# Simulating the Finals for 2013 : Pre-Week 3

/The week leading up to the Preliminary Finals is always revealing of the TAB Bookmaker's methods because he chooses to post markets for both of the Preliminary Finals, for all possible Grand Finals Quinellas, and for all four remaining teams for the Flag.

By applying some basic probability theory to these prices we can unwind the overround in each and determine the profit-free assessments he's most likely making about each outcome and each team.

This week, it turns out, reconciliation of the Preliminary Final and GF Quinella markets can best be achieved by applying an Overround Equalising methodology to them both. That approach produces probability assessments for these markets as shown in the top half of the table at left, for which the mathematical agreement is extraordinarily high. (For example, a Fremantle v Geelong GF requires that Freo beat Sydney and that Geelong beat the Hawks. Multiplying the probabilities shown here for the respective Preliminary Finals gives 0.738 x 0.363, which is about 26.8% - very close to the 26.7% probability calculated from the GF Quinella prices.)

Next, looking at the prices in the Flag market and again assuming that an Overround Equalising approach is appropriate, we can calculate the implicit probabilities shown in the Market for the Flag section.

Then, knowing the Bookmaker's underlying probability assessment of each team for the Flag and his underlying probability assessments for both Preliminary Finals, we can infer his current probability assessments for all four possible GF matchups by recognising that any team's probability of winning the Flag is equal to its probability of winning its Preliminary Final times the sum of its probability of beating each of the teams in the other Preliminary Final times the probability of that team's winning its Preliminary Final.

For example, Sydney's probability of winning the Flag is equal to:

*Prob(Sydney beats Fremantle in PF) x [Prob(Sydney beats Hawthorn in GF) x Prob(Hawthorn beats Geelong in PF) + Prob(Sydney beats Geelong in GF) x Prob(Geelong beats Hawthorn in PF)]*

When you do the maths for the system encompassing the four potential Flag winners with one equation of the type shown here for each, you wind up with three equations in four unknowns (recognising that the sum of the four teams' probabilities must sum to 1). To solve that set of equations you need to set the value of one of the unknown GF probabilities, say the probability that Hawthorn beats Fremantle in the GF should that GF arise, which I've done in the bottom section of the table above for five plausible values of that probability. I've also converted these probabilities to realistic market prices assuming a flat 5% overround. On the assumption that Geelong would most likely be mild favourites to defeat Sydney in a Cats v Swans GF, Set 4 seems to be the set of probabilities most likely to be near to the TAB Bookmaker's.

That set has Hawthorn as about 62% favourites against either potential competitor in a Grand Final, and the Cats as about 57% favourites against the Swans, and about 63% favourites against Fremantle.

**FINALS SIMULATIONS**

In addition to divining the mind of the TAB Bookmaker I've this week also run the usual simulations based on my own probability assessments for the various possible remaining contests, which I've based on the same MARS-Rating based model that I've used in previous weeks.

Not for the first time - and assuredly not for the last - my assessments are quite different from the TAB Bookmaker's, mostly notably this week in relation to the Swans' and, to a lesser extent, the Hawks' chances.

It's therefore no surprise then that the identified value in the Flag market relates solely to the Hawks (estimated positive expectation of 17%) and to the Swans (estimated positive expectation of 6%).

In other markets, the only other value is in the GF Quinella price for a Geelong v Sydney GF of $9.36, which offers an estimated positive expectation of almost 30%.