The Puck Stops Here

One issue to address in the sabermetrics and hockey problem of adjusting +/- ratings is the quality of teammates a player has. Since players will play different roles on their teams, different players will share ice time with different quality of linemates. Some players will play with better linemates than others. This will show up in their +/- rating. Players who play with better quality linemates will have better +/- ratings. This is very similar to the way quality of opposition influences +/- ratings. Credit this calculation goes to Gabriel Desjardins of behind the net.

This effect can be addressed in the same manner as with quality of opposition. The average on/off ice adjusted +/- can be calculated averaged over the time each teammate is played with. When we do this, we get the following top 10 quality of teammate rankings (for players who played 50 or more GP last season):

Top 10 Quality of Teammates Ratings 2007/08

Rank	Player	Team	Q of Team	Adjusted +/-
1	Tomas Holmstrom	Det	0.89	+0.37
2	Brian Rafalski	Det	0.61	+0.53
3	Henrik Zetterberg	Det	0.56	+1.80
4	Daniel Alfredsson	Ott	0.55	-0.13
5	Pavel Datsyuk	Det	0.49	+2.05
6	Nicklas Lidstrom	Det	0.46	+1.66
7	Milan Michalek	SJ	0.45	+1.89
8	JP Dumont	Nas	0.45	+0.74
9	Daymond Langkow	Cal	0.44	+0.91
10	Tomas Plekanec	Mon	0.43	+0.92

This first thing I notice upon looking at these numbers is that they are much larger than the quality of opposition numbers. Sami Pahlsson led the NHL with a 0.18 quality of opposition and this would be well outside the top ten in these numbers. I do not believe that the difference is really as big as these numbers show. I think it is an effect of averaging over many different opposition teams that decreases those numbers. A player has only a few regular linemates, so there is far less averaging that occurs to reduce values. One or two exceptional teammates will boost a quality of teammate ranking significantly. This is why Detroit dominates the rankings with five of the top six. Daniel Alfredsson is on the list for playing with Dany Heatley and Jason Spezza. Milan Michalek makes it playing with Joe Thornton. JP Dumont makes it playing with Jason Arnott. Daymond Langkow makes it playing with Jarome Iginla. Tomas Plekanec is the onö ly player on the list who is not directly tracved to somebody in the top 20 on/off ice adjusted +/- rankings. Plekanec is probably the weakest member of the Montreal number one line, so his inclusion makes sense.

We can also look at the 10 worst quality of linemates last season:

Worst 10 Quality of Teammate Ratings 2007/08

Rank	Player	Team	Q of Team	Adjusted +/-
1	Aaron Downey	Det	-0.69	-1.26
2	Kirk Maltby	Det	-0.67	-1.61
3	Rob Niedermayer	Ana	-0.65	-0.94
4	Blair Betts	NYR	-0.62	-0.67
5	Jed Ortmeyer	Nas	-0.62	-1.52
6	Matt Ellis	LA	-0.59	-0.58
7	Travis Moen	Ana	-0.58	-1.08
8	Dallas Drake	Det	-0.56	-2.46
9	Sami Pahlsson	Ana	-0.54	-1.23
10	Kris Draper	Det	-0.53	-1.58

Detroit dominates both the top and bottom of this list. I don't think this is reality. I think this isn't reality. It's a problem from the fact that Detroit has several high adjusted +/- players (Datsyuk, Zetterberg and Lidstrom). Those who play with them have high quality of teammates and those who don't appear to have low quality of teammates. The Anaheim line of Rob Niedermayer, Travis Moen and Sami Pahlsson is a case of players pulling each other down. They play against tough opposition and have poor adjusted +/- rating as a result. Since they play together, they appear to have low quality of teammates as well. I would argue Matt Ellis, Blair Betts and Jed Ortmeyer are probably the only players on this least who legitimately have weak teammates. However, even if this does not always deliver players with poor quality of teammates it is useful as it will give an adjustment for players who have had +/- ratings unfairly lowered because of comparison to players with top ones on their team. The Detroit players probably do have worse adjusted +/- ratings than they should. That may not be because of poor quality teammates, but it appears as such from flaws in the method. That said it is no truer that a player appearing on the worst teammates list is actually a good player then it is true that a player on the best teammates list is actually a bad player.

Quality of teammates can be calculated from on/off ice adjusted +/- values. These rankings are dominated by any dominant teams (Detroit in 2007/08) at both the top and bottom. Those who play with the best players have the best quality of teammates and those who don't appear to have the worst quality. Nevertheless, this is a useful thing to keep in mind when making sense of +/- ratings because even in the cases where it appears to fail it has value. Those players who appear to have poorly ranked quality of teammates are the players who most suffered from comparison to teammates in the off ice portion of their adjusted +/- rating, so they are undervalued, but not directly from low quality teammates. It's a case of high quality teammates they do not regularly play with.