Maths & Sport

I like sport. I like maths. I like sport and I like maths. This book therefore looks very interesting indeed.

The Hidden Mathematics of Sport

The Hidden Mathematics of Sport

There is an awful lot of interesting mathematics within sport. For example, I love all of the statistics that are available in cricket. I like browsing batting averages, bowling averages, run rates and strike rates. In football these days, they track things like number of passes attempted and their success rates for every player in every game. They even track things like how far each player has run – I absolutely love this kind of thing.

As well as statistics there are the mechanics – the speed of a tennis player’s serve, the maths behind the spin that they put on the ball when they hit a top spin or a back spin. What are the physics behind backspin on a snooker ball or reverse swing in cricket?

Recently, during a game of badminton, I smashed the shuttlecock and it hit @Biltawulf on the shoulder. Within a few seconds a massive red lump sprung up. A shuttlecock weighs about 5 grams. How fast must it have been travelling to cause such an injury? To demonstrate how much of a geek I am, that was the exact thing going through my head while he sat on the floor and blubbed.

Anyway, maths within sport is interesting to me so I’m going to buy this book. I suspect I’ll either love it or hate it. Why might I hate it when it’s about two things I love? Well, just because it combines two subjects I like doesn’t necessarily mean it will combine them well.

The book appears to cover many aspects of the mathematics behind sport but the BBC have reduced it to this on their website:

Can you calculate the world’s greatest sports person?

This makes me more than a bit suspicious. It reminds me a bit of when the Daily Mail does a story like “Scientists find the formula for perfect apple pie” and the equation is something like:

Tastiness of Apple Pie = {[(Colour of apples) + (Temperature of oven)] / (Butteriness of Pastry)} + (Pie Tin)

And it makes no sense to anyone who has ever done a sum in their life. I mean, in what units would the result of the above equation be measured?

When these things come out in the press, Ben Goldacre investigates and finds out that the story was created by some nobody who had been paid by an apple pie manufacturer’s PR company to come up with an equation for their marketing.

The story about making a formula for the world’s greatest sportsman is suspicious for similar reasons. I don’t really see how mathematically you could compare Sachin Tendulkar with Tiger Woods. The sports of cricket and golf are too different to simply make a sum that says one of these great sportsman scores 97/100 and the other scores 96/100.

I would go further and say that even within a sport it is very difficult to make a sum that accurately ranks all competitors.

If you look at Formula 1 statistics then Michael Schumacher is top in most of them. I think Ayrton Senna was better than him though and I think Jim Clark was better than both of them. Schumacher’s stats are relatively inflated due to the fact that he had a very long career and he spent most of it in a faster car than his rivals. Also, he was dominant in a period which featured no other truly great drivers. Senna died just before the start of Schumacher’s period of dominance and Hamilton and Vettel got their chance just after he retired. Mika Hakkinen was a very good driver but it wasn’t exactly the same as having Prost, Piquet and Mansell lining up on the grid next to you. If an equation to measure just the skill of a Formula 1 driver existed it would already be massively complicated just to take into account how good their car was and how good the people they were racing against were.

Let’s now have a look at football and that Man United team who won the treble in 1999. What formula would you use to compare the performances of Peter Schmeichel with those of Eric Cantona? It’s in the same sport, in the same team, in the same year and against the same opposition and it’s still hard to conceive of how one would go about making an equation which would accurately measure their relative performances.

Maths is a fantastic tool for some things but not for all things. “Who is the best sportsman?” is a topic of conversation to be had subjectively over a few beers. Maths cannot solve subjective problems and we shouldn’t expect it to.

Someone could try to make an equation to do just this and the first time they ran it, it might say Phil Neville were better than Paul Scholes. “Bollocks”, they’d think, “I must have got something wrong,” and they’d adjust it until Paul Scholes came out better than Gary Neville. That’s not using maths to solve a problem – that’s knowing that outcome and fitting bad maths around it. After the first round of tinkering, the new equation might say that Audley Harrison were better at boxing than my mum and then it would have to be reworked again.

They’d then continually rework it until at last it fitted perfectly with their opinions. Hoorah!

No, not hoorah. All that has been done in this exercise is trying to manipulate maths to fit with opinions and if that’s all we are doing we should just use our opinions as a basis and leave the maths out.

If this book understands when to apply maths and when not to it could be very good indeed.

Either way, it’s now in the post, so I’ll let you know.