## Why are teams that score the first goal winning so frequently?

Francois Laplante/FreestylePhoto

Teams that score the first goal are 21-1 in this round, I look into what could be causing that

It's the statistic that's been all over the internet over the past few days. Teams that score the first goal are 21-1 (prior to last night) in this second round. As a result, players have been spouting cliches like "we just need to get the first goal" even more than usual. But the question needs to be asked, is this actually a notable statistic? Are teams that score the first goal winning more than could reasonably be expected by chance.

Sidenote: This is what we call an analytical approach. There is a difference between analytics and statistics. Analytics recognize that some statistics are predictive and explanatory, and others are just noise. Analytics largely involve trying to sort out which are which.

To begin with, I calculated the records of teams when scoring the second and third goals of the game in this second round. I wanted to see whether this was simply a case of lopsided victories (although I kind of already knew the answer). Sure enough, teams that scored the second goal of the game have gone 14-7 (67%), and teams that have scored the third goal are 12-8 (60%). A while back, Eric Tulsky found that teams that score the first, second, and third goal all win approximately 67% of games. If you consider that the average NHL game finishes something like 4-2, it makes sense that the team that scored 67% of the goals would have a 67% chance of scoring the first goal.

So the rates at which teams that have scored the second and third goals of the game are approximately what would be expected. So why is the winning team scoring 95% of the first goals in this round? Well we can use a chi-squared test to find the p-value, and thus determine whether to reject the null hypothesis. In non-stats talk, we can find the probability that teams could go 21-1 when scoring the first goal completely by chance.

I won't bore you with the math, but the result is that there is only between a 0.5% and 1% chance that this 95% winning percentage could happen completely by chance, considering the expected 67% winning percentage.  That passes just about any scientific level of significance, so it looks like there's something material going on here.

In order to look at this a little closer, I examined how these teams won their games. Presuming a team has a 50% chance of scoring the next goal at any time (it's simplistic, but we'll go with it), then one would expect that the team that scores first would surrender the next goal 50% of the time. In the 22 games that have taken place in this round (again, going into last night), 10 times has the score been tied after 0-0, which is definitely on the low side, although it's a small sample so it's not too ridiculous.

There seem to be two main possible explanations for this record. Either teams are driving the play significantly more with one-goal leads, or their goalies are preserving those leads better. I looked at both.

The average Fenwick For Percentage when leading by a goal is about 46.1%, so a number significantly higher than that for round two of the playoffs would explain some of this. Instead, though, teams have been less effective with one-goal leads here, with only 45.0% of the unblocked shot attempts.

The save percentages, however, have been significantly better. This regular season, save percentage up a goal was 92.1%, but in this round has been 94.3% (Note: That's only 5v5, but it still gives a decent idea). So clearly either teams have been doing a better job specifically defending when up a goal, or goalies have been at their best preserving leads. Likely some of both.

So what does this all mean? Well, at a certain point crumbling when allowing the first goal becomes a self-fulfilling prophecy, but until that point it certainly isn't a death sentence. That said, there is something going on here that's more than chance, so as annoying as it is to see the statistic referenced incessantly, it is at least somewhat telling.

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