This is Part 9 in a many-splendored series of answers to frequently asked questions about hockey analysis. Here are Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7 and Part 8.
The corollary to Quality of Competition (see Part 2) is Quality of Teammates. Rather than averaging the relative +/- (see Part 1) of a player's opponents, we average the relative +/- of a player's teammates based on how much ice time they had together. (You can find 2008-09 leaders at 5-on-5 here.)
What you see at the top of the list for Quality of Teammates are guys who played as particularly effective lines: Parise/Zajac/Langenbrunner; Hossa/Datsyuk/Holmstrom; Perron/Oshie/Berglund; Krejci/Lucic/Wheeler. And at the bottom, a lot of defensive forwards - Rob Niedermayer, Travis Moen and Sami Pahlsson were dead last in each of the last two seasons (while they were with Anaheim, they were perhaps the most extreme line in the entire NHL - they played exclusively together more than any other pairing, and they are at the top or bottom of every statistical category we can come up with.)
Quality of Teammates has some of the same properties as Quality of Competition. For example, we can pick a team - say the 2008-09 San Jose Sharks - and see how that team's lines were configured. From San Jose's chart, we get the following:
I haven't looked at very many teams, but the Sharks seem to be a great example of the relationship between Qualcomp and Qualteam. By Qualteam, their first line was Marleau/Thornton/Setoguchi - and so it was by Qualcomp too. Todd Mclellan believed use them as his first line, and opposing coaches matched up against them as though they were the first line. The same is true for line 2 (Pavelski/Michalek/Clowe) and line 3 (Chechoo/Roenick/Grier) or Marcel Goc, the 4th line center. Travis Moen spent much of the season in Anaheim and was used a bit differently, but essentially every other player's role made sense to both the Sharks coaching staff and to opposing coaches.
One major difficulty with using this simple formulation for Quality of Teammates is separating the performance of one player from another. Unlike Quality of Competition, where it's exceedingly unlikely for two players to match up together even 5% of the time, some players play together almost all the time. In some cases we couldn't separate them no matter what we do - the Sedin twins played together over 90% of the time last season. Even if we thought Henrik Sedin was better off centering Alex Burrows and Pavol Demitra, we have no ice time data to prove it.