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08-22-2011, 01:05 PM
Czech Your Math
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Originally Posted by plusandminus View Post
If I was asked to rank the following seasonal ES stats for players, without paying any attention at all to context, I would rank them as follow (with a tie for 2nd best):

72-50 +22 1.440 112 161.28
60-40 +20 1.500 100 150
40-20 +20 2.000 60 120
45-30 +15 1.500 75 112.5
7- 4 + 3 1.750 11 19.25
3- 1 + 2 3.000 4 12
GD=GF-GA (goal difference). GS=GF+GA (goal sum).

1. The guy with a GF/GA of 3.000 looks far too good compared to the others.
2. The lower numbers, the more extreme GF/GA. (It's a bit like pts per game. The fewer games played, the more extreme points per game.)

That's why I generally think one should be careful with using GF/GA.
The metric I've been tinkering with does not use any formula akin to (GF/GA)*(GF+GA). Neither does Overpass' adjusted plus-minus. Also, I agree that small sample sizes tend to lead to skewed results. That is why taking the best X seasons or career numbers are going to be more reliable for almost any metric.

In your 60/40 vs. 40/20 example, context is very important. First, it tells you in what environment the data was created. Second, it tells you what impact the player's performance is going to have. Since one player has 20/20 more than the other, if the R-Off of his team was > 1.0, then his performance did not help his team, while if it was < 1.0 it did help his team.

Originally Posted by plusandminus View Post
3. Player ice time share during ES vary a lot between players. So does the amount time the player was not on the ice. No matter if one use real ice times, or take GF+GA, the differences are big.
4. Thus, when comparing "with" and "without", we would be comparing for example a GF/GA based on very low numbers, with a GF/GA based on very high numbers.

I'm not convinced yet regarding how good the win formula, and other formulas are at handling the things I mentioned above. Maybe they are great.
Again, that's why need multiple seasons to have any real solid data.

Maybe I should focus more or solely on the player's portion of the formula. I came up with the distribution of team's ES wins while thinking of some way to address Overpass' concern that players on great teams are hampered by the team's strong R-OFF. Honestly, getting credit for "just showing up" is not that great, although it's actually "playing a lot for great teams", and usually it's very good players who get lots of ice time over many years on great teams.

The player's portion is calculated by deducting his ES goals for/against from the team totals. The better the ratio and the more goals he was on ice for, the more impact it will have on the estimated win% differential, but it's more complex than multiplying the GF/GA ratio by the sum of ES GF + GA.

Originally Posted by plusandminus View Post
The above seems based a lot on GF/GA, and I think GF/GA can "lie".

Let's say we have a 2-3 result without player on ice (GF/GA=0.400).
Player on ice doing 5-3 will make his team win 7-6, despite GF/GA=1.667.
Player on ice doing 2-1will only make his team draw 4-4, despite GF/GA of 2.00.

As I said, maybe the win formula and other formulas have methods to guard for such contradictions.
All stats can "lie", 76% of statisticians can attest to that.

I'm not using GF/GA ratio as an absolute metric. In referring to Overpass' adjusted plus-minus, I do think R-ON/R-OFF is a valuable metric. It tells you in % terms how much more effective the team was with that player on the ice than without him on the ice, and that's a valuable piece of information.

Originally Posted by plusandminus View Post
By themselves, I think both are equal. Context may make one look better, but I'm not sure GF/GA is the best way to determine that.
I may be wrong.
They are similar, but not equal in most cases. An extra 10 GF and 10 GA is outstanding on the '75 Capitals and rather weak on a dynasty team.

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