The Drivers of Overround

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What features of a contest, I wondered this week, led to it having a larger or smaller overround than an average game? In which games might the bookie be able to grab another quarter or half a percent, and in which might he be forced to round down the overround?
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Predicting a Team's Winning Percentage for the Season

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In recent blogs where I've been posting about a win production function the goal has been to fit a team's season-long winning percentage as a function of its scoring statistics for that same season. What if, instead, our goal was to predict a team's winning percentage at the start of a season, using only scoring statistics from previous seasons?
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Underachieving and Overachieving Teams

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A couple of blogs back I described some win production functions, which relate a team's winning percentage in the home-and-away season to characteristics of its scoring during that season, in particular to its rate of scoring shot production and its conversion of those scoring shots relative to its opponents'.
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What 1% of Overround Worth?

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Over on the Simulations blog I've been investigating how the returns to Kelly-staking and Level-staking respond to different levels of variability and bias in the bookmaker's team probability assessments, and to different levels of overround in that bookmaker's market prices. In this blog I'll investigate, using a purely mathematical approach, how a punter's expected return varies as the overround varies, depending on the size of the bias in the bookmaker's probability assessment and in the true probability of the team being wagered on.
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Applying the Win Production Functions to 2009 to 2011

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In the previous blog I came up with win production functions for the AFL - ways of estimating a team's winning percentage on the basis of the difference between the scoring shots it produces and those it allows its opponents to create, and the difference between the rate at which it converts those scoring shots and the rate at which its opponents convert them.
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Win Production Functions for AFL Teams - 1897 to 2010

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Right now I'm reading Wayne L Winston's Mathletics, a book about the use of fairly simple mathematics and sports statistics to gain insights into the results of American sports. Inspired by this book, in particular by a piece on Pythagorean Expectation which relates the season-long winning percentage of a baseball team to the total runs that it's scored and allowed, I wondered if an AFL team's win percentage could be similarly predicted by a handful of summary statistics about its own and its opponents' scoring.
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A Little Behind in the Scoring

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We've not had a proposition bet for a while, so here's a new one for you. We're going to pick a large number of games at random and, based on the half-time score in each, I'll pledge to bet on the team that's scored the greater number of behinds whether they be the raging favourite or the deserving underdog. It both teams have scored the same number of behinds at the main break or if the game ends in a draw, the bet is a push and neither of us need reach into our pockets. Otherwise, I collect if the team that had scored the greater number of behinds at the half goes on win, and you win if the team that had scored the lesser number of behinds at the half goes on win. Simple.
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Tipping Without Market Price Information

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In a previous blog I looked at the notion of momentum and found that Richmond, St Kilda, Melbourne and Geelong all seemed to be "momentum" teams in that their likelihood of winning a game seemed to be disproportionately affected by whether they'd won or lost their previous match.
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A Friendly Wager on the Margin

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You're watching the footy with a mate who leans over and says he reckons the Cats will win by 15 points. How much leeway should you give him to make it a fair even money bet? Surprisingly - to me anyway - the answer is 24 points either way. So, if the Cats were to record any result between a loss by 9 points and a win by 39 points you should pay out.
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Introducing MAFL's First Neural Network

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I've been leery of neural networks for some time because of their perhaps undeserved reputation for overfitting data and because of the practical difficulties that have existed in using them for prediction. Phil Brierly's Tiberius software includes an implementation of neural networks that has, at least for now, converted me. As a consequence, I'm adding one final margin predictor to the mix for 2011.
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Margin Prediction for 2011

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We've fresh tipsters for 2011, fresh Funds for 2011, so now we need fresh margin predictors for 2011. This year, all of the margin predictors are based on models that produce probability forecasts, which includes the algorithms powering ProPred, WinPred and the Head-to-Head Fund and the "model" that is the TAB Sportsbet bookmaker. The process for creating the margin predictors was to let Eureqa loose on the historical data for seasons 2007 to 2010 to produce equations that fitted previous home team margins of victory as a function of these models' probabilities.
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The Calibration of the Head-to-Head Fund Algorithm

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In the previous blog we considered the logarithmic probability score on ProPred, WinPred and the TAB bookie and found that the TAB bookie was the best calibrated of the three and that relative tipping performance was somewhat unrelated to relative probability scores. For the Head-to-Head Fund, whose job in life is to make money, the key question is to what extent do its probability scores relative to the TAB bookie's shed light on its money-making prowess.
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Assessing ProPred's, WinPred's and the Bookie's Probability Forecasts

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Almost 12 months ago, in this blog, I introduced the topic of probability scoring as a basis on which to assess the forecasting performance of a probabilistic tipster. Unfortunately, I used it for the remainder of last season as a means of assessing the ill-fated HELP algorithm, which didn't so much need a probability score to measure its awfullness as it did a stenchometer. As a consequence I think I'd mentally tainted the measure, but it deserves another run with another algorithm.
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Home Team Wagering: Rumours of Its Death Have Been Greatly Exaggerated

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I should probably have noticed this sooner, but last year was quite a profitable year for blindly wagering on Home Teams. A gambler who level-staked the AFL Designated Home Team in every game in the head-to-head and in the line market would have recorded an 8.4% ROI on his or her head-to-head wagers and a 4.1% ROI on his or her line wagers.
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Why You Should Have Genes in Your Ensemble

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Over on the MAFL Wagers & Tips blog I've been introducing the updated versions of the Heuristics, in this post and in this post. I've shown there that these heuristics are, individually, at least moderately adept at predicting historical AFL outcomes. All told, there are eleven heuristics, comfortably enough to form an ensemble, so in the spirit of the previous entry in MAFL Statistical Analyses, the question must be asked: can I find a subset of the heuristics which, collectively, using a majority voting scheme, tips better than any one of them alone?
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Ensemble Models for Predicting Binary Events

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I've been following the development of prediction markets with considerable interest over the past few years. These are markets in which the opinions of many engaged experts are combined, the notion being that their combined opinion will be a better predictor of a future outcome than the opinion of any one of them. It's a notion that has proved right on many occasions.
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