Variations on a Theme: Different Formulations of Quality of Competition

One very nice innovation on Quality of Competition came from Jonathan Willis at Copper 'n Blue. In order to calculate Quality of Competition, you normally need 1) TOI totals for every player; and 2) head-to-head icetime totals for every player combination. This data is only available for the NHL, and it's only available for the last three years. What Willis did was to use goal events as a proxy for icetime. That is, in the absence of TOI, Willis assumed that the total number of goals a player was on the ice for was a reasonable proxy for the amount of time he spent matched up against specific opposing players.

That changes the Quality of Competition from:

QoC = sum[(Opponent Rating)*(Opponent TOI)]/TOI

Where Rating = (GFON/60 - GAON/60) - (GFOFF/60 - GAOFF/60) for each opponent.

To something like:

QoC = sum[(Opponent Rating#2)*(Opponent + and - per GP)]/(Opponent + and - per GP)

Where Rating#2 = (GFON/GP - GAON/GP) - (GFOFF/GP - GAOFF/GP)

Or something very similar - I don't think it matters very much whether you use GP or total events as a proxy for TOI.

At any rate, I generated Quality of Competition four different ways for the Edmonton Oilers. Rankings among regular players are below:

QC0 QC1 QC2 QC3
ETHANMOREAU 3 3 5 1
SHELDONSOURAY 2 2 12 12
STEVESTAIOS 9 8 3 5
JASONSTRUDWICK 20 20 8 6
LUBOMIRVISNOVSKY 8 10 17 17
SHAWNHORCOFF 1 1 2 4
ALESHEMSKY 5 7 7 19
ALESKOTALIK 17 17 16 7
DENISGREBESHKOV 11 9 13 14
FERNANDOPISANI 3 6 9 11
MARC-ANTOINEPOULIOT 17 18 15 15
ROBERTNILSSON 11 15 6 10
PATRICKO'SULLIVAN 9 11 11 13
DUSTINPENNER 5 4 10 20
LADISLAVSMID 16 14 4 3
ANDREWCOGLIANO 13 13 1 2
KYLEBRODZIAK 19 19 20 8
ZACHERYSTORTINI 21 21 19 18
TOMGILBERT 5 5 18 16
SAMGAGNER 13 16 14 21
LIAMREDDOX 13 12 21 9

QC0 is Quality of Competition as calculated on my site. QC1 is the same TOI-based calculation, but it includes only the off-ice stats for games the player played in (for simplicity of calculation, QC0 includes all of a team's games.) QC2 assumes total TOI is known, but uses goal events (+ and -) as a proxy for head-to-head icetime. QC3 is the same as QC2, but uses games played as a proxy for TOI.

Some results are similar: everybody loves Horcoff and Moreau; everybody hates Stortini. But there are some substantial differences between these systems too. The TOI based ones favor Sheldon Souray, Dustin Penner and Tom Gilbert, while the proxy systems like Jason Strudwick, Ladislav Smid and Andrew Cogliano.

So my question is - given that I see maybe one Oilers game per season - which system seems to be closest to the right answer? Is the difference tolerable?

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