17 June 2002
Number crunching that could help England win the World Cup
If England score first against Brazil, what are the chances that they will go on to win? And if Ronaldo is through on goal with only Seaman left to beat, should an English defender risk a red card with a professional foul?
These are the kind of questions that Dr John Haigh, Reader in Mathematics and Statistics at the University of Sussex, has been collecting data on as he watches the World Cup.
"In most professional football we expect a team to win about two-thirds of the games in which it scores first and draw about one-fifth of them," says Dr Haigh. "If the number of goals in a match is low, then the first goal is very important, while if it is high, scoring first is almost irrelevant."
Brazil, who are renowned for their attacking flair, took 67 minutes to score their first goal against Belgium and only added one more. However, England supporters should perhaps bear in mind Brazil's recent winning scorelines of 5-2 against Costa Rica and 4-0 against China.
There are 64 matches in the World Cup, and of these Dr Haigh expects to see about 40 matches in which the team that scores first will win, 12 in which there will be a draw, only about 8 in which the trailing team comes back to win, and 4 no score draws.
Data also shows that although the times at which goals are scored is fairly random, more goals are scored on average in a given five-minute period later in games than earlier, and also that 'goals beget goals' i.e. the more goals that are scored up to a certain point, the more will be scored after that point. This could suggest we should expect a bonanza of English goals to match whatever tally the Brazilians manage.
When defending against the Brazilian onslaught, and if faced with a clear goal-scoring opportunity, should a cynical defender risk a red card to stop a goal being conceded?
"A player should risk a red card if, and only if, the crucial moment occurs at a certain time in the match," says Dr Haigh. "Very late in a tight game, the statistics suggest that doing the nasty deed may be best for your team. But as a football fan, I dislike this implication."
Dr John Haigh's article 'On the ball' appears in the latest issue of Plus magazine, an internet magazine which aims to introduce school pupils to the practical applications of mathematics. It can be found at http://www.plus.maths.org.
Notes for editors
For further information, please contact Peter Simmons or Alison Field, University of Sussex, Tel. 01273 678888, Fax 01273 877456, email P.J.Simmons@sussex.ac.uk or A.Field@sussex.ac.uk.
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