How Many Quarters Will the Favourite Win?

Over the past few blogs I've been investigating the relationship between the result of each quarter of an AFL game and the pre-game head-to-head prices set for that same game. In the most recent blog I came up with an equation that allows us to estimate the probability that a team will win a quarter (p) using as input only that team's pre-game Implicit Victory Probability (V), which we can derive from the pre-game head-to-head prices as the ratio of the team's opponent's price divided by the sum of the two teams' prices.

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Deriving the Relationship Between Quarter-by-Quarter and Game Victory Probabilities

In an earlier blog we estimated empirical relationships between Home Teams' success rate in each Quarter of the game and their Implicit Probability of Victory, as reflected in the TAB Bookmaker's pre-game prices. It turned out that this relationship appeared to be quite similar for all four Quarters, with the possible exception of the 3rd. We also showed that there was a near one-to-one relationship between the Home Team's Implicit Probability and its actual Victory Probability - in other words, that the TAB Bookmaker's forecasts were well-calibrated. Together, these results imply an empirical relationship between the Home Team's likelihood of winning a Quarter and its likelihood of winning an entire Game. In this blog I'm going to draw on a little probability theory to see if I can derive that relationship theoretically, largely from first principles.

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The Changing Nature of Home Team Probability

The original motivation for this blog was to provide additional context for the previous blog on victory probabilities for portions of games. That blog looked at the relationship between the TAB Bookmaker's pre-game assessment of the Home team's chances and the subsequent success or otherwise of the Home team in portions - Quarters, Halfs and so on - of the game under review.

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Victory Probabilities for Portions of Games

If the Home team is rated as a 75% chance of winning an upcoming game of AFL, what chance is it of winning the 1st quarter? The 2nd quarter? The 1st half? The 2nd half?

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In-Running Models: Confidence Intervals for Probability Estimates

In a previous blog on the in-running models I generated point estimates for the Home team's victory probability at different stages in the game under a variety of different lead scenarios. In this blog I'll review the level of confidence we should have in some of those forecasts. More formally, I'll generate 95% confidence intervals for some of those point forecasts.

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