Pulling the Goalie: Savvy or Stupid?

Last week I was sort of ranting about the mindset of many hockey people.  Basically, that they stick with old ideas because they always have, not because there is any inherent logic to doing so.  One of the things that really perplexes me in a hockey game is pulling the goalie late in the 3^rd, when a team is down by a goal.  Although I am unable to back this up with any statistics, it strikes me as a bad idea that more often than not, ensures the trailing team won’t win the game.

The thought is, that with an extra attacker on the ice, the chances of scoring a game tying goal are increased.  But the catch of course, is that you no longer have a goalie.  There’s no way the opposing team’s chances of scoring a goal are not also greatly increased.  So the question is, do the benefits of having an extra player outweigh the disadvantage of not having a goalie?