Assessing Probability Forecasts: Beyond Brier and Log Probability Scores

Einstein once said that "No problem can be solved from the same level of consciousness that created it". In a similar spirit - but with, regrettably and demonstrably, a mere fraction of the intellect - I find that there's something deeply satisfying about discovering that an approach to a problem you've been using can be characterised as a special case of a more general approach.

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Modelling Miscalibration

If you're making probability assessments one of the things you almost certainly want them to be is well-calibrated, and we know both from first-hand experience and a variety of analyses here on MatterOfStats over the years that the TAB Bookmaker is all of that.

Well he is, at least, well-calibrated as far as I can tell. His actual probability assessments aren't directly available but must, instead, be inferred from his head-to-head prices and I've come up with three ways of making this inference, using an Overround-Equalising, Risk-Equalising or an LPSO-Optimising approach.

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Explaining Variability in Game Margins

Some seasons are notable for the large number of blowout victories they force us to endure - a few recent seasons come immediately to mind - while others are more memorable because of their highly competitive nature. To what extent, I've often wondered, could we attribute a season full of sizable victory margins to the fact that strong teams were more often facing weak teams, making the magnitude of the defeats predictable if still lamentable, versus instead attributing them to on-the-day or random events that were genuinely unforeseeable pre-game?

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Home Team and Away Team Scores Across VFL/AFL History

About 18 months ago I investigated the statistical properties of home teams' and away teams' scoring behaviour over the period from the start of the 2006 season to the middle of the 2012 season taken as a whole. In that blog, using the VGAM package, I found that the Normal distribution provided a reasonable fit to the scores of Home teams and a much better fit to the scores of Away teams over that entire period.

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A Comparison of SOGR & VSRS Ratings

Earlier posts on the Very Simple Rating System (VSRS) and Set of Games Ratings (SOGR) included a range of attractive graphs depicting team performance within and across seasons.

But, I wondered: how do the two Systems compare in terms of the team ratings they provide and the accuracy with which game outcomes can be modelled using them, and what do any differences suggest about changes in team performance within and across seasons?

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The Dynamics of ChiPS Ratings: 2000 to 2013

Visitors to the MatterOfStats site in 2014 will be reading about ChiPS team Ratings and the new Margin Predictor and Probability Predictor that are based on them, which I introduced in this previous blog. I'll not be abandoning my other team Ratings System, MARS, since its Ratings have proven to be so statistically valuable over the years as inputs to Fund algorithms and various Predictors, but I will be comparing and contrasting the MARS and the ChiPS Ratings at various times during the season.

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Introducing ChiPS

In years past, the MAFL Fund, Tipping and Prediction algorithms have undergone significant revision during the off-season, partly in reaction to their poor performances but partly also because of my fascination - some might call it obsession - with the empirical testing of new-to-me analytic and modelling techniques. Whilst that's been enjoyable for me, I imagine that it's made MAFL frustrating and difficult to follow at times.

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Set of Games Ratings: A Comparison With VSRS

A few weeks back, Tony introduced the Very Simple Rating System (VSRS). It’s an ELO-style rating system applied to the teams in the AFL, designed so that the difference in the ratings between any pair of teams plus some home ground advantage (HGA) can be interpreted as the expected difference in scores for a game involving those two teams played at a neutral venue. Tony's explored a number of variants of the basic VSRS approach across a number of blogs, but I'll be focussing here on the version he created in that first blog.

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