As a road-test of the Brownian Motion-inspired models we created for an earlier blog, I applied one of them to the in-running scores of the 2012 Hawthorn v Sydney Grand Final as a way of tracking the teams' victory probabilities as the match progressed.
For this purpose I used the model that was fitted to all Grand Finals across the period 1980 to 2011. It yielded the probability estimates shown as the rightmost column on the table below.
Since most Grand Finals have been won by the Home team across the period from 1980 to 2011, the model assigns a high probability to a Hawks victory at the start of the game, and this probability only increases as the Hawks' surge takes place at the back end of the 1st quarter. The Hawks finish the quarter with an estimated victory probability of over 87%.
However, by the time the Swans have established a 16 point lead near to half time, the model assesses the Swans as narrow favourites, the Hawks entering the main break with an estimated victory probability of just 42.5%. This estimate for the probability of a Hawks win is only slightly less than that which was implicit in the TAB head-to-head prices at that point, which was 45%.
After the Swans had extended their lead to its maximum of 28 points about 10 minutes in the 3rd team, the Hawks' estimated chances had slumped to just 20.9%, but their resurgence over the remainder of the quarter, which saw them end the term down by just 1 point, re-established them as favourites to win. At three-quarter time the model estimated the Hawks' chances at 58.3%.
At the 11-minute mark of the final term, the Hawks had extended their lead to two clear goals and their victory probability had grown to 81.6%, but this fell away rapidly when the Swans kicked the next 19 points, unanswered, to find themselves at the 22-and-a-half minute mark up by 7 points and assessed as nearly 4/1 on favourites. The next three scoring shots were all Hawks behinds, but they came too slowly to increase the Hawks' victory probability, before a final goal from the Swans all but snuffed out any flickering hope for the Hawks.
For me, it's interesting to see how much the modelled team probability estimates respond to scoring, especially to goals, even as early as the latter part of the 2nd quarter. The two Swans goals between the 17:35 and 22:39 marks in this second term dropped the Hawks' estimated victory probability by almost 20%. That seems a bit excessive, though in the context of recent Grand Final history where leads were precious and often decisive, I suppose it might be justified.
I'll leave it for readers to determine how well the probability "worm" accurately tracks the ebbs and flows of the teams' fortunes in the 2012 Grand Final, but constructing it was interesting exercise for me in the practical use of an earlier model.