It’s just a few hours until the beginning of the 2014 NHL playoffs, and while most people are focused on previewing and trying to predict the first-round series, I thought it might be worthwhile to offer some thoughts on home-ice advantage. In my research on prediction of single games, the one variable that predicted winning more consistently than any #fancystat is simply the building the game is played in: across over 10,000 NHL games between 2005 and 2013, the home team won about 55.3% of the time. There are lots of reasons why this is the case. Having the last change allows the home team’s coaches to set up more favorable on-ice match-ups, and the rules give the home team’s centers a small but real advantage in the faceoff circle. Other work indicates that home teams get fewer penalties called against them and spend less time on the penalty kill. Insofar as identifying other variables that consistently predict single-game victories in NHL hockey is next to impossible, any model for predicting the outcome of short series probably needs to lean significantly on home-ice effects. I’ve described my own playoff model before, but the gist of it is this: a measure of each team’s overall strength is combined with an analytic model of home-ice advantage to forecast the probabilities of winning the series for either team.
Here’s how the home-ice piece works. First, let’s assume that Team A and Team B are perfectly mediocre and perfectly evenly matched (mGF% 50% for each team), but Team A starts the series with home-ice advantage. Assuming the NHL’s 2-2-1-1-1 series format and a 55.8% win probability for home teams (i.e., the home-ice win % in the eight postseasons going back to 2006), Team A has a 51.8% probability of winning the series, while Team B has (1 – 51.8%) = 48.2% chance of winning. This is before any games have been played.
The interesting thing here is how the conditional probabilities change once we start playing games. Let’s say Team B wins Game 1 on the road. Now the probabilities look like this:
If you win Game 1 (again, assuming the teams are evenly matched), your probability of winning the series jumps to 65.75%; you need three more wins in three remaining home games and three remaining road games, while your opponent still needs four wins and only has three games left at home. Team A can no longer win in four (obviously), but their probability of winning in five is unchanged: they still need to win two home games and two road games, or (2*Pr(W|H))*(2*Pr(W|R)) = (2*0.558)*(2*0.442) = 0.0608. For B to sweep, they need to win one road game and two home games, or Pr(W|R)*(2*Pr(W|H)) = 0.442*(2*0.558) = 0.1377.
If Team A ties the series at 1-1, their win probability improves a bit, but they still need to win three games with only two more on home ice, while Team B needs three wins with three remaining home games. Because Game 6 is a home game for B, they’re more likely to win in six than in seven, which would require a road win in the deciding game.
Keeping this going, let’s say Team B wins both games at home to take a 3-1 series lead. At this point, they need just one more win, meaning their overall probability of taking the series is very high (86.2%). If they can take one more road game (probability = 1 – 0.558 = 0.442), they win in five. If they lose Game 5 but win Game 6 at home, they clinch with a probability of (Pr(L|R)*Pr(W|H)) = (0.558*0.442) = 0.3117. However, if A wins Games 5 and 6, with the same probability of 0.3117, they get Game 7 at home, which puts Team B at a disadvantage.
As you can see, home-ice advantage implies that the probability of winning a seven-game series fluctuates a lot as teams move through the games. (Yes, I will be tracking such fluctuations during the playoffs at Puck Prediction.) There are a few implications of this that are worth keeping in mind as you watch the 2014 postseason:
- The first team to a two-game advantage in the series (i.e., 2-0, 3-1) has a very high probability of closing it out.
- As such, if you’re starting a series on the road, getting at least a split in the first two games is vital for your chances of winning.
- If you get to a two-game advantage, especially if you’re starting the series on the road, you need to clinch the series as quickly as possible. Your probability of winning drops sharply if you let the other team back into it.