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.
Read MoreFor today's post I'm also going to find eras by employing that same package, this time using as the metric for each season the fitted optimal Pythagorean Expectation Exponent.
Read MoreMost 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.
Read MoreI'll be using that same dataset today to investigate the extent to which there is a correlational structure in the quarter-to-quarter scoring of the teams in a football contest.
Read MoreLast weekend while following the progress of a game I was struck by an odd thought: have two games ever had the same scoreline at the end of every quarter?
Read MoreIn the previous blog we looked in some detail at the performance of each of the MatterOfStats Margin Predictors in terms of how well they've done in predicting the final margins in games involving a particular team as the home or as the away team.
Today I want to provide, initially, a team-based summary of that same analysis.
Read MoreI wondered then how C_Marg's team-by-team performances might compare with the other MatterOfStats Margin Predictors.
Read MoreIn 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?
Read MoreIn the previous blog we looked at MatterOfStats' new Margin Predictor, C_Marg, and quantified just how different it was from each of the other Margin Predictors. Today I'm going to do the same thing for another of the predictors that's based on the ChiPS Team Rating System, C_Prob.
Read MoreIt's been quite a year for upsets in the AFL so far. One of the ways of quantifying just how surprising these results have been is to use surprisals, about which I've written previously on a number of occasions
Read MoreIf 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.
Read MoreIn the previous blog I fitted four separate quantile regressions to game margins at the end of each quarter using the TAB Bookmaker probability as the sole regressor
Read MoreA 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.
I first heard about quantile regression, I think, over a decade ago and, for whatever reason, could never quite understand it nor fathom a useful application for it here.
Read MoreA 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.
Read MoreEinstein 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.
Read MoreIf 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.
Read MoreWe 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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