Surprisals, you might recall, are a way of measuring the likelihood of the result of a chance outcome. They're measured in bits, and one bit of surprisal is the amount of surprise that you should feel in correctly predicting the toss of one unbiased coin.
So, 1 bit of surprisal is equivalent to an even money outcome, 2 bits to a 3/1 outcome, 3 bits to a 7/1 outcome and, more generally, n bits of surprisal is produced by a result with odds of (2^n-1)/1.
One way we can use surprisals is to determine which team has produced the most surprising set of results in the season to date. To do this we measure the surprise associated with a team's win or loss using that team's pre-game bookmaker odds.
When we do that for season 2010 we get this:
Overall then, Carlton have been this season's surprise team so far. Their average result has generated 1.15 bits of surprisal. This has largely been due to the surprisals produced from their five wins, for which they've averaged 1.29 surprisal bits per win.
Essendon have been the second most surprising team this season. Their ranking is also due to the surprise associated with their wins, of which there have been three, averaging 1.51 bits of surprisal each.
Richmond's results - all losses - have been least surprising. They've generated just 0.32 bits of surprise per loss. This is about the amount of surprise you'd feel if you rolled an unbiased die and it failed to come up a 5 or a 6.
In the table above we've looked at outcome surprisals - basically how surprising it's been that a particular team won or lost, with surprise assessed using the head-to-head bookmaker prices.
We can also determine how surprising a team's margin of victory or loss has been. To do this we use the points start that bookmakers are offering and measure surprise relative to the expected margin of victory or loss.
On this measure, the teams are ranked as followed:
Carlton's results have been surprising it seems not just in terms of their wins and losses, but also in terms of the magnitude of these wins and losses relative to what the bookmaker expected. Their five wins have produced over 3.5 bits of surprisal each. (Surprisal measures for margins are almost always higher than for head-to-head results because there are many more potential margin results than there are head-to-head results.)
Melbourne's margins (mainly their margins of handicap-adjusted victory) have been next most surprising, and Geelong's have been third most surprising.
Least surprising in terms of margin results has been West Coast, and the Dogs' results have been only a little more surprising.
We considered surprise at the level of the team, but what about at looking at it by round. In other words, which rounds have so far produced most and least surprise and what has this meant for the various Funds?
Round 5 - the round in which the Heuristic-Based Fund made most of its money - was the round whose results were most surprising, both in terms of which teams won and lost and in terms of the margins of those victories and losses.
The least surprising round in terms of head-t0-head results was Round 1, and the least surprising round in terms of handicap-adjusted margins was Round 3.
On average this season, each game has produced 0.87 bits of outcome surprisal and 2.60 bits of margin surprisal. These are both quite close to the surprisals produced across season 2009 where we saw 0.84 bits of outcome surprisal and 2.59 bits of margin surprisal per game.
This season's been surprisingly unsurprising then, I guess.