2012 Round 2 : Don't Expect to Be Too Surprised

The AFL scheduler's seen fit to cram the 9 games of Round 2 into a 5-day rather than an 8-day timeframe this week, so Investor's will know the fate of their 7-bet SuperMargin extravaganza sometime on Sunday night, just as the last of their hot cross buns are digesting.

(Actually, no one I've ever known has proven capable of purchasing precisely the right number of hot cross buns to see them polished off by the end of Easter Sunday, but we'll let that slide for the sake of the imagery.)

Here are the markets that we were facing today and how the Margin Fund - still the only Fund that's active - has responded:

All of the prices you see in this table were posted at around noon, except those for the line market on the Sydney v Fremantle game, which the TAB Bookmaker mulled over for a little over an hour longer, for reasons that will forever be unknown to we casual observers. I like to imagine him dithering over the possibilities, paralysed by the enormity of the decision before him, fearful of the torrent of wagering that his decision would unleash. In truth, it was probably the fact that his '7' key was stuck or something equally as mundane.

Note that, while the 3% overround has persisted in the line market, 5.5% to 6% overrounds have made an unwelcome appearance in the head-to-head market. That's lower than the average overround we saw in the head-to-head market last year, but much higher than what we saw in Round 1.

With seven home-team favourites in the round it's not especially startling that Investors should find themselves with seven wagers. Most of these SuperMargin wagers are for victory margin "buckets" that align with or are adjacent to that which the TAB Bookmaker would himself select. As a result, they're priced at $7.00 or, in one case, at $7.50. The notable exception is the wager on the Roos to win by only 20-29 points, which is considerably less than the margin of 80-89 points most expected by the TAB and which is consequently priced at $17.

Landing any one of those seven wagers, even those at the lowest price, will be enough to ensure breakeven for the weekend; landing two, or landing either of the two bets priced above $7, will be enough to secure a profit.

In head-to-head tipping there's unanimity in six contests, and in two more of the matches it's only HSH that disagrees with the herd. In the ninth game - Essendon v Port Adelaide - the dissenters in the 10-3 verdict are Consult the Ladder, Easily Impressed I and Follow the Streak.

The Margin Predictors are even more sheep-like in their tipping this week, with unanimity the feature of all nine contests and with the TAB favourites being the target of that groupthink in every case.

Only the Sydney v Fremantle, and the Geelong v Hawthorn clashes (and, arguably, the Lions v Blues contest if we consider CN2's prediction) have elicited so much as mild uncertainty amongst the Predictors. For six of the nine contests the average and the median margin predictions sit at around 6 goals with standard deviations of around 2 goals or less.

It's fair to say then that neither the Head-to-Head Tipsters nor the Margin Predictors expect much surprise from the results in Round 2. Using the notion of surprisals we can show that the TAB Sportsbet Bookmaker feels the same way.

We've spoken before about surprisals, which allow us to measure, in bits, the information content in an outcome by calculating -log2(probability of the outcome). The higher the number of bits associated with an outcome, the more surprising it is. We can extend this notion and talk, prior to the game, about the "expected surprisals" of a head-to-head result by weighting the surprisals of both possible outcomes (ignoring the draw) by the probability of their occurrence.

So, for example, consider a game where the head-to-head prices are $3.30/$1.33. If the team priced at $3.30 were to win, we'd experience -log2(1.33/(3.30+1.33)) = 1.8 bits of surprisal, and if the other team were to win we'd experience -log2(3.30/(3.30+1.33)) = 0.5 bits of surprisal. Prior to the game the probability we'd attach to the team priced at $3.30 would be 1.33/(3.30 + 1.33) = 29%, and to its opponent would be 100% - 29% = 71%. So, before the game, we'd expect it to provide 0.29 * 1.8 + 0.71 * 0.5, or about 0.87 bits of surprisal.

Following this approach and calculating the expected surprisals for all games in 2011 and 2012 and then grouping by round (see table at left), we can show that the average expected surprisals from the games in Round 2 of season 2012, based on the TAB Sportsbet prices, is the third lowest we've seen in that period, greater only than the average expected surprisals for Rounds 20 and 23 of season 2011. In one of those rounds - Round 20 of 2011 - the actual results generated a remarkably low 0.423 bits of surprisal. That's only about as surprising as failing to toss two heads in successive tosses of a balanced coin.

(For interest, I've also shown the actual average surprisals generated by historical results, which shows considerable variability in average actual surprisals and not altogether uncommon divergence between the expected and the actual surprisals produced. In football, it seems, surprise often comes when you don't expect it - even though you can quantify how much of it you expected. The linear correlation between expected and actual surprisals per round was only +0.40 in 2011, so it's true to say that expected surprisals explained only about 16% of the variability in our actual levels of surprise across the season - which is surprisingly low. I think.)

No matter how you look at it then, we shouldn't expect to be much surprised by the Round's results. In fact, quantitatively we should expect to experience about 0.7 bits of surprise per game.

Our Head-to-Head Probability Predictors expect to be even less surprised by the round's results: in almost every game they're more confident about the favourite's chances than is the TAB Sportsbet Bookmaker. 

The only non-trivial exception to this is for the Roos v GWS clash, where the TAB rates the Roos about 94% chances, while ProPred, WinPred and H2H Unadjusted rate them between 82% and 91% chances; that's not exactly a major divergence of opinion either.

The Line Fund rates the Pies (-35.5), the Crows (-30.5) and the Saints (-55.5) as the teams most likely to emerge victorious, net of their respective spreads on line betting, while it's most nervous about, though on balance marginally swayed by, Port Adelaide's (+25.5), Fremantle's (+7.5) and Hawthorn's (-10.5) chances.