Pareto distribution and goal scoring

[soireeculturelle]

Did a piece about Vanek, who had 20 shots in 5 games with no goals before getting a hat trick on 5 shots last night, and that led me to take a look at the distribution of goals. Turns out he usually scores 65-75% of his goals in 20% of his regular season games, and goes scoreless in more than 2/3 of the season. Same patterns holds across players and years. Not quite the 80-20 rule, but somewhat close, and an indication that any scorer is streaky.

full text: http://canadiens.nhl.com/club/news.htm?id=710315

Click to read more...

 

[hatterson]

Interesting look at it. How many players did you run the numbers for in terms of number of games with a certain amount of goals? I see Vanek and Patches in the article, did you break down any more?

I'd be curious if all players follow the pattern or if certain ones who don't appear as high on the hat trick list but still score a lot (Kessel and Stamkos are two that jump out) are a little more weighted to scoring in more games versus in bunches.

 

[schuckers]

Looks more like a classic Poisson

Numbers for Pacioretty from your column followed by the approximate expected goals/game in ( )'s using a Poisson rate of 30/61:

41 (38), 12 (18), 6 (4), 2 (1)

Numbers for Vanek in 08-09 using a rate of 40/73 similarly:

44 (42), 19 (23), 9 (7), 1 (1)

Numbers for Vanek in 13-14 using a rate of 24/66 are:

47 (45), 15 (17), 3 (3), 1 (0)


There are some differences from the theoretical here but generally the Poisson does pretty well. There is some evidence out there that a generalized version of the Poisson fits data like these better.

 

[soireeculturelle]

Numbers for Pacioretty from your column followed by the approximate expected goals/game in ( )'s using a Poisson rate of 30/61:

41 (38), 12 (18), 6 (4), 2 (1)

Numbers for Vanek in 08-09 using a rate of 40/73 similarly:

44 (42), 19 (23), 9 (7), 1 (1)

Numbers for Vanek in 13-14 using a rate of 24/66 are:

47 (45), 15 (17), 3 (3), 1 (0)


There are some differences from the theoretical here but generally the Poisson does pretty well. There is some evidence out there that a generalized version of the Poisson fits data like these better.

I'll look into that. There's only so much that I remember from my college stats courses...

Fact of the matter is, the local media was beginning to talk about vanek "needing to get going," which is kind of a specious argument considering he was already shooting at an elite rate to begin with. would do a lot in terms of managing expectations if more fans knew that, even for the best scorers, it's usually a good bet to assume that they wont score at all 2/3 of the time.

 

[soireeculturelle]

Ovechkin in 2009-10 (50 goals in 72 games):
30 goals (60% of goals) in best 15 games (20% of season)
No goals in 37 games (52% of season)

Stamkos in 2011-12 (60 goals in 82 games)
32 goals (53%) in best 17 games (21% of season)
No goals in 37 games (45% of season)

 

[Ohashi_Jouzu*]

I'll look into that. There's only so much that I remember from my college stats courses...

Fact of the matter is, the local media was beginning to talk about vanek "needing to get going," which is kind of a specious argument considering he was already shooting at an elite rate to begin with. would do a lot in terms of managing expectations if more fans knew that, even for the best scorers, it's usually a good bet to assume that they wont score at all 2/3 of the time.

Well you would get a good laugh from posters on the Habs board who are pretty firm in their conviction that 26 minutes of ice time with Plekanec without a goal, on a new team, without practicing, and in a checking role, was enough to conclude that they wouldn't work together. Heck, you can find a coach on the Habs bench who apparently thinks the same way, lol.

 

[soireeculturelle]

Well you would get a good laugh from posters on the Habs board who are pretty firm in their conviction that 26 minutes of ice time with Plekanec without a goal, on a new team, without practicing, and in a checking role, was enough to conclude that they wouldn't work together. Heck, you can find a coach on the Habs bench who apparently thinks the same way, lol.

there's no perfect, criticism-proof way to deploy most NHL players. getting a bunch of offensive zone starts with desharnais and pacioretty jives with how vanek was used with NYI and BUF earlier in the year, and a lot of fans were complaining about that when he was taking less of those draws alongside plekanec. the fact of the matter is, most NHLers can play with most other NHLers. you could optimize your whole team at the expense of getting the most possible production out of 1 line. plus, in real life it's never as simple as 1+1+1=3.