In the last post, I discussed how the Poisson distribution can model scoring in hockey (and other sports such as soccer and lacrosse). I looked at how we can estimate a team's "true" expected winning percentage based on their average goals scored and allowed.In this post, I'll illustrate how the same method can estimate the probability of which team will win a particular game. I'll also calculate the probability of which team would win a best-of-7 series.
Let's say the Washington Capitals are playing the Boston Bruins. The Bruins score 3.3 goals per game and allow 2.2, while the Caps score 3.1 goals per game and allow 2.8. (Actually, those are goals per 60 minutes of regulation play. I exclude OT goals and shoot-out goals.)
The Bruins' goal distributions look like this (from the last post):
And the Caps' goal distributions look like this:
The Bruins are clearly the better of the two teams. Their goal distribution is skewed higher than their goals allowed. The Caps' distributions are closer together.
The average goals per game in the NHL is 2.8. When the Caps' 3.1 G/gm offense goes up against the Bruin's 2.2 G/gm defense, we could expect the Caps to score 2.5 G/gm. I look at it this way: 2.2 G/gm is 0.6 G/gm less than average for a defense. The Caps would therefore score 0.6 G/gm less than they usually do.
And because the Caps allow the league-average number of goals per game (2.8), we could expect the Bruins to score their season-long average of 3.3 G/gm. Now we have baseline expected scoring rates for each team in this particular match-up. The resulting Poisson distributions look like this:
Like I did in the last post, we can add up the probabilities of each possible goal combination. All of the permutations in which the Bruins win add up to 54.7%, and all the permutations in which the Capitals win add up to 29.2%. They'd tie in about 16% of the games, so if we split those games evenly, we get a 62.7% chance that the Bruins would win.
But this doesn't account for home ice advantage (HIA). In the NHL, the team with home ice wins about 55.4% of the time. Using a logistic adjustment (that is described in detail here), we can translate HIA into a logit value of 0.094. The Bruins' 62.7% win probability translates into a logit value of 0.520. Add them together if the game is at Boston, subtract the HIA logit from the game probability logit if the game is at Washington. Assuming the game is at Washington, we get a net logit of 0.426, which translates into a win probability of 62.7% for the Bruins. If the game were at Boston, it would be a 64.9% win probability for the Bruins.
At this point in the NHL season, the top playoff spots are already claimed. So many fans are more interested in how a best-of-7 playoff series would turn out. Given the Poisson model game probabilities, the Bruins would have a 76.1% chance of winning a playoff series vs. the Capitals.
Rather than post NHL game probabilities and series probabilities for the next few months (I'm not that interested in hockey), I've made my Excel spreadsheet available for anyone who's interested. I made a handy little interface with 2 drop down menus to select which teams you're interested in. It will calculate team expected winning percentages, game probabilities, and series probabilities.
Note that this model does not consider the end of game situations in which a trailing team pulls its goalie in favor of an additional skater. I would suspect this causes a slight amplification of goals scored for good teams, and goals allowed for poor teams. It would make ties slightly more likely than the model would expect, and it would make 2-goal victories slightly more common and 1-goal victories slightly less common than expected.
I'll repeat my disclaimer from part 1 of this post. I doubt much of what I've done here is original at all. In fact, in the past couple days I found a few hockey stats sites which I'm certain cover Poisson modeling and much more.
Posts
12 comments: