“It is hugely complicated. In fact, compared to football I think Quantum Physics is relatively straightforward.”
– Professor Stephen Hawking

Even you, Stephen?

If you pick up basically any newspaper in Ireland or the UK today, you’ll probably find a story about Professor Stephen Hawking’s “formula for World Cup success”. At first glance, it doesn’t look good: The World’s Most Famous Scientist appears finally to have succumbed to the temptation of nonsense formula publicity.

Irish bookies Paddy Power have paid an undisclosed sum to the Prof to put his name to some nonsense about pitch temperatures and WAG ratios. Hawking has said he’ll donate his fee to the Motor Neurone Disease Association and Save the Children’s Syria appeal, so maybe he just saw this as an easy way to get his charities a freebie donation.

Anyway, they got their money’s worth: the resulting blog post contains not one but TWO formulae, and a citation of prior work, and an explanation of the technique used to derive them.

Stephen’s had some fun with his assignment: he’s performed a logistic regression on a few arbitrarily-chosen explanatory variables to produce a model for the probabilities of England winning the world cup, and of scoring a penalty.

First of all, he alludes to the work of Hagemann, Strauss, and Leißing, which claims that teams who play in red are more likely to win. It’s not clear if he factors this into his model.

Here’s the model for England winning the World Cup (labelled “England’s World Cup Success Formula” in the press release):

\[ \frac{\hat\pi}{1-\hat\pi} = X_0 \left( \frac{ e^{0.34\gamma + 0.3\eta\theta + 0.08\beta_1} }{ e^{0.18T + 0.04\log(\alpha) +0.23\beta_2 + 0.11\beta_3 + 0.28\delta + 0.3\epsilon} } \right) \]

And here’s the model for whether a player will convert a penalty into a goal (sadly, and inevitably, labelled “Formula for the Perfect Penalty”):

\[ \frac{\hat\pi}{1-\hat\pi} = X_0 \left( \frac{ e^{0.7\alpha + 1.13\beta_1 + 1.09\beta_2 + 0.9\delta + 0.3\theta_1 + 0.3\epsilon} }{ e^{0.06\alpha_2 + 0.9\eta + 0.7\theta_2} } \right) \]

So far so nonsense-formulaic, but do they mean anything? The $\frac{\hat\pi}{1-\hat\pi}$ bit is the probability of success over the probability of failure, i.e. the betting odds, given values for the explanatory variables used on the right hand side. Disappointingly, the Professor hasn’t really shown his working. While he gives some of the input data for his model in the text (58% of penalties taken with a run up of three steps or less result in a goal, et cetera), he doesn’t specify in his post which Greek letters go with which variables, and doesn’t say what data he used so we can reverse-engineer it. Sad. (Fortunately, he included his working-out in the press kit, and the Daily Mail saw fit to publish it all.)

What he has given us, however, is this rather fab little video where Hawking appears in front of a couple of blackboards displaying the formulas, explains his method, and cracks a couple of choice one-liners.

[youtube url=https://www.youtube.com/watch?v=iJFQ1QG5Hno]

So, he’s selected an appropriate model for the task, cited some prior research and working, and recorded a video to explain it, with some good jokes. However, the Nonsense Formula Disapprove-o-Matic 3000 is still emitting a low hum of digital opprobrium. How have the newspapers who were handed this PR masterpiece reported on it?

The Aperiodical’s Nonsense Formula Disapprove-o-Matic 3000

Well done all of you for not using the word “boffin” on this occasion. And dumbfounded congratulations to the Daily Mail for again somehow doing the most rigorous examination of the work and publishing all the working-out. Here’s a fun challenge: compare the two stories the Telegraph published in its sports and science sections, and work out what extra scientific detail they added.

In the long and ignoble history of nonsense formulas, this is definitely one of the better examples. This kind of analysis and modelling really is used by sports psychologists and betting firms: it’s a textbook application of statistical methods to tell skeptical students about. But in the end, some digits and Greek letters have appeared in newspapers sandwiched between a scientist’s name and a brand’s, without most of the pieces of information required for them to be usable. I do wish this would stop happening.

More information

Stephen Hawking EXCLUSIVE: The maths that show us how England can win the World Cup at Paddy Power’s blog

Google News search for Hawking football formula stories

How to do a logistic regression in R

“When the Referee Sees Red…” by Norbert Hagemann, Bernd Strauss and Jan Leißing, in Psychological Science (closed-access; $35)

Thanks but no thanks to Nathan Barker for bringing this to our attention.