Modelling Team Scores as Weibull Distributions : Part II

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In a previous post I discussed the possibility of modelling AFL team scores as Weibull distributions, finding that there was no compelling empirical or other reason to discount the idea and promising to conduct further analyses to more directly assess the Weibull distribution's suitability for the task.

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Home Team and Away Team Scores Across VFL/AFL History

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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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The Ten Most Surprising Things I've Learned About AFL So Far

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The last few months have been a generally reflective time for me, and with my decision to leave unchanged the core of MAFL algorithms for 2014 I've been focussing some of that reflection on the eight full seasons I've now spent analysing and predicting AFL results.

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MARS Rating Changes and Scoring Percentages: 1897-2013

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The idea for this blog sprang from some correspondence with Friend of MAFL, Michael, so let me start by thanking him for being the inspiration. Michael was interested in exploring the relationship between team performances and the resulting change in their MARS Ratings across a season, which I'll explore here by charting, for each team and every season, the for-and-against percentage they achieved in all games including Finals, and the change in their MARS Rating per game during that same season.
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Defensive and Offensive Abilities : Do They Persist Across Seasons?

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In the previous blog we reviewed the relationship between teams' winning percentages in one season and their winning percentages in subsequent seasons. We found that the relationship was moderate to strong from one season to the next and then tapered off fairly quickly over the course of the next couple of seasons so that, by the time a season was three years distant, it told us relatively little about a team's likely winning percentage. There is, of course, an inextricable link between winning and scoring, and in this blog we'll investigate the temporal relationships in teams' scoring in much the same way as we investigated the temporal relationships in teams' winning in that previous blog.
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Team Scores - Statistical Distribution and Dependence

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In the most recent post on the Simulations blog I assumed that Home Team and Away Team scores were independently and Normally distributed (about their conditional means). I'll investigate both these assumptions in this blog.
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Estimating Fair Head-to-Head Prices : Part I

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You'll recall that the total overround embedded in the head-to-head market, ignoring the possibility of a draw, is calculated by summing the reciprocal of the head-to-head prices for each team. So, for example, if the head-to-head prices for a game were $1.20 / $4.60, the overround would be 1/1.2 + 1/4.6, which is 105.1%. Some subtract 1 from this figure and would report this overround as 5.1%.
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The Increased Importance of Predicting Away Team Scores

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In an earlier blog we found that the score of the Home team carried more information about the final game margin than did the score of the Away team. One way of interpreting this fact is that, given the choice between improving your prediction of the Home team score or your prediction of the Away team score, you should opt for the former if your goal is to predict the final game margin. While that's true, it turns out that it's less true now than it once was.
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Finding Non-Linear Relationships Between AFL Variables : Alternative Measures to MIC

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The Maximal Information Coefficient (MIC) that we explored in the previous blog is not the only non-linear measure of the pairwise relationship between any two continuous variables.
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Finding Non-Linear Relationships Between AFL Variables : The MINER Package

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It's easy enough to determine whether or not one continuous variable has a linear relationship with another, and how strong that relationship is, by calculating the Pearson product-moment correlation coefficient for the two variables. A value near +1 for this coefficient indicates a strong, positive linear relationship between the variables in question, so that high values of one tend to coincide with high values of the other, and vice versa for low values; a value near -1 indicates a strong, negative linear relationship; and a value of 0 indicates a lack of any linear relationship at all. But what if we want to assess more generally if there's a relationship between two variables, linear or otherwise, and we don't know the exact form that this relationship takes? That's the purpose for which the Maximal Information Coefficient (MIC) was created, and recently made available in an R package called MINER.
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Measures of Game Competitiveness

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All this analysis of victory margins, and a query from Dan about a recent blog post, has had me wondering about victory margin as a measure of the competitiveness of games. Within a given era - say 10 years or so - during which the average points scored per game won't vary by too much, victory margin seems to be a reasonable proxy for competitiveness, but if you want to consider a broader swathe of AFL history, it strikes me as being deficient.
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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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