Im with on pulling the goalie earlier, but pulling the goalie on a power play means you leave an empty net with no downside for the defending team chucking it down the ice, since a short handed team can’t have icing called against them.
Miami (OH) in an NCAA tourney game once pulled the goalie with 12 minutes left down 6-2. They scored 3 unanswered goals before eventually giving up an empty netter with 7 seconds left.
Coaches have come a long way on this, similar to analytics discussion on going for it on fourth down. Most never used to pull their goalie until inside the last minute or down by more than 1.
I used to operate the scoreboard for rec league games at a hockey arena. Every once in awhile, a team would play the whole game with an empty net because their goalie didn't show up. Usually meant chaos.
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One game their goalie was late, so they played the first 10 minutes 6-on-5… when he went in, they had a 3-2 lead.
https://www.youtube.com/watch?v=MQWQ8SV2wb4&ab_channel=tongSanh
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3132563
Enjoy dense, PHD Level, Research