## Monday, May 13, 2013

### NHL Playoffs: Two Weeks In

Hey there!

The playoffs have been going on for two weeks now, and I am pleasantly surprised to say that they've been going pretty well in terms of what my model has output. In fact, of the six series that have wrapped up so far, the team that won each one of them was given the highest probability by my model. For instance, my model originally gave the following:

Blackhawks (77.0%) to beat Wild (23.0%)
Red Wings (59.1%) to beat Ducks (40.9%)
Sharks (62.2%) to beat Canucks (37.8%)
Kings (56.9%) to beat Blues (43.1%)
Penguins (64.2%) to beat Islanders (35.8%)
Senators (84.1%) to beat Canadiens (15.9%)

It also predicted the following at the outset:

Rangers (62.1%) to beat Capitals (37.9%)
Bruins (76.7%) to beat Maple Leafs (23.3%)

These last two series will be wrapped up tonight, and hopefully I can keep my success streak up. Currently, though, with a 6-0 record I am very pleased with the model so far. Wish me luck!

Today's post is gonna look a little bit about some of the behind-the-scenes math that goes into this model.

What's really important is to be able to take the odds of winning an individual game and convert those into the odds of winning the series as a whole. Fortunately this can be done pretty easily using a binomial distribution.

It turns out that there are a grand total of 70 ways for a best 4 out of 7 series to work out. They break down as follows:

• 2 ways for a 4-0 (or 0-4) shut down (12.5% chance if teams are even)
• 8 ways for a 4-1 or 1-4 finish (25.0%)
• 20 ways for 4-2 or 2-4 (31.25%)
• 40 ways for 4-3 or 3-4 (31.25%)
Because NHL playoff series allow for between 4 and 7 repeated games, any advantage that a team has in an individual game gets compounded. For instance, a 50/50 chance of winning a particular game translates to a 50/50 chance of winning the series, but a 60/40 chance of winning a game becomes a 70/30 chance of winning the series as a whole. This can be visualized as follows:

The way that I've set up my model allows for the number of games previously won to factor into the probability for the series, which is convenient for allowing the model to update every day following the results from the previous nights' games. The effect of having a game in hand looks something like this:

One other factor that could have an effect is home team advantage. The series get close to balancing out the number of home games between the two teams, but whenever a series ends on an odd number of games the team who had the first home game ought to have an advantage since they've had more home games, right?

Looking at the last 3 seasons of the NHL, 54.55% of games are won by the home team and 45.45% of games are won by the away team. If we factor this into the model, we get something like this:

Well that's not much of an advantage at all, is it? Probably a good thing.

So there you go. See you again next week!

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