## Tuesday 25 June 2013

### All's fair in love and soccer

Not!
I was at a pizza cookout at Chris del Bosque's place last night and I forgot to ask him about measuring tons of timber per hectare - sorry, I promised!  But there were rather a lot of blokes around the earthen pizza-oven that Chris and pals built in his yard three years ago, and the talk turned to footie.  In particular a famous 1986 penalty by Zico where Brazilian effortlessly out-psyched the goal-keeper.  It was part of a quarter final penalty shootout against France.  It's on youtube.

In soccer, as in other sports and indeed other aspects of 'real' life, when an arbitrary decision has to be made between two opponents: who kicks off the first half, whether to play the East or West end of the pitch in that half - it is decided by tossing a coin.  At the end of a game if the teams are score-equal, there is a penalty shoot-out with each team taking turns to fire a penalty from the spot 11m from the goal line. If the score is still equal after that ordeal, then the first team to score a goal wins the match.  Who fires first is decided by coin-toss.

But as mathematicians Steven Brams & Zeve Sanderson point out in an article put up in May while the odds may be even at kick-off, they are definitely not even in penalty shoot-outs.  The sudden death after 5 shots each is the obvious advantage.  But being science trained they went off and got some data and found that the team that gets first penalty kick wins 60% of the time - that's a 60/40 = 50% advantage.  That's not an arbitrary decision, so Brams and Sanderson hold that it should not be decided by coin-toss.  It should rather be decided by auction.  Each team bids to go first by saying that they'll take their penalties from a spot further from the goal-line to obtain the 50% advantage.  The odds are then, by definition, perceived to be fair by both sides.  If you think the other side has an unfair advantage you can out-bid them.

I liked that a lot. It shows that even the rock solid certainties about our world and how it ticks can yield interesting insights if you question your assumptions. The + plus magazine where I found the article is a nifty trove for all sorts of recreational math.