Sometimes it works, sometimes! I've seen it work and seen teams score the game tying goal to take the game to overtime. The thought process is if they don't pull their goalie they're going to lose anyway, may as well "give it a try".
Google tells me this:
During the 2019 – 2020 season, teams scored 14.5% when removing the goalie from the net during a one-goal deficit. The previous year was also 14.5% and the year before that was 15%. A success rate from Hockey-Graphs represents either tying the game or moving the match to overtime with a goal.
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