Saturday, July 19, 2008

Making Sense Of +/-

In a sabermetrics and hockey discussion of defence, the usual starting point is +/- ratings. +/- ratings give a player a plus when he is on the ice for an even strength or short-handed goal and a minus when he is on the ice for an even strength or short-handed goal. This statistic does not measure defence per se. It is an attempt to measure the overall quality of a player. A high scorer can have a good +/- rating without playing great defence because he is high scoring and a lower scorer can have one if his team allows fewer goals when he is on the ice than they score. It is one measure where good defence may come out, if a player appears much higher in the +/- ratings than he should be from offence alone.

The biggest problem with +/- ratings is comparing between different teams. A player on a good team will have a good +/- because his team regularly scores more goals than they allow (independent of the player involved) and a player on a bad team will have a bad +/- rating because his team regularly allows more goals than they score (independent of the player involved). In order to attempt to compare players on different teams, it is necessary to establish a baseline for a given team to compare individual player with.

The most successful method to do this (in my opinion) is the on and off ice +/- calculated on behind the net.

The theory behind this technique is to compare +/- ratings for players when they are on the ice with that of their teammates when they are off the ice. This is best done when ice time is normalized out of the problem. Hence, instead of reporting +/- ratings as counting stats (as is done by the NHL), they are reported as +/- ratings per 60 minutes of ice time.

As an example, let's look at Selke Trophy winner Pavel Datsyuk. Datsyuk plays for the Stanley Cup winning Detroit Red Wings and thus should have a good +/- because of his team. He is also a good scorer and a good defensive player. This should give him a good +/- after adjustment for his team as well. When Datsyuk was on the ice last season, Detroit scored 4.04 goals per sixty minutes and allowed 1.84. This makes him +2.20 goals per 60 minutes. When Datsyuk was not on the ice, Detroit's offence was much less spectacular scoring only 1.90 goals per 60 minutes, but their defence allowed only 1.75 goals. Thus when Datsyuk is off the ice, his team had a 0.15 +/- rating. This gives Datsyuk a net +2.05 on and off ice +/-. This is a very good number and is strong evidence that Pavel Datsyuk is one of the best players in the NHL.

Of course, these numbers are not perfect. All players on a team are not used in the same situation. Some players match up against the opposing team's best scorers and others against weaker players on the opposing team. Some players tend to play with better linemates than others. These factors will also affect +/- ratings.

In an attempt to find good defensive players statistically, +/- ratings are a start. This can be significantly improved by comparing them to a baseline for a given team (so that comparison between different teams is possible). Comparing a player's +/- when he is on the ice against his team's +/- when he is off the ice is a very good way to do this.

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