How Surprising Were the Round 7 Results?

We've used the surprisal metric a number of times here on MoS as a measure of how surprised we're entitled to feel about a particular head-to-head result. 

Here, for example, is a quote from a 2012 blog on surprisals and probability scores

Surprisals, you might recall are a measure of the “surprise” associated with an outcome. Specifically, n bits of surprisal is the amount of surprise associated with an outcome carrying a pre-game probability of 1/2^n. So, for example, using this definition an outcome that was an even money bet pre-game is associated with 1 bit of surprisal, while a 3/1 shot carries 2 bits of surprisal, a 7/1 shot 3 bits of surprisal, and so on. Surprisals are typically measured in bits.

In essence, what surprisals provide is a number, based on some pre-game probability, that measures the "surprise" inherent in the outcome.

(For some other MoS pieces on surprisals, see this one on season average surprisals where pre-game probabilities were estimated using the teams' MARS Ratings or this one on the relationship between surprisals and crowds. If you perform a site search on "surprisals" you'll find even more posts.)

Last weekend's results were certainly, in the colloquial sense, "surprising", with all nine contests won by the team that was lower on the ladder at the start of the round than were their opponents. But, quantitatively, how surprising were they, and how much more surprising were they than other home and away rounds from other seasons?

We can answer that question using the surprisals metric, with pre-game probabilities derived from the opening TAB head-to-head prices. I have this data for the TAB from 2006 onwards, and have employed the overround-equalising methodology to calculate probabilities from prices.

When we do this we find that the average surprisal per game this week was 1.38 bits. That's the second-highest value for any home-and-away round since 2006.

The highest average came in Round 19 of 2009, mainly because of the Eagles' narrow win over the Dogs in that week when they were priced at $9.50. 

In the chart below are the pre-game probabilities and surprisals for every home and away game since R1 of 2006, with the 8 games from Round 19 of 2009 and the 9 games from Round 7 of 2017 called out.

You'll notice that there was a draw amongst the results from that 2009 round involving Essendon and the Brisbane Lions. In that case the surprisal value is defined as the average of the value you'd get assuming Essendon won and what you'd get assuming the Brisbane Lions won. 

So, in an historical context, we can say that last weekend's results were full of surprisals.