Daniel Finkelstein at the Times
Posted in xn--kfs74mzzid01b.com edit by anonym on January 7th, 2009
http://www.timesonline.co.uk/section/0,,7973,00.html
Maximum Likelihood is a general way of computing model parameters. But before you can compute any specific MLE (Maximum Likelihood Estimate), you already need to specify your model.
Re-reading my original post now, it really makes no sense at all. I realize that you need both a model and an estimator. I think the point I was trying (badly) to get at is the difference between empirical and "physical" models. You can plug the results of 2500 games into a computer and use a Poisson distribution and MLE to generate empirical coefficients that (apparently) predict match results for that league fairly well. But to me it is more enlightening to start simple, estimate that teams score goals at a rate given by the league average, then account for team differences by estimating that teams score at a rate given by the team average, then account for home field advantage by estimating that teams score at different rates given by the team averages home and away, then account for strength of schedule differences, by weighting home and away goals by strength of opponent, etc., etc. That way, by looking at the changes in the coefficients as your estimates get more complex, you can understand the relative importance of the individual factors that contribute to more accurate predictions, rather than just having a long list of numbers that predict well but have no "physical" meaning.
"The Fink Tank is produced in partnership with the Decision Technologies Research Group at the University of Warwick"
http://www.timesonline.co.uk/section/0,,7973,00.html
Thanks for the link, Microbrew, fascinating stuff. I find it interesting (disappointing?) that they use a Poisson model to predict the results, then use maximum likelihood estimation on top of that to fit the data. Guess Voros is right, you do need a supercomputer to do this right. Just one question: why bother with the Poisson model at all, if you are just going to curve fit to the data in the end anyway?
I think you've got it backwards--they use the MLE to get the attack/defense coefficients for each team. They use those coefficients to calculate the expected goals per team in a head-to-head matchup, and then plug that into the poisson function to calculate the likelihood of each particular result--click on the "latest forecasts" link to see the results.
Thx for posting this, Microbrew ... I haven't had the chance to look at it in detail, but I might be able to offer some clarification, anyway.
Maximum Likelihood is a general way of computing model parameters. But before you can compute any specific MLE (Maximum Likelihood Estimate), you already need to specify your model. So Finkelstein is (presumably) using a Poisson Model for both estimation and prediction.
To elaborate, the idea is that it's impossible to "curve fit" without (implicitly or explicitly) assuming a model; likewise, it's impossible to use a (non-trivial) model without having a procedure for fitting it.
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