First to score wins - misleading stats?

Are some stats self-proving truths? Specifically, there is frequent mention of the team to score first being the one to win the game (or the team to win game one being the more likely to win the series). In football, there's talk of how often the team ahead at halftime is the team that wins the contest. For Cornell, for instance ...


cornelbigred.com [cornellbigred.collegesports.com]
>>> One of the best indicators of Cornell's success this season has been the first goal of each contest. The team is unbeaten (12-0-1) when scoring first, but if the opponent strikes the initial blow, the Big Red is just 3-4-1.

Ari's column, Groundhog day [www.elynah.com]
Perhaps the most telling stat is that in the 13 games Moulson has scored a goal, Cornell is unbeaten with a record of 12-0-1. In games where Moulson does not score a goal, the Big Red is 3-4-1 (3-5-1 if the game which Moulson did not play at Dartmouth is included).

... is this cause and effect, or effect and cause, or one stat incorporated into the other?

If every game were a one-goal game (and for Cornell hockey, that's not far off, it sometimes seems) at the end ... if you backed out the initial Cornell goal (say each time we hit the post), then every game would end in a regulation tie.

In other words, you have to wonder if the mere fact of scoring the first goal is the statistical difference, nothing more, in many games, rather than some mystical momentum builder. Statisticians have already debunked the idea of the hot shooting hand in basketball.

Dartmouth scored first and beat us by 1 in a 2-1 game.
BC scored first and beat us by 1 in a 3-2 (+ENG) game
Harvard scored first and beat us by 1 in a 1-0 game.
Cornell scored first and beat Vermont by 1 in a 2-1 game.
Union scored first and lost by 1 in overtime, 2-1 (I guess the "lost by 1 in overtime" is redundant)
In these games, save Union, the first to score won because the rest of the way the teams traded goals.