Sunday, July 17, 2005

Goals Created

Continuing my series of posts on sabermetrics and hockey, we will now address the topic of goals created. This post is a bit of a footnote to my hockey player rating method post because that rating method uses goals created in its framework. The idea of goals created is presented by Daryl Shilling in his hockey project.

The idea behind goals created is to try to estimate how many goals a given player created for his team. They are estimated as follows:

Goals Created (GC) = (G * 0.5) + (A * (2 – (LWA/LWG)))

Where LWA is league wide assists and LWG is league wide goals in the season in question. This formula is an approximation. There is no deep basis to show that (for example) a goal scorer is responsible for the creation of exactly half of the goals he scores.

Let's look at some results of this formulation.

The 10 best careers ranked in terms of goals created are:

1 Wayne Gretzky 887
2 Gordie Howe 850
3 Mark Messier 631
4 Phil Esposito 599
5 Steve Yzerman 596
6 Ron Francis 596
7 Mario Lemieux 581
8 Marcel Dionne 578
9 Brett Hull 555
10 Stan Mikita 552

This is certainly a list of ten very good offensive players.

I've seen that formula floating around, but I'm still not sure about the rationale behind the (2-(LgA/LgG)) part. So here's a theoretical one I've been thinking about:
We know that roughly 75% of all goals have 2 assists, about 20% of goals have 1 assist, and about 5% are unassisted. On unassisted goals, the goal scorer should get 100% of the credit, because he did all the work. On 1-assist goals, the scorer and assister should split the credit 50-50; on any goal, I figure 4 things have to happen: the shooter gets open, the passer sees the open shooter, the passer makes the correct pass, and the shooter scores... it's 50-50 because half of those acts belong to the shooter and half to the scorer on a 1-assist goal. On 2-assist goals I credit the scorer with 50%, the first assist with 30%, and the 2nd assist with 20%. The rationale being that on 2-assist goals, you can tack on another act to the original 4: the 2nd assister making his pass. He doesn't get a "vision" credit, because I've found that the 1st assist requires far more vision than a second assist, which can be outlet passes, etc. So, let's compute the values for each type of point:
*Goals: .05*(1) + .95*(.5) = .525
(full credit on unassisteds, plus half credit on all assisted goals)
*1st Assists: .2*(.5) + .75*(.3) = .325
(half credit for assists on 1-assist goals, plus 3/10 credit on the first assist of a 2-assist goal)
*2nd Assists: .75*(.2) = .15
(1/5 credit on all 2nd assists)
So now we have as our formula:

GC = .525*(Goals) + .325*(1st Assists) + .15*(2nd Assists)

...but the NHL doesn't differentiate between 1st and 2nd assists in its records. So we have to lump all assists together, then assume the league ration for all players. Using data from 2000-01, I found that of the 11504 total assists, about 56% were 1st assists and 44% were 2nd assists. Those figures seem as good as any, so let's plug them in the equation:

GC = .525*(Goals) + .325*(.56*(Assists)) + .15*(.44*(Assists))

Simplifying, we finally get:

GC = .525*(Goals) + .248*(Assists)

Whew! I think that this makes more sense than The Hockey Project's formula, even though basic assumptions still must be made for either formula to work.
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