2011 - Simulating the Finals - Part III - A Codicil

As Dave Hughes might say, I'm confused.

The TAB Sportsbet bookmaker has installed the Eagles as favourites over the Blues for this week's clash on Saturday. I'd debate the logic of that, but the game is at Subi, so fair enough. But then he's also gone and priced:

• a Carlton v Collingwood GF at $5 and a West Coast v Collingwood GF at $7
• a Carlton v Hawthorn GF at $26 and a West Coast v Hawthorn GF at $34
• a Carlton v Sydney GF at $34 and a West Coast v Sydney GF at $51

So, the Blues are considered the underdogs this week in playing the Eagles but are more likely to beat Geelong on the way to a Grand Final appearance than are the Eagles. In fact, if you do the maths, the implication is that the Blues are about twice as likely to beat the Cats in the prelim as would be the Eagles. That seems perverse.

To see how I've worked this out, consider what's required for a Carlton v Collingwood and for a West Coast v Collingwood Grand Final.

• A Carlton v Collingwood GF needs Carlton to beat West Coast and then Geelong, and for Collingwood to beat whichever team they face in the Prelim.
• A West Coast v Collingwood GF needs West Coast to beat Carlton and then Geelong and for Collingwood to beat whichever team they face in the Prelim.

Now we know from this week's head-to-head prices for the Blues v Eagles game that the probability the Blues beat the Eagles is considered to be about 1.55/3.90 or 39.7%, and the probability that the Eagles prevail is therefore 60.3%.

So we have: 

• for a Carlton v Collingwood GF the probability is 0.397 x Prob(Carlton beats Geelong in Prelim) x Prob(Collingwood makes GF)
• for a West Coast v Collingwood GF the probability is 0.603 x Prob(West Coast beats Geelong in Prelim) x Prob(Collingwood makes GF)

There's about a 41% overround in the GF Quinella market at the moment so, assuming that all wagers are equally weighed down with overround, that means the $5 price for a Carlton v Collingwood GF should really be $5 x 1.41 or about $7.05, which implies a probability of about 14.2%. Similarly, the $7 price for a West Coast v Collingwood GF should be $9.87, which implies a probability of about 10.1%.

Hence: 

• From the Carlton v Collingwood GF probability we can say that 0.397 x Prob(Carlton beats Geelong) x Prob(Collingwood makes GF) = 0.142, and
• From the West Coast v Collingwood GF probability we have that 0.603 x Prob(West Coast beats Geelong) x Prob(Collingwood makes GF) = 0.101

Together these imply that Prob(Carlton beats Geelong)/Prob(West Coast beats Geelong) = 0.603/0.397 x 0.142/0.101, which is about 2.1.

Similarly, looking at the probabilities for a Carlton v Hawthorn and a West Coast v Hawthorn Grand Final, we have Prob(Carlton beats Geelong)/Prob(West Coast beats Geelong) =  0.603/0.397 x 0.0273/0.0209 = 2.0.

Lastly, looking at the probabilities for a Carlton v Sydney and a West Coast v Sydney Grand Final, we have Prob(Carlton beats Geelong)/Prob(West Coast beats Geelong) =  0.603/0.397 x 0.0209/0.0139 = 2.3.

The only logical conclusion I can draw from all this is that the TAB Sportsbet bookmaker thinks the home ground advantage for the Eagles this week is very large indeed.

(By the way, based on our simulation results and current market prices, the only GF Quinella offering value on the TAB at the moment is the Collingwood v Geelong pairing at $1.75.)