The statistics on your chances of winning when you only score one goal are extremely low. Kampersal hammers even more on getting the first goal as it relates to PSU as he has some statistics on PSU when they are scored on first as opposed to being the first to score that have a significant variance.
I can't speak for Penn State, but this is one of my statistical pet peeves. There's nothing magical about scoring the first goal specifically. Yes, there is a fairly high correlation between scoring the first goal and winning, but that is not the same thing as saying that scoring the first goal is especially important. There are three relevant pieces here:
1) Some of this effect is simply a matter of one team being better than the other. The better team is more likely to win the game,
and they are more likely to score the first goal. A fair amount of the correlation between scoring the first goal and winning is nothing more than one team being better. If you want to look at the importance of the first goal, you have to control for this.
2) If you score the first goal of the game, you have guaranteed that you won't be shut out. If there is an X percent chance that a game will end in a shutout, you have eliminated the possibility that it will happen to you. However, you also eliminate this possibility if you score the second goal, or the third goal, or any goal. There is nothing specific to it being the
first goal.
3) The third part is sort of a generalization of the second. Every shot a team takes has a probability of becoming a goal. What that probability is depends upon who the shooter is, where the shot is taken from, who the goalie is, where the defenders are, and other factors. For this purpose, what that probability is for any given shot doesn't matter, other than that it is between 0 and 1. When you stipulate that a team scores first, what you are doing is saying that the probability of a shot is now 1, rather than whatever it was at the instant the shot was taken. But that has no effect on the probability than any other shot will go in. It does mean that the number of shots you will take during the game has declined by a small amount, since once the puck goes in, there won't be a rebound, but this effect is small. But the number of goals that you should be expected to score during the game has increased by (1 - the probability that the shot had to go in when it was taken). By declaring that a team scored the first goal, you have increased the total number of goals that they are expected to score. But, again, this is true of every other goal over the course of the game.
What is important is not the correlation between scoring first and winning. What's important is the correlation between scoring the first goal and winning, compared to the correlation between scoring other goals and winning. A few years back, I sat down and calculated this, though I lost the work a couple of new computers ago. What I found is that there is a slightly larger correlation between scoring the second goal and winning than there is between scoring the first goal and winning. Other than that, the differences were negligible.
In short, the focus shouldn't be on the first goal specifically. What matters is just scoring goals and not giving up goals. In other words, the null hypothesis is the winner here.