Tuesday, October 30, 2007

First Sign Of A Dominant Team

One statistic problem that is important in sabermetrics and hockey is that of discrete counting stats. These are numbers where an even either occurs or it doesn't, such as goals or wins. It is not meaningful to score half a goal or win a quarter of a game. You either win the whole game or you do not win at all. You either score a whole goal or you do not score at all. The minimum possible error in interpreting numbers of this sort is two discrete events (and in many cases this theoretical error far underestimates the actual errors in the numbers). If one team has one fluke win and another team lost a game they should have won, their difference of two wins that this creates is completely meaningless. For all intents and purposes they are tied. They have the same number of wins within the minimum possible noise inherent in their win totals.

Putting aside complicating issues such as quality of opposition (in an uneven schedule), this means it takes several games before a picture emerges where any one team is ahead of the pack. Right now if we rank teams in the NHL based on the number of games they did not win (this includes losses in both regulation and in overtime and shootouts), there are three teams that are basically in a dead heat for first in the NHL. They are Detroit (9-3 one loss a regulation tie), Ottawa (9-1) and Philadelphia (7-3). From that information alone, we can conclude that any of these three teams have been the best team in the NHL so far this season (of course we have other information which I am neglecting at this point - information that may enter other teams into the argument). In order to better determine which of these teams is playing the best from their discrete wins/losses totals we must wait until more games are played.

Thus, we like to look for other statistics which are strong proxies for win loss records. Other statistics, which may also be discrete numbers, but accumulate at a faster rate so that we can have a better look at how teams are doing outside of the noise of discrete counting errors.

I think the statistic that most quickly accumulates that is well enough correlated with winning and losing that it is worth discussing is shots on goal. In the average NHL game a team will have twenty or thirty something shots on goal. After approximately ten games played, the differences between most teams in shots on goal are becoming statistically meaningful. The correlation between taking shots on goal and scoring and not allowing shots on goal and not being scored on and thus winning and losing from the shots on goal totals are meaningful enough that they give us a good picture of how well teams re performing. Of course, there are complicating factors such as shot quality and quality of goaltending on a given team which they do not capture, but nevertheless, they give us a first good look at how well teams are performing.

Due to the problem of teams having played different numbers of games played, we will take the discrete shots on goal numbers as ratios of shots on goal per game played. The discrete counting error is carried through into these ratios (along with any other errors that may exist), but they provide meaningful numbers.

With one look at the shots on goal per game numbers, it is clear that there has been a dominant team so far this season. That team is the Detroit Red Wings. They lead the NHL in shots on goal per game with 34.2 (this is a small lead over Carolina's 34.0 shots per game). They also lead the NHL in the least shots allowed per game. This lead is much more meaningful since their 22.5 shots per game is well over a shot better than the second place San Jose Sharks with 24.2 shots allowed per game. From those numbers, Detroit has clearly been the most dominant team in the NHL so far. Of course we can argue about just how well shots on goal really do correlate with winning. We can argue about if those numbers are flukes that cannot hold up throughout the season. We can argue many points that question just how dominant Detroit has been and will be this season. However, leading the NHL in most shots per game and in least shots allowed per game simultaneously is very impressive. I think the Detroit Red Wings have been the best team in the NHL so far and by a significant margin. I think this little analysis shows it very well.

For the record, Detroit led the league last year in shots with 33.8 shots per game with the Panthers second at 33.3 shots per game. They also led the league in fewest shots on goal allowed with just 24.6 shots per game against with the Dallas Stars second with 25.4 shots per game against. So, Detroit leading in both categories is nothing new and this is why they gave the Ducks the biggest challenge en route to their cup win. They are the best team in the NHL.
Who counts the shots for every game?
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