being less tired/injured etc. But has anyone done a statistical analysis to show if this is the case or not? Obviously there’s a big confounding factor (a team that loses less is probably just flat out better) but I think this could probably be corrected for using regular season results.

Example in case it isn’t clear: COL beat STL 4-0 in the first round, VGK beat MIN 4-3, now COL plays VGK with 3 fewer games played recently and would be argued to have an advantage.

I’m mostly interested in the hockey case, but other sports with significant injury risks would answer the question too.