A percentage of "crucial" goals (that is, goals that I have listed above minus garbage goals divided by total goals against)...
Very nice work running those numbers. Nothing of what I'm about to say is intended to be critical, I'm just hoping to help you refine the analysis a bit.
First of all, I think you should consider revising the quoted formula. Right now it rewards goalies for letting in garbage goals, because every garbage goal effectively cancels out a crucial mistake.
I'll use the example of Jacques Plante in 1955. I did this quickly so my count might not match yours exactly (I didn't check the two minute thing because you said it was partially subjective and it was also not always easy to tell whether Hodge or Plante was in net), but it looks like Plante let in the first goal of the game once, he let in a goal that broke a third period tie twice and he let in a go-ahead goal in the third period once. That should give him at least four "crucial" goals against.
On the other hand, he gave up six garbage goals in the high scoring Stanley Cup Finals that year based on your definition. I agree that it's fine to disregard them because who cares what happened when the score is 5-0, 5-1, 4-1 or 5-2, none of them had any significant impact on the Habs' win probability. But no amount of blowout goals against erases the fact that the Canadiens with Plante in net still blew a 2-1 lead in the third period of game 1 of the Finals and lost 4-2, which was a crucial swing in a series they lost in 7. So it seems a bit odd to suggest that Plante's final playoff score would still somehow work out to 0%.
Perhaps a better formula would be to subtract the garbage goals from the total goals first, and then divide the crucial goals by the new "meaningful but not crucial" amount. That would put Plante at 17% (4/23), for example.
But even that denominator might still have a bit of a problem, because the other thing with this type of analysis when interpreting it is that (like with all goalie stats) you have to factor in what kind of team the goalie is playing on. For example, here were the scores after two periods in every one of Montreal's games in the 1955 playoffs:
2-0
3-1
0-4
2-2 (1 crucial GA in 3rd)
4-1
1-1 (2 crucial GA in 3rd)
0-7
3-2
4-1
1-4
4-2
0-2
There were only three games in the entire Montreal postseason where the game was a one-goal game at any point in the third period, and Jacques Plante gave up three crucial goals in those three games, and just one in all the other games combined (the first goal of the game). That's not all that surprising, really, because that's pretty much what we'd expect based on your definitions.
Compare that to, say, the 1999 Dallas Stars, who entered the third period with the score within one goal in 20 of 23 games during their Cup run. That means that a much higher percentage of the goals are going to count as "crucial" even if the goalie isn't giving up very many of them. For example, 15 of the 21 goals scored in the Stanley Cup Finals would count as crucial, and despite his sparkling 1.26 Finals GAA Ed Belfour would get dinged for an awful 78% crucial goals percentage over those 6 games just because the score was basically always close. In the 1955 Final, just 9 out of 46 goals overall and only 3 of 15 third period goals would count as "crucial". I'm not convinced that Sawchuk and Plante trading blowouts actually means they were more reliable than a guy winning a crazy goalie duel.
It might be possible to narrow the situations down to where you are comparing similar score lines, i.e. looking only at games that enter the third period within a goal. Or you could potentially focus solely on each goalie's GAA in each specific situation. The problem is that you will probably end up with a very small sample size, so who knows how meaningful it is, but so it goes with pretty much any attempt at 3rd period/OT type analysis in the playoffs. Anyway, great start, I'll be interested to see where this goes in round 2.
