## uh, carry the one, ...

Math 10

We're about 15% of the way into the NHL season, long enough to briefly revisit how many points it looks like it will take to make the playoffs.

To recap, in the '03/'04 season, 315 of 1230 (25.6%) of games were tied after regulation. The same number this season would mean 315 "extra" points spread amongst the 30 teams, since there is a 3rd point awarded in all games tied after 60 minutes. That's an average of 10.5 points per team, or put another way, the average point total this season would be 92.5.

Through 187 games so far this season, 39 have been tied after 60, or 20.9%. Extrapolated over the entire season, this amounts to 257 extra points, 8.6 per team, or an average point total of 90.6.

This is slightly interesting: roughly 20% (1 - (20.9/25.6)) fewer games this year are tied after 60. Why such a big difference?
1. More goals means a lower likelihood of a tie (this should be self-evident)
2. Fluke (small sample size)
3. Both
I'd wager the answer is (C). The increase in goal scoring we've seen thus far (~1 GPG, yes?) doesn't seem like enough to account for a 20% reduction in reg. ties (this is calculable, just not by me). It should cause some decrease, though (soccer has few goals, lots of reg ties; basketball & football have lots of points, and few reg. ties).

Anyway, the average point total for NHL teams this season should end up in the 91-92 range; if you have reason to believe otherwise, I'd love to hear why in the comments.

Math 20

For starters, if you're not familiar with the difference between mean and median, go read this brief, simple explanation.

The median team in each NHL conference is the one in 8th place: there are 7 teams ranked above it, and 7 below. The mean point total in the NHL over the past four seasons (where there was both ties and the OTL point, and 30 teams) has been roughly 86.5.

Over that same period, the eight 8th-place teams (2 per conference X 4 seasons) have had a point total higher than the mean 7 times, the '02/03 NYI being the only team to make the playoffs with a point total lower than the NHL mean.

Furthermore, the 9th-place team (ranked one below the median) has had a point total higher than the mean 4 out of 8 times. This is a mathematical way of expressing something Oilers fans know twice already: sometimes you can have an "above average" team and miss the playoffs, even though more than half of the teams make the playoffs.

Out of the admittedly small sample size of eight, the median (8th-place) team has finished an average of 3 points higher than the mean, while the 9th-place team has finished an average of 3/4 of a point below the mean.

I'll invite explanations from the readers on why this is as well. Mathematically speaking, it arises from the fact that the worst teams are statistically worse than the great teams are statistically great.

If you had to guess at the point totals for the 8th-place teams this season, you should add 3 to the expected mean, which translates to the 94-95 point range.

Math 30 & Physics 30

Colby Cosh has done us a service by bringing up binomial distribution, if only for the purpose of looking soberly at this concept called "consistency":
...the absence of ties is going to make winning and losing streaks longer as a matter of statistical course. I'm not suggesting this is relevant to the Oilers, but even a .600 hockey team whose wins are randomly distributed will lose five straight games at some point in more than half (54.3%) of its 82-game seasons.

Yes. You take a deck of 82 cards, containing 41 red and 41 black. Shuffle them up and start dealing them in a straight line. It is not bizarre to see streaks of 3, 4, 5, or even more of either colour. What would be bizarre is if you didn't see that. (And the chance of them alternating evenly is statistically negligible, on the order of your chances of winning the 6/49 three times, then being struck by lighting).

If there are more reds in the deck than blacks, then a streak of blacks less likely, but not at all unlikely or weird. This is just the way things are.

Of course, this isn't totally comforting to a fan concerned about her team's losing streak, because in the hockey version of the deck of cards, we don't know in advance how many reds and blacks are in there. (If you deal 5 straight blacks off the top of the deck, it may just be that's because it's chock full of black cards). But it should lend some perspective.

The hockey media, fans, me, etc. are always compelled to explain why, why! a team is on a roll, or struggling, or whatever. It's fun. But the fact remains that if your team's games were all settled by a coin flip, you'd see these streaks too. (And my recollection of thermodynamics is that nothing ever happens that makes the universe less disorderly, so the idea that your team's hard work ethic & leadership should reduce "inconsistency" is impossible for me to swallow).

-- End Geek Transmission