Intangibos
High-End Intangibos
Not 100% sure they have exactly what you are looking for, but my search for most stats starts here: NHL Stats, History, Scores, & Records | Hockey-Reference.com
I'm just wondering the statistics of empty net/extra attacker goals. It seems like you get a 3:1 ratio of goals against/for with the empty net and you're only scoring an average of 0.04 goals for at even strength per minute. Not only that but the other team has the same odds of scoring while 5 on 5 anyway. It seems like pulling to goalie early to get the 1:3 ratio would easily be worth it if the goal per minute with the extra attacker was high enough to offset your chance of scoring 5v5 while not getting scored on as well.
I'm 100% positive they have analytics for this, but honestly I'm surprised teams don't pull their goalies earlier especially when they're down 2. Given that the odds of scoring 2 goals within 6 minutes is like 0.04% anyway why wouldn't you pull the goalie earlier to see if you can pot one. If you close a 3-1 game to 3-2 you can put the goalie in and reevaluate if there is enough time left or keep him out if there isn't much time left. 25% of the time (when a goal is scored) you'll have cut the lead and if the 75% chance of getting scored on is the result you threw away a 1/20 chance of scoring 2 goals at even strength, again while the other team has the opportunity to score on you as well.
In a 3-1 game given the odds that you're actually score twice I'm not sure if pulling the goalie earlier is a significant risk at all. You would almost certainly need to pull your goalie anyway to get 2 goals in 6 minutes, so why does it matter if you pull him at 6 minutes or 3 minutes? Not only are 2 in 6 unlikely, but scoring 2 in 3 if you would pull him at 3 minutes is very unlikely so you're risking even less
Anyway I would just love to do/see the math but I don't know the goals/60 with an extra attacker to see if the risk is worth it, but it seems like it must be when you're down more than 1 goal as you're very unlikely to come back anyway. I'm sure I'm wrong because analytic firms get paid a lot of money for this kind of stuff, but I would love to see exactly where the equilibrium is because I'm surprised we don't see goalies heading to the bench early for what seems like a low risk high reward play. Maybe I'm just doing the math wrong because it's late but this isn't exactly calculus
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