Interesting paper here showing that teams would be slightly more likely to win games if they pulled their goalies earlier.

http://people.stat.sfu.ca/~tim/papers/goalie.pdf
A brief summary:

*Most NHL teams pull their goalies with 1:00 left if trailing by one goal, and with 1:30 left trailing by two. *

The study suggests that a better strategy would be for teams to pull their goalies with 3:00 left trailing by one goal (which gains teams an average of 0.05 points in the standings every game this strategy is used), and 6:00 left if trailing by two goals (gaining teams an average of 0.03 points per game).

Of course, if a team is on a power play it is advantageous to pull the goalie even earlier than that, and when shorthanded they should be more conservative.

It is estimated that NHL teams would on average gain one point over an 82-game season if they simply decided to pull their goalies at the 3:00 mark instead of 1:00, regardless of situation.
I suppose that there could be additional benefits in adjusting for game situations (e.g. pulling the goalie even earlier if there is an offensive-zone faceoff, or a weak defensive pairing is on the ice for the leading team, or the trailing team's first line is taking a shift, or if you have a below-average goalie in net etc.)

Of course if the strategy becomes common, opponents could adjust by, say, practicing taking shots at an empty net from 200 feet away.

Could this be a viable way for teams to pick up an extra win or two over the course of a season?