Outshooting leads to winning. News at eleven.

Doogie

You’re another one that throws out some gems. I suspect that you don’t understand what you are saying.

I think most people see these types of comments and just assume: “This kid sees the game differently, he doesn’t like what is being inferred. Plus he’s taken a couple of University math courses lately.” Still, I feel moved to comment.

OLE regressions aren’t the key to the kingdom. Remember trivia craps? Simulate that and run an OLE regression on the stats for a season … you will come to the irrevocable conclusion that trivia ability is insignificant and the ability to throw hot dice is key. Your scatter plot will look even more random than that above.

A good published paper on the subject, in a statistics or mathematics journal, will almost certainly start with a general scatter plot … more or less what Derek has done. No error bars, no trend line. It’s a check for real effects. They will probably compute an r value … but will warn that the value itself doesn’t have much meaning. Other than a large r value indicates that there is likely to be value in performing a study on the data. The size of the sample and the underlying sample (frame) size have an impact, as does the variation in frame sizes … but an experienced guy, whether a mathemetician or a hockey fan who reads places like this a lot … they’ll have a pretty good sense of whether or not it makes sense to proceed.

From there, the mathematically pure, but subject naive route would be to compute the ability distributions for, in Derek’s case SH%/oppSH% and SF/SA … the structure would be a bit hairy. And being subject naive you’d probably assume ability distributions of the Dirchlet form dispersed through multinomial or multivariate normal distributions.

That’s some big math. And it would be more sensible, though even more work, to break it down into it’s components. That’s what Thinker B was doing with the rookie shooting% in a recent post at IOF. He used a binomial dispersion, the gain in using a multinomial dispersion is very small … and the math is miles simpler that way. Thinker ‘B’ also had knowledge of the subject matter, that is evidenced by the fact that he referred the rookie shooter back to the population of forwards, he knew that defenders have far less opportunity to bury shots, and therefore didn’t constitute the same peer group.

In baseball, Brad Null has done some terrific work with nested Dirichlet’s, Jim Albert has done some terrific work with nested beta’s. Googlescholar those Doogie, quite a few papers from both are publicly available. Jay Bennett is another.

In games of with a large degree of inherent randomness (baseball, hockey, trivia craps) regression analysis is just an inappropriate tool to separate the two. You will end up wih player evaluations that have tragically poor predictive value.

Career trajectories would be a better application,though essentially there we are looking at best fit lines. And even there a Bayesian approach makes more sense if one is trying to fit trajectories to individual players, and not the group as a whole. Least squares won’t work worth a damn even there, not unless the individual errors are weighted. Because if a player had 200 AB in 2003 and 550 AB in 2004 … and you were fitting a multinomial regression for batting average … using simple OLS error regression will be a train wreck. If you weighted the error of each point to 500 AB … then it would be fairer.

Even then you would end up with some players with screwy looking career trajectories … because chance alone demands that. So to get some more Thinker B action going … you take these players in the study to represent the population, compute the actual spread of curvatures you would expect from chance alone, then work back to determine the most likely true career trajectory of each player. So a guy whose career trajectory might look like a bowl (concave) with OLSE, goes more of a shallow dish with weighted OLSE, and to a shallow convex (upside down) dish with the population correction.

You could argue that some form of an intra class correlation system, a random effects model regression, would be the best option. You would be wrong, but at least you’d be in the conversation. RE modelling would be the best choice if we were ignorant of the source of results (test scores, adverse reactions to drugs,etc.) … but that’s not the case with batting average. We know where batting average comes from, it’s hits divided by at bats. And we know (thanks to the work of Bill James and hundreds of others over the years) that bernoulli dispersion is an effective model for simple BA. We also know of park effects, PED effects, injury effects etc. And the result of the study would likely show certain types of players had a comparable career trajectory. So you could lump these player types into classes and try again.

So that would be a place where you could sensibly apply regression analysis in hockey. Granted I’ve simplified a touch. I don’t see you or godot doing that, though.

I know you guys probably both feel that “outshooting doesn’t matter” and bust in with this stuff for that reason alone. That doesn’t bother me, Doogie. Guys like Scott, Derek, Tyler, etc … I don’t think that they fully realize how bewilderingly naive your comments are, and they don’t have math backgrounds, so there is a chance that they will find yours, godot’s,etc comments discouraging. My hope is that, by pointing out your folly, they learn to ignore you in a casual way, understanding that you just don’t like what the information is implying.

It’s for the greater good, Doogie.