Modelling Team Scores as Weibull Distributions

A recent paper on arxiv provided a statistical motivation for that interpretation of the Pythagorean Expectation formula by showing that it can be derived if we consider the two teams' scores in a contest to be distributed as independent Weibull variables under certain assumptions.

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How Many Eras of VFL/AFL Football Have There Been?

Most sporting codes with a history of any significant length will eventually be described in terms of having passed through a number of eras, one or both ends of which are usually defined by some relatively obvious characteristic that forms the basis of the discussion.

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The Responsiveness of Bookmaker Prices To Winning and Losing

In this blog I'm seeking to answer a single question: how are a team's subsequent head-to-head bookmaker prices affected by the returns they've provided to head-to-head wagering on them in recent weeks? More succinctly, how much less can you expect to make wagering on recent winners and how much more on recent losers?

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Making History with VFL/AFL Final Scores

If the historical game data that I have is correct, we've gone very close to witnessing history this weekend, with the Hawthorn v Fremantle final score of 137-79 coming within a kick of finishing, instead, as a 131-79 win, or as a 138-79 win. Neither of these final scores were ever recorded in the 14,373 game history of the VFL/AFL between 1897 and 2013.

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Presentation to the Sydney Users of R Forum (SURF) - 2014

A few blogs back I mentioned that I was preparing a presentation for the Sydney Users of R Forum and promised to post it here once I'd delivered it.

So, here it is (it's about a 5Mb PDF). 

It's based on an earlier blog from this site on The Ten Most Surprising Things I've Learned About AFL So Far.

Feedback and comments welcomed.

More Ways to Derive Probability and Margin Predictions From Head-to-Head Prices

A couple of weeks ago, in this earlier blog, I described a general framework for deriving probability predictions from a bookmaker's head-to-head prices and then, if required, generating margin predictions from those probability predictions.

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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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Do Favourites Kick Straighter Than Underdogs?

We know that the TAB Bookmaker is exceptionally well-calibrated. Teams that he rates 80% chances win about 80% of the time and, more generally, teams that he rates X% chances win about X% of the time. Put another way, teams rated X% chances score more than their opponents X% of the time.

What about other scoring metrics, I wondered?

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