Freo, faves and other tipping blunders

by Burkard Polster and Marty Ross

The Age, 21 March 2011

It’s been a thrilling summer of cricket. Who will ever forget that epic battle between Canada and Kenya? But enough is enough, and now it’s footy season. Which means another season of frustrating footy tipping.

How should you go about your tipping? What’s the clever secret that will make you champion of your local comp? There are many theories, but in the past there has only been one inviolable rule: never tip Fremantle away.

Actually, last year Freo won 4 out of 10 away from Subiaco. So, even that rule may have to be revised.

Some tips take very little thought, even if there are temptations. For example, successfully tipping Port Adelaide to upset Collingwood (Boo!) would make you Monday’s talk of the playground, and would feel extra special if you’re a Saints fan. However, such bravado is clearly not part of a winning strategy.

The trouble is, of course, that a great upset tip still only gains you 1 point in the comp. And, most times you’ll simply fall a tip behind. In practice, it is even worse than that, and it applies to closer games as well.

For example, consider tipping Essendon to beat the Bulldogs in Round 1. It’s a fairly even match, with betting sites currently rating the Bombers about a 40% chance of winning. However, since most comps offer no bonus for correctly tipping an underdog, it is likely that only about 30% of tipsters will pick the Bombers. What this means is, if you pick the underdog in five such 60-40 games, on average you’ll lose a tip to about 70% of the tipsters.

This suggests that we should just tip the favourites. That may feel wrong, since it is rare for all the favourites to win. In fact, there was not a single round in 2010 when all eight favourites won. Indeed, there was only one round where seven of the favourites won.

That’s not too surprising. If we imagine all eight games are 60-40, then the chances of the eight favourites winning is (3/5)⁸, about 1.7%. So, we’d expect to tip all games correctly about once every 60 rounds. Of course, games can be lopsided, with favourites such as Collingwood very likely to win. But it’s still not easy to tip eight.

The table below gives the current probabilities for Round 1, as judged by betting sites. Some simple multiplication then suggests there is about a 2% chance of all the favourites winning. So, it should hardly be a surprise if it doesn’t eventuate. But, to many, it seems that it is: betting companies make a regular and handsome profit from punters underestimating the difficulty of predicting multiple outcomes.

If picking the favourites gives little hope of tipping eight, it is still more likely than any other selection. So, it’s clear, your best strategy is simply to tip the favourites, and our Maths Masterish work here is done. Perhaps.

Let’s see how well tipping the favourites would have worked in 2010. There were 22 rounds last year. That gives a total of 176 games, and 113 of these were won by the favourite. (We’ve included the two draws in that total, since most tipping comps count a draw as a correct tip for all tipsters).

Now, 113 is a respectable total, well ahead of the 88 we’d expect from flipping coins. But how many tipping competitions would that total have won? Below is a table of some of last year’s comps.

So, tipping favourites will not likely suffice for winning the office comp. And what about those mega competitions, the ones offering a trip to the moon for you and three of your mates? Forget it. There are simply too many tipsters, no matter what you do. Given 50,000 people or more throwing darts, there will just be way too many bullseyes. And, the more people throwing darts, the higher the winning total is likely to be.

Nonetheless, tipping favourites will likely work for beating your family. And even for the office competition, it’s the smart way to play the early season, at least until you find yourself behind. But, at some point, you’ll probably just have to go with your gut.

So, you’re just about ready to tip Round 1. There’s just one final question to be answered: can you hold your nerve and tip Freo at the Gabba?

Puzzle to Ponder: Assuming the probabilities for Round 1 are accurate, what are the chances that at least seven favourites will win. Suppose these same odds applied in every round of the 2010 season. Is it then surprising that there was only one round with at least seven favourites successful?

Burkard Polster teaches mathematics at Monash and is the university's resident mathemagician, mathematical juggler, origami expert, bubble-master, shoelace charmer, and Count von Count impersonator.

Marty Ross is a mathematical nomad. His hobby is smashing calculators with a hammer.