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# Defensive Contribution

Having thoroughly messed up goaltender performance metrics, I lay awake a while last night pondering what to do next. I thought, "I'm a contrarian. Nobody looks at defensive contribution. Let's look at that."

One thing about defensive contribution puzzled me. While I'm no expert on Game Theory, hockey is obviously a zero-sum game. Team A scores a goal means Team B yields a goal. We all know that a goal prevented is as good as a goal scored, or at least that's what I tell my beer league team between periods. Given the zero-sum thing, I would think that the magnitude the value of defensive contribution would be similar to the magnitude the value of offensive contribution. But if you look at GVT in 2009-2010, Alex Ovechkin led the league in OGVT at 26.9, while Zdeno Chara and Chris Pronger led the league in DGVT at 8.9. The asymmetry bothers me.

I intend to sit down and figure out how to calculate DGVT at some point. For now, it looks like doing taxes. So I tried to figure out another method of getting at defensive contribution. A method where, ideally, somebody else does the hard work for me. An approach dawned on me that is probably too good to be true. If this works, somebody must have already described it, although I didn't find any links. If I'm stealing your idea, I apologize

I occurred to me that if I compare GAON/60 and GAOFF/60 the players essentially have done the math for me. The difference has to reflect the individual player's (plus possibly his partner's) contribution, with the team and goaltender effects averaged out. All we have to do is adjust the GAOFF/60 to the league average and we can easily calculate a defensive GVA for the player.

First we compute average GA/60. For NHL defensemen I get 9495 goals against in 232572.47 minutes played. That works out to GA/60 = 2.45 .

How to adjust GAOFF/60? Well, we can add/subtract or multiply/divide. I looked at both. The results tend to be pretty close.

For these examples, I'm looking at 5v5 data. Chris Pronger played 1437.46 minutes at even strength. His GAON/60 was 1.96 and his GAOFF/60 was 2.66. The difference 2.66 – 1.96 gives his GVA/60 of +0.70. His GVA computes to +0.70*1437.46/60 or +16.77.

Multiply/Divide example

Again for Pronger. His ratio of GAON/60 to GAOFF/60 is 1.96/2.66 or 0.7368. This times 2.45 gives his adjusted GAON/60 or 1.80. GVA/60 computed this way is 2.45 – 1.80 or +0.65. GVA is +0.65*1437.46/60 or +15.45

Appendix A contains 5v5 GVA computed both ways for the top 20 defensemen in 2009-2010. The full table is at http://spreadsheets.google.com/ccc?key=0An-GS2MUpN1mdFNkZWYyMlFsb0dUUmUxaDJ5UFFya0E&hl=en&authkey=CKrE1o4D. The differences are generally small. Computationally, add/subtract is easier. Also, if GAOFF/60 is 0, multiply/divide blows up. Using the add method, Mark Fistric led the league at 33.5. Jack Johnson finished last at -37.44. Using the multiply method, Mark Fistric again led the league at 25.77. Jack Johnson again was last at -56.98 From a symmetry standpoint, add/subtract looks more appealing.

Issues

I can see where this method would tend to inflate the value of a good defenseman on an otherwise poor team or inflate the lack of value of a poor defenseman on an otherwise good team (cough, Jack Johnson). Conversely, a good defenseman on a good team is going to have his value somewhat understated. Potentially, you could use QualComp and QualTeam to fine tune GVA, although I'd have to sit down and think about whether this is helpful.

Appendix A