Maybe I'm late here, but of course goal differential has an extremely high correlation to a team's position in the standings. Games are won on goals scored and goals allowed. Nothing else matters on the scoreboard. It's like saying the team that scores first in a game wins more than 50% of the time - of course they do.
Goals for and goals against are the result. Corsi and Fenwick are predictors of goal differential.
The thing with goals in the NHL is that there are so few of them, and with so few events, you typically don't see a trend until you are deeper into the season.
Shot attempts are much more frequent, which is why a lot of people use them to analyze game trends, and ultimately puck possession. Of course Corsi/Fenwick don't have as a high a correlation to goal differential when predicting the standings, but the correlation is significant, and can typically be analyzed with a smaller sample size.
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