Now that the Super Bowl is over, let’s turn our attention to the one sport that every Yalie cares about: men’s hockey.
Following its incredible run to the national championship last year, the team has just over a quarter of the season left before the playoffs begin. Currently, the Bulldogs are ranked 13th in the country. But here’s some bad news: berths in the NCAA Tournament are determined by the Selection Committee, which uses a mathematical formula (based on records against common opponents, head-to-head competition, and strength of schedule) to determine which 16 teams get to play in the Tournament. Right now, there are 19 teams that have a higher ranking than the Elis using that formula.
Of course, with at least eight games left in the season and ECAC playoffs coming up, the Bulldogs can significantly improve their rankings. Two areas that the Elis could improve on are the power play and the penalty kill. Right now, the Yale special teams play is ranked an abysmal 56th in the country.
But other statistics suggest that Yale is better than its record. The Bulldogs field top-10 level scoring offense and defense. More impressively, Yale’s goal differential is ranked sixth in the country. Four of the teams ahead of the Elis could very well be the number one regional seeds in this year’s NCAA Tournament.
One reason that the win percentage of the Bulldogs obscures their true strength is something that almost impossible to measure: luck. More specifically, luck in close games. Four of the Elis’ six losses this season were determined by two goals or less, with three determined by only one goal. Hockey can be a fickle sport. An irregular bounce of the puck could be the difference between a win and a loss.
Thanks to better statistical tools, we can derive some imperfect measures of just how lucky a team is. Baseball sabermetrician Bill James pioneered an empirical tool called Pythagorean expectation, which estimates how many games a baseball team should have won based on runs scored and runs allowed. The logic behind this estimate is simple: A team that consistently outscores its opponents should win more games. Thus, a lucky team’s win percentage would be higher than its Pythagorean expectation while the opposite is true for an unlucky team. Luck is especially important in close games since a lucky team wins more close games than it should, thus boosting its overall record.
For hockey, the Pythagorean expectation is determined by a formula that divides goal scored, raised to an exponent, by the sum of goal scored and goal allowed, both raised to the same exponent. The trick here is to find what the exponent is. Too high and the Pythagorean expectation would skew upward, too low and the expectation would skew downward.
For baseball, Bill James showed that an exponent of two has significant predictive power. But since hockey can end in ties, a lower exponent is needed. Hockeyanalytics.com suggests that an exponent of 1.86 works best for hockey.
Based on my analysis, out of the top 20 teams in the country, five teams have a Pythagorean expectation higher than their actual win percentage — suggesting that they are better than their records suggest. Of those five teams, only three teams have a win percentage differential greater than five percentage points: Notre Dame, New Hampshire and Yale. Though Notre Dame and New Hampshire lag behind Yale in national rankings, they are actually more likely to make the cut for the NCAA Tournament, which partially confirms Pythagorean expectation’s analytical power. Teams that have outperformed their Pythagorean expectations include traditional powerhouses such as Minnesota and North Dakota, as well as some of Yale’s ECAC rivals like Cornell and Clarkson.
However, the Pythagorean formula above is static, meaning that it doesn’t take into account how win expectation evolves as a team’s characteristics change. For example, a team that averages six goals scored and three goals allowed should win more than a team that averages two and one, but the static Pythagorean model predicts the same record for both of these teams.
To account for this, I use an exponent that’s based on each team’s total goals per game and some empirically derived parameters. This dynamic analysis confirms the results of the basic Pythagorean model: Yale’s win percentage is about six points too low. Over of the course of an entire season, this translates into about a two-win deficit for the Elis, a difference big enough to decide whether they can make it to the NCAA Tournament.
Statistical analysis suggests that the Bulldogs have been somewhat unlucky, especially in closely contested matches. Four of Yale’s games already resulted in ties this season. The Bulldogs had a grand total of seven ties combined over the last three seasons. As the season goes on, however, Yale should perform closer to its Pythagorean expectation.
Of course, my analysis is limited by a number of factors. The formulas I used are based on results from the NHL, past results do not necessarily extrapolate to the future and the sample size in my analysis is small (about 25 games), especially compared to baseball (162 games in a season). Moreover, the team has had to deal with a slew of injuries to key players since winter break, and a healthier lineup would help tremendously as the Bulldogs head toward ECAC playoffs.
However, the Pythagorean expectation does reveal some interesting insights into Yale’s season, and college hockey, so far. With a little luck, the Bulldogs maybe the Bulldogs can replicate the magical run from last season?