Sunday, January 11, 2009

The Bruins

The Bruins have been one of the surprise teams this year, what with them having the best record in the league at the halfway point (few would have predicted this to be so). They also have the best goal differential, so it's not as if they've been lucky in the conventional sense by winning a lot of close games. However, just because a team's record is proportional to its goal differential doesn't necessarily mean that it hasn't been lucky.

This is a chart showing how the Bruins have fared in various game situations so far this season. The numbers are as of 01/07/08. A couple things can be said about these numbers:

1. The Bruins success appears to largely be a product of the percentages. They have the best shooting percentage in the league, as well as the best save percentage. This also holds true at even strength.

2. For a team with such a good record and goal differential, the Bruins are anomalous in that they're pretty average with respect to shot differential. In fact, they get outshot on average.

The Percentages

The problem for Boston is that there isn't a great deal of repeatability in terms of the percentages, particularly at even strength. This post by Tyler at mc79hockey demonstrates how the sum of a team's even strength shooting percentage and its even strength save percentage tends to regress to 100 as the season progresses. The Bruins currently sit at ~105. If I was a betting man, I'd place money on that figure significantly decreasing by April.

Are Boston's percentages at all sustainable?

We know from past posts that, while fluctuations in the percentages do indeed have little sustain in the future, a team is able to reliably influence its shooting/save through shot quality. Shot quality is moderately correlated with the percentages and is substantially reliable. Thus, over a sufficiently large sample of games, there would still likely be team-to-team variation in the percentages, with this effect being mediated by shot quality.

In past seasons, the team that leads the league in shot quality for typically has a shot quality index of roughly 1.1. That is, that team takes shots that, on average, are 10% more likely to result in a goal than the average team.

Conversely, the team that leads in the league in shot quality against typically has a shot quality index of roughly 0.9. That is, that team allows shots that, on average, are 10% less likely to result in a goal against than the average team.

If we make the very conservative assumption that Boston currently leads the league in both shot quality for and shot quality against, then we can estimate the Bruins' expected shooting percentage based on these adjustments.

Expected shooting percentage = shot quality for index * league average shooting percentage
Expected save percentage = 1- ( shot quality against index * league average shooting percentage)

League average shooting%: 0.0917

Boston's expected shooting percentage: 1.1*0.0917 = 0.10
Boston's expected save percentage: 1-(0.9*0.0917)= 0.917

Boston's actual shooting percentage: 0.118
Boston's actual save percentage: 0.93

Therefore, even if we assume that Boston currently leads the league in both shot quality for and shot quality against, the Bruins' have still outperformed their expected shooting percentage and expected save percentage. While far from constituting definitive proof of good luck, it is suggestive of it.

In actuality, the Bruins have not been leading the league in either shot quality for or in shot quality against. Hockeynumbers tabulates data on shot quality that is periodically updated throughout the season. While the data is only available for specific game situations (EV, PP, SH), figures for overall shot quality can be obtained by dividing each team's expected goals for/goals against by their corresponding shots for/shots against total, and then expressing the resulting figure relative to the league average.

In addition to having a negative shot differential, the Bruins are below average in both shot quality for and shot quality against, thus making it even less likely that they'll replicate their impressive shooting/save percentage in second half. Indeed, Boston is in the red in terms of its expected goal differential, as is nicely illustrated here

Boston's 'true' even strength shooting/save percentage

As displayed in the table at the beginning of the post, the fact that Boston has managed to lead to the league in both shooting and save percentage is largely tied to even strength play -- that is, the overall percentages are largely being driven by the exceptional even strength percentages. Therefore, the sustainability of Boston's overall percentages is critically contingent upon sustaining its high percentages at even strength. Boston's shooting/save percentage at even strength will likely fall to something more reasonable by the time the season has ended. At the same time, however, it's unlikely that its EV shooting/save percentage is merely average.

To illustrate this, assume that Boston's true underlying even strength shooting percentage is exactly league average (~0.084), with the same holding true for its even strength save percentage (~0.916). The Bruins have taken 890 shots at even strength so far this season, while allowing 920. If a team with a true EV shooting percentage of 0.084 takes 890 shots, the probability of shooting 0.109 or better by chance alone is remote (about 4 times per thousand). Likewise, if a team with a true EV save percentage of 0.916 has 920 shots against, the probability of having a save percentage better than or equal to 0.939 by chance is equally minuscule (about 5-6 times per thousand). Thus, Boston's underlying EV shooting/save percentage -- while almost certainly lower than what they've attained thus far -- is probably above average. Therefore, a complete regression to the mean is unlikely.