21-10-24

 I watch hockey. I know. And it gets even sillier. I'm a Leafs fan. They lost against Montreal in the first round last year. Most considered the Leafs the better team and their regular season record suggested as much. In fact, the team they lost to, Montreal, ranked lower in the league than what should have qualified them for a playoff berth. 

A million years ago I remember listening to some statistician talk about how a best of seven series is only slightly better than a coin toss in the world of professional sports. In the playoffs you would think that the teams that make it are, well, pretty good. Or relatively evenly matched. 

The NHL had 31 teams last year. Each team has about 22 players (active rosters being between 19 and 23 players, maybe, or something like that, ruled by a maximum salary cap) (I'm probably wrong about the minimum) So 31 teams X 22 players per team, there are 682 NHL level players, give or take, in a given season. Those guys must be pretty good, right? I mean, the worst guy in the league is probably better than 99% of the people who play hockey. We're watching the top 1% of hockey players. So that being said, the worst team in the league is probably pretty good. And the playoffs do away with half of the teams who are pretty good. 

So you have a team like the Leafs facing off against Montreal in the first round. The Leafs won the division, the Canadians came in last. And they played some hockey. Montreal won. Losing to such a mediocre team (LAST IN THE DIVISION) had many Leafs fans upset. 

Here's the deal; the worst team in the NHL is pretty good. The top 16 teams are even better. Montreal was 16th (actually 18th based on points, but...). Let's say Toronto is better. Substantially better. At this level, let's say they win 60% of the games, Montreal wins the other 40%. That's a big chasm considering they are both top half of an elite league-ish. Toronto will win 50% more games. The 60/40 split means Toronto will win 3 games for every 2 games Montreal wins. 3 is 50% more than 2. That seems pretty dominant and as a Leafs fan I'd be upset losing to Montreal. Right? Throw my $189 sweater on the ice upset. 

So I found a random number generator on TheInternet™. And I made it pick numbers randomly between 1 and 20. I clicked it 45 times. And old school, pen on paper, I marked off a victory for Toronto if the number was between 1 and 12 (60% of 20) and marked off a victory for Montreal if the number was between 13 and 20 (40% of 20). Toronto had a much better chance of hitting. Right? 

At the end of 45 cycles I started at the first roll and counted forward until one team had won 4 games and thus a series. Then I started at the second number. Then the third. 

At the end of it, Montreal theoretically won 23 best of seven series, Toronto won 17. That would suggest despite being the better team, Toronto would lose more often. 

Of course this isn't true. Toronto, by the very nature of how we set up the theoretical trial, is the better team. 

I remember a show or podcast or article or something, suggesting that in professional sports, if we genuinely wanted the best team to win any series at that level, we'd have to make every round over one hundred games. Any thing less and it's possible for the weaker team to move forward by chance. 

All that to say, hockey season has started again. I'm watching. But I don't know why.