# 2011 - Simulating the Finals - Part I

/This week's results won't have any bearing at all on which teams play in the Finals and have only an outside chance even of altering the ordering of the finalists and, in so doing, altering the venues at which games will take place in the first week of the finals.

So, rather than simulating the results of what will largely be an inconsequential round, I've instead decided to simulate the finals series itself.

To do this I've assumed, for reasons of simplicity, that home team designation, venue experience and interstate travel are all irrelevant when it comes to Finals, and that we can adequately assess one team's chances against another solely by reference to the current difference in their MARS Ratings. For this purpose I've fitted a simple binary logit to the results of the season so far, excluding draws, to come up with the following:

*Probability of Victory = logit(0.0509 x Difference in MARS Ratings) [where logit(x) = exp(x)/(1+exp(x))]*

(Note that this formulation, without an intercept term, ensures that the probability of victory of the two participating teams sum to 1.)

Using this equation and the teams' respective MARS Ratings at the end of Round 23 gives us the following matrix of team-versus-team probabilities:

Basically, Collingwood is likely to beat any team it encounters along the way to a near inevitable Grand Final appearance, and Geelong and Hawthorn, for the most part, can decide between themselves which of them will meet and most likely be beaten by the Pies in the Grand Final.

Here are the results of the simulations using that probability matrix:

The results on the left are the only ones relevant to the final series we will actually face; those on the right are based on the hypothetical scenario of Carlton finishing 4th on the ladder, which is now an impossibility.

From the data in the first column on the left-hand side we can see that Collingwood's chances of winning the Flag are about 2 in 3, Geelong's about 1 in 6, Hawthorn's about 1 in 8, West Coast's 1 in 100, and Carlton's 1 in 25.

The second column provides the simulation results for the probability that the relevant team makes the GF but loses it. Summed, the first and second columns provide an estimate of the likelihood that the team makes the Grand Final, which for Collingwood is about an 81% chance, for Geelong is almost 50%, for Hawthorn about 40%, for West Coast just shy of 10%, and for Carlton just over 20%.

Shown in the third column is not this sum but, instead, the conditional probability of a team winning the GF on the assumption that it makes the GF. For Collingwood this is an astonishingly high 82%.

Underneath the table on the left are the probabilities associated with the four most likely Grand Finals.

Comparing the probabilities shown here with the current prices on the TAB reveals that Collingwood at $1.75 for the flag represents significant value, as does $3.50 for a Collingwood v Geelong Grand Final, $1.30 for Collingwood making the Grand Final, and $2.50 for Geelong making the Grand Final.

Turning now to the data on the right of the table above we can answer the hypothetical question: how would Carlton's chances have been altered had it finished 4th, as its MARS Rating suggests it should have and as a kinder draw may have allowed them to.

Broadly the answer is not a lot. Its flag chances would have edged up from about 4% to about 5% and its chances of making the GF would have risen from about 22% to 29%. Further the likelihood of a Collingwood v Carlton GF would have risen from 17% to 23%.

Carlton's gains are, roughly speaking, Geelong's and West Coast's losses; the other team's prospects change very little.