The curse of poor maths skills (oh, all right… Kennett’s curse)

(Update: you can see a table of Kennett curse calculations here.)

When Geelong beat Hawthorn for the eleventh straight time last weekend

When Hawthorn beat Geelong in the 2013 preliminary final, ending a run of eleven straight losses to the Cats, salivating journos had the opportunity to rehash everything they’d already written about Kennett’s curse, on Friday, Thursday and every other day during the week. But of all the things written about Kennett’s curse, the one I’m stunned not to have read is: E(X) = (1 – p^r) / (p^r.(1 – p))

This roughly translates as: if two teams play a whole bunch of football matches, how many would you expect them to play before one team suffers from X: Kennett’s curse?

The answer, with the curse at 11 games, assuming that both teams have an equal chance of winning each match, is 4094 – and Geelong and Hawthorn have only played 152.

The key assumption, though, is “equal chance”. If the Geelong edge is as little as 55-45 – good enough to win 11 games out of every 20 – the calculation for E(Kennett) drops to just 1592. (If Hawthorn has the edge, it blows out to 11864… yikes.)

Surprisingly, providing a general formula for the probability of a string of wins within a longer series of matches isn’t easy, but you can do it using a ridiculously complex formula. Using it for a string of 11 wins within 150 matches, at a fifty-fifty chance of winning for each team: Kennett’s curse will occur 3.3% of the time. (Update: you can see a table of Kennett curse calculations here.)

A quick and handy way to work out the probability of winning streaks within match sequences (K wins in a row within N matches, probability of a win is p, of a loss, q).

A quick and handy way to work out the probability of winning streaks within match sequences (K wins in a row within N matches, probability of a win is p, of a loss, q).

But hasn’t this “experiment” of teams playing sequences of matches against each other been performed many more times than just now, with Geelong and Hawthorn?

Geelong beat North Melbourne 23 times in a row in the 1920s and 30s, with not an ex-premier in sight. Essendon won 20 straight against St Kilda from 1981-1991, the fabled “crap team curse”. But genuine rivals have met in many, many sequences of matches. There are 66 combinations of rivalries just amongst the clubs comprising the VFL in 1986, on the eve of expansion – the probability of none of these resulting in an eleven-game “curse” is equal to 0.03366 = 0.109, or around 10.9%. Of course, only a fraction of these rivalries are as evenly-fought as Hawks-Cats – but only 21 or so are needed to bring the probability of a “curse” down to 50-50.

So, when Geelong-Hawthorn rolls around again – make sure that any discussion of the Kennett curse includes a healthy dose of of the fancy formula above.

Or maybe just direct people to the blog.

The proportion of the time a streak of 10 wins arrived after exactly 10 to 11000 matches, as observed in simulated coin-flips. A 10-win streak with the 10th win in the 150th match happened less than 1/2200th (around 0.045%) of the time.

The proportion of the time a streak of 10 wins arrived after exactly 10 to 11000 matches, as observed in 2 million simulated coin-flips. A 10-win streak with the 10th win in the 150th match or earlier happened about 6.75% of the time. The black and blue sections of the graph, starting / stopping around 1200 on the horizontal axis, shows the division at which 50% of the 10th wins came both earlier and later. The red line shows the average number of matches for a 10-win streak.

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