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Does it really help to score first?

UPDATE: The more I look at this piece, the more I wished I had just hit "Delete". I worked up some numbers, thought I had something interesting, started writing the piece, dug a little more, started to wonder whether it was worth it, and by the end, while becoming less enamoured of where I was headed, I figured I'd stitched enough together that I should just put it out there anyway. In retrospect, I really shouldn't have bothered.

The following scene is sure to replayed throughout NHL telecasts this spring, whenever an important game is on tap:

Polished announcer: "... yes, this is a big one tonight indeed. So tell me, [color commentator], what do the [insert your favorite team] have to do tonight to pull out the victory?"
Crusty Ex-player/coach: "well, if there's one thing all my years in the league have taught me, [polished announcer], it's that they really need to get that first goal of the game, and avoid playing from behind."

This is, of course, one of those hallowed cliches that is taken for granted; that the first goal of an NHL game shifts the advantage significantly towards the team with that initial lead. I went back through the 2005-6 and 2006-7 regular season data, to find just how often the team that scored the first goal went on to win the game. In 2005-6, such teams had a .662 winning percentage (that's raw wins, not including points for OT/SO losses), while in 2006-7, those teams won at a .676 rate. At first glance, that's not bad at all.

By throwing out a statistic like "scoring the first goal helps you win", we are, however, narrowing down the field of possibilites to exclude some losing scenarios, which makes the winning percentage appear greater than it should. In 2005-6 there were 119 shutouts, and last year 150 (out of 1,230 regular season NHL games), so one way to look at "scoring the first goal" is that a given team has also ensured that at least they won't be shut out. If a typical, .500-level* NHL team has a 6.5% chance of getting shut out on a particular night (this season's rate), and all I told you about a game in progress was that this team had scored a goal, you could already bump their expected winning percentage up to .535 or so since you know they're not getting blanked that evening. That one-goal lead is nice, but it's hardly decisive.

To put it perhaps a bit more simply, scoring a goal is a Good Thing in a hockey game; to say that "when a Good Thing happens, [your favorite NHL team] tends to win" isn't very enlightening, unless the numbers involved are in the extreme.

But what about the second goal scored? Is there anything special about the fact that the team scoring the second goal has either established a 2-0 lead, or evened things at 1-1, making the second goal a good indicator of victory? That appears to be more of a tipping point for a given contest; if the score becomes tied at 1, expected winning percentages revert back to roughly .500 for each side, whereas a 2-0 lead resulted in figures of .842 and .827 for the 2005-06 and 2006-07 seasons. So much for that other old adage about the two-goal lead being the most dangerous lead in hockey, eh? It looks dominating when compared with the one-goal advantage.

So keep this in mind as you settle in for nail-biting time as the playoffs approach; the first goal of the game is certainly interesting, but the second may be more likely to determine the outcome.
*Again, talking about pure winning percentage here, none of those Overtime/Shootout Loss points!

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