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Thursday, April 22, 2010
When is the first goal of a period scored?
Using data kindly provided by Gabriel for the last five seasons, half of the games had their first goal scored within the first 509 seconds of the first period.
Half of the second periods occurred with the first goal scored in the first 411 seconds of that period.
Half of the third periods occurred with the first goal scored in the first 458 seconds of that period.
Here are the median results for the playoffs:
period median seconds
1 501
2 410
3 479
4 448 (78 OT games)
5 461 (16)
6 597 (3)
7 543 (1)
Generally speaking, we see the “out of the gate” period scoring in the regular season and playoffs is similar for the first three periods: take your time in the first period, come out faster in the second period.
I was more interested in the overtime. And we see that the longer the game lasts, the longer it takes for that first goal of the period to come. I was watching the Bruins / Sabres OT game, and I was wondering when I should expect that first goal. It seems to be that half the time, I should expect a goal within the first 8 minutes or so, somewhere around the 460 second mark (459 in the regular season, 463 in the playoffs).
Could we have calculated that mathematically? Well, in the data I have, there is one goal scored every 644 seconds, or an average of 0.00155 goal scored per second. Or, every 0.99845, there is no goal scored. What exponent can we raise that number to, so we get a value of .500? (This is where logs work out well, kids, and why you should stay in school.) The ln(.5) divided by the ln(1-1/644) gives you the exponent. And that answer is 446 seconds. That is, we should have been able to figure it out that if there is an equal chance of scoring at any point in the period, half of the first goals would occur within the first 446 seconds.
Now, naturally, scoring right off the center-ice faceoff in second number one is impossible. But, anyway, I like it when the empirical (around 460) and the theoretical (446) match up so well.
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