All you young stats geeks out there: "Mutual +/-"

Motivation

A couple of things inspired this FanPost.  First, after making a line generator -- based on our perception that Coach Q jumbles lines hoping to catch lightning in a bottle -- I figured it would be nice to find out which players actually play best with each other.  Second, I was looking for yet another way to procrastinate and realized that NHL game reports like this one aren't hard to parse.

Actually, it's the other way around; I figured out how to write a program to read the reports, and this is just the first (read: easiest) thing that came to mind when brainstorming something statistic-ky to do.

Formulation and Results

To figure out who plays well with who, I made up a statistic called Mutual +/-.  Basically, it is the +/- (even-strength and shorthanded goals for minus against) when two players are both on the ice.  Calculating it is simply a matter of noting who is on the ice when a goal is scored and tallying +'s and -'s in a grid.

Here are the Mutual +/- numbers for the 82 games of the Blackhawks' 2009-2010 season (apologies to the sight-impaired; larger version available upon request):

To read the table, pick a player, and as you scan across, each number is your chosen player's Mutual +/- when he is on the ice with the player in that column.  The gray numbers running down the diagonal are the traditional +/- numbers for each player over the course of the season (the eagle-eyed or stats-minded among you will notice the table is symmetric across the diagonal).

Note that this isn't the most useful of numbers; it will obviously be skewed because certain lines or pairings will have been more stable, and some combinations may not have been on the ice for long.

Also, these numbers aren't as revealing for forward lines as they are for defensive pairings, because it only considers two players at a time.  To figure out optimal lines, the table above would have to be a cube instead of a square!

ADDENDUM (4/14):  As requested I've made extra grids that adjust the Mutual +/- numbers by the goals scored (for and against) and TOI for each player pair.  Since the goals are the "unit" used for +/-, I multiplied by those to weight productive pairs; for TOI, I divided, to adjust for time spent together.

• Weighted Mutual +/- [Mutual +/-] x [# Goals]
• TOI Adjusted Mutual +/- [Mutual +/-] / [TOI]
• Consolidated Mutual +/- [Mutual +/-] x [# Goals] / [TOI]

Observations

• Even in their limited time, the "Hammer of the Gods" line (Sharp-Toews-Hossa) is clearly making an impact; Sharp and Hossa are +13 when together.  You couldn't construct a better line.
• Brouwer clearly benefited from his time on the top line; his numbers with Toews and Kane stand out from those with rest of his past/current linemates.
  
• Fourth Line Magic?  Kopecky and Eager are a whopping +10 together.  Not surprising given how they ended the season, but amazing nonetheless.  Fraser's numbers are better than Burish's (though Burr hasn't played nearly as many games).
• It may be because of his negative +/-, but it looks like Byfuglien shouldn't play with anybody.  Except, perhaps Sharp, Versteeg, and Hossa -- some indication of what line he may have done well on when he was a forward.
• Other notable forward minuses:  Ladd-Bolland (second line woes?), Brouwer-Kop, Ladd-Versteeg.
• No surprises on the blue line:  Marlboro 72 was the best pairing (though with the most time together), and Hammer Soup was the next best.  The rest are pretty much all the same.
• Interesting to see that Sopel doesn't do as well with D2K or Hendry, though.  In fact, Duncs doesn't have good numbers with anybody but Seabs and Cam Barker.  Small sample size, perhaps.
• Bang for our Buck:  Our big ticket players (Tazer, 20 Cent, D2K, Panda, Soup) play really well together.  Yay!  Sharpie and T-Bone have also been great this year.
• Get well, Soupy!  While Keith and Seabrook give the forwards a Mutual +/- total of +55 and +53, respectively, Campbell gives them a still-very-respectable +43.  Hjammer gives them +17 and Sopel +6.  This sum/total doesn't actually mean anything, but does tell a thing or two about the offensive contribution of our blueliners.
• For some reason, Madden on the ice with the Hammer Soup pairing has not been good.  Is there something he isn't telling us?  (Hjammer & Ladd also seem to have something going on)
  
• I know that +/- doesn't make much sense for goalies (I guess it's basically a team goal differential), but how much less lazy Kaner has been playing in front of Niemi is rather striking.
• These numbers are slightly incomplete due to the omission (for space reasons head asplosion aversion) of Andrew Ebbett, Jack Skille, Jake Dowell, and Radek Smolenak (remember him? yeah, me neither).

As a final note:  Please go ahead and point out any errors, or any new statistical analysis you'd like to see.  I can't guarantee anything (I threw out 90% of the ideas I came up with... I'm being Kaner-lazy at this) but if there's any light to be shed, I wouldn't mind giving my new toy a spin.

Also, thanks for putting up with some pretty heavy writing... without pretty pictures (like gmh's) to wash it down.