Thursday, August 07, 2008

Individual Goals Against Averages

I have written several sabermetrics and hockey posts this summer about adjusting +/- ratings. This is a useful method to rank NHL players. It is not an entirely simple or solved problem, but it is one that will likely lead to some sabermetric advances in the future.

If we want to rank defensive values of players, it might be a more useful starting point to look at the number of goals scored when a player is on the ice. It is possible to give each player a goals against average in the same manner that goaltenders get them. In order to remove some interpretation problems, for starters, I will look only at the time a player plays in an even strength 5 on 5 situation. These numbers are very raw and have some of the same problems as +/- does. The raw individual GAA numbers are strongly dependant upon the team in which a player plays. Good defensive teams allow fewer goals and thus their players have lower GAAs. Similarly, bad defensive teams allow more goals and their players have bad GAAs. This effect must be corrected for. There are other problems with strength of opposition and strength of teammates that need to be taken into account. Statistics to calculate these GAAs can be found on the behind the net website.

We can start by looking at the raw numbers and in further posts try to adjust them to make them more meaningful. As a context, we can compare to goaltender's GAAs. They are not exactly the same thing because goalie stats do not measure only 5 on 5 situations. They include penalty killing and power play situations. Among goalies who played 25 or more games last year (enough time to have meaningful numbers), Chris Osgood of Detroit led the NHL with a 2.09 GAA and Johan Hedberg of Atlanta was the worst with a 3.46 GAA. We will find that individual players have a much larger range in their GAAs. This is because, unlike goalies, many players only play in certain situations that will tend to help or hurt their numbers and goalies play the entire game. It is unreasonable to believe that a position player has more of an effect on a team allowing goals than the goalie does, despite the larger range of GAAs. This is an artifact of the situations in which individual players play that much be removed from the raw numbers to make meaningful player evaluations.

Here are the 10 best individual player GAAs among players who played 50 or more games in 2007/08:

Top 10 Individual Goals Against Averages 2007/08
1George ParrosAna0.88
2Kent HuskinsAna1.22
3Mathieu SchneiderAna1.27
4Shawn ThorntonBos1.27
5Johan FranzenDet1.33
6Brad MayAna1.34
7Michael SameulssonDet1.34
8Travis MoenAna1.35
9Blair BettsNYR1.38
10Johnny OduyaNJ1.38

Clearly, all the players on this list are from good defensive teams. Many are not players that are typically thought of as being particularly good defensively who are played in situations where goals are unlikely. Only a couple on this list are players I would consider good defensive players.

Anaheim dominates the list. They had the second best team GAA (behind Detroit), but their coach Randy Carlyle tends to match players to situations on the ice with more regularity than Mike Babcock of Detroit does.

George Parros leads the league in individual GAA, but he does it playing against very low quality opposition. This result is mostly a result of Anaheim trying to hide their goon from any tough situations. Next up come defencemen Kent Huskins and Mathieu Schneider. They generally do not play against the toughest opposition (Chris Pronger, Scott Niedermayer and Francois Beauchemin do on the Anaheim defence), but unlike a forward they cannot be as well hidden from tough situations. Shawn Thornton is next. He is another who regularly plays against weak opposition. Next up is Johan Franzen of Detroit. He too plays against relatively weak opposition as Pavel Datsyuk and Henrik Zetterberg generally play against the toughest players or Kirk Maltby and Kris Draper do. Since he is on neither of those lines he benefits from easier opposition, although Detroit does not match lines as much as Anaheim does. Brad May is another Anaheim player who is kept from tough situations. Mikael Sameulsson is a Detroit player who regularly plays with Johan Franzen. Travis Moen is the first player who plays against tough opposition. His presence on this list says a lot about his defensive ability. Blair Betts is another beneficiary of weak opposition. Finally, Johnny Oduya is on this list. He plays tough minutes in New Jersey (not as tough as Moen's minutes), but they do not keep him away from top scoring players. Of the players on this list only Moen and Oduya play against the top lines on a regular basis. They are players who are among the best defensive players in the NHL.

Here are the worst 10 individual GAAs from the 2007/08 season among players with 50 or more games played:

Worst 10 Individual Goals Against Averages 2007/08
1Vincent LeCavalierTB3.80
2Ilya KovalchukAtl3.77
3Martin St LouisTB3.69
4Mike CammalleriLA3.56
5Brad RichardsDal3.53
6Paul RangerTB3.52
7Todd WhiteAtl3.50
8Kyle BrodziakEdm3.44
9Patrick O'SullivanLA3.44
10Filip KubaTB3.43

This list is dominated by players on bad teams who play against tough opposition. Usually bad teams have ineffective checking lines and put their most talented offensive stars out against the top line in a game (particularly if they are losing and want to attempt to comeback). Thus, we have a list of some of the best offensive players on some of the worst teams in the league. In fact, given the chance, I would happily trade the players with the 10 best individual GAAs for those with the 10 worst.

Vincent LeCavalier is the worst from the weak Tampa Bay Lightning. He is a very good offensive player. He is followed by Ilya Kovalchuk, the best offensive player on the weak Atlanta Thrashers. Martin St Louis is another Tampa star near the top of our list. Next up is Mike Cammalleri, one of the best offensive players on the weak Los Angeles Kings. Brad Richards is next. He would have done even worse had he not been traded to the Dallas Stars at the trade deadline, as they are far better defensively than the Tampa Bay Lightning. Paul Ranger is the first Tampa Bay defenceman on this list. Todd White is next as a frequent Kovalchuk linemate in Atlanta. Kyle Brodziak is a rookie who struggled to learn to play defence in Edmonton (who was a weak team but not as weak as the ones the other players on the list come from). He is the first forward on this list that is not used in an offensive role on many occasions. Patrick O'Sullivan is next. He plays an offensive role on the weak Los Angeles Kings. Filip Kuba is the final player. He plays against top lines on the weak Tampa defence.

Although these raw individual GAA numbers do little to tell us who the best defensive players (or worst) in the game are, they are a starting point from which that information can be obtained. Generally, the league leaders are players on strong defensive teams who play against weak opposition (there are a few exceptions). Generally the worst numbers in the league are players who play strong offensive games on the weakest teams (again there are some exceptions). Turning these numbers into something more useful is a process that I will try to explore in the future and show some of the unsolved problems revealed.

Are you going somewhere with these posts? By that I mean are these posts a prelude to something meaningful in the form of a formula to calculate a more complete and accurate player rating stat?
With these posts I am exploring sabermetrics as far as it has been pushed so far. I will do better than merely showing individual player's GAAs - but I cannot lead to any definitive complete and accurate rating stat because one does not exist. There will be many useful raitings along the way (on/off ice adjusted +/- is an example of a useful one - even if there are open questions about how exaclty to include strenght of opposition and apparent strength of teammates).

It is useful to lay out what is known and how it is useful to the puzzle and speculate on what still needs to be done to complete the puzzle.
As a fantasy hockey junkie, I appreciate the statistical musings and ramblings for what they are, without need for a particular overarching payoff.
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