# Likely Grand Final Prices

By combining the Flag prices we're seeing on the TAB for the four teams with the prices for each of the four possible Grand Final pairings that we're also seeing there, and by assuming that the overround embedded in each price within a market is the same, we can mathematically derive the probabilities that the TAB bookmaker must logically hold for every possible GF result.

I'll spare you the maths (it's just solving a set of four linear equations and I think I went through some of the detail last year - and if I go too far into the maths of it all I should really be posting this blog in the Statistical Analyses journal) and just share the results with you.

On the left are the current TAB prices in the Flag and GF Quinella markets and the implicit probabilities they imply under the assumption of equal overround in each price. On the right is a chart depicting the combinations of probabilities that are consistent with these market prices. There's insufficient information in the market prices alone to define a unique set of probabilities for all four GF matchups, but if you choose the probability for any one of the games the three remaining games' probabilities are uniquely determined.

As we move along the x-axis in the chart we're altering our assumption about the bookmaker's assessment of Collingwood's chances of beating Geelong should that be the eventual Grand Final matchup. This probability is actually constrained to be within a reasonably narrow range because, for values much outside the range I've included in the chart, the probability for the Hawthorn v West Coast GF moves outside the permitted (0,1) range for a probability.

My guess is that the bookmaker's current views are most like those towards the middle of the chart, say Collingwood as 55% chances to beat the Cats, making Hawthorn narrow favourites over West Coast, Geelong almost 70% favourites over the Hawks, and Collingwood as about 85% chances should they wind up meeting the Eagles.

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