Page last updated at 13:53 GMT, Friday, 19 December 2008

A Strictly mathematical fiasco?

By Tim Harford
Presenter, More or Less, BBC Radio 4

John Sergeant and his dancing partner  Kristina Rihanoff
John Sergeant's withdrawal from the competition proved disastrous

If you want to succeed at Strictly Come Dancing, you need the full package: The clothes, the moves, the smile. The ability to add up would not go amiss, either.

Last week's voting fiasco on Strictly saw the show's organisers effectively giving up on the whole point of the format, cancelling the dreaded "dance-off" and declaring that all three couples would proceed to the final.

The apparent problem was that two couples tied for first place in the judges' affections, giving them three points each and leaving Tom Chambers and Camilla Dallerup languishing in third place with a single point.

Only the leading couple could avoid the dance-off, so while the viewers were being invited to phone in and save Tom, it was ever so slowly dawning on the show's producers that even if every single viewer voted for him, he couldn't magically leap into first place.

The BBC's head of entertainment, Jon Beazley, said the bungle had been "unforgivable" but blamed the "exceptional circumstances" of a tie at the top of the leader-board. But were the circumstances really so exceptional?

Odds on

More or Less, BBC Radio 4's programme about the numbers in the news, does not think so. Inspired by an email from a listener, we looked at how often we should expect a tie.

See the numbers being crunched

In principle, judges could award anything between 0 and 40 points, which makes a tie seem very unlikely - especially with two dances and so a maximum score of 80 points in the semi-final format.

But even John Sergeant, mocked as "a dancing pig in Cuban heels", never received fewer than 12 points out of 40, and as the competition progressed the producers should have noticed that the scores were bunching ever more tightly at the top of the range.

In the quarter-final and semi-final, the judges never awarded fewer than 33 points out of 40.

More or Less listener Dirk Nachbar, confined to his hospital bed with nothing to do but ponder the mathematics of Strictly Come Dancing, pulled out his laptop computer and ran a computer simulation of 10,000 judging rounds.

He wanted to work out how often the leading couple would tie if the scores ranged from 33 to 40. Our own simulations produced the same answer as his: almost one time in eight. Not exactly "exceptional circumstances".


But perhaps we should not focus too much on those exceptional circumstances, because even without a tie the viewers would have had a job saving Tom and Camilla from the dance-off after the judges had put them in last place.

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The only way to do it would be if the viewers' ranking precisely reversed the ranking of the judges. That would create a three-way tie and put Tom and Camilla through on a tie-breaking technicality.

That is not likely either, and surely Strictly Come Dancing was never meant to descend into Strictly Come Tactical Voting?

All these problems would have been avoided if the semi-finals had contained four couples rather than three, competing for two safe slots rather than one.

In other words, some kind of problem was all but guaranteed when John Sergeant withdrew a month ago from the show after weeks of being lauded by the public and slated by the judges.

Last week's farcical semi-final was the revenge of the "Dancing Pig".

Tim Harford is the "Undercover Economist" at the Financial Times, and the presenter of More or Less, which broadcasts on BBC Radio 4 on Friday 19 December at 1330 and Sunday 21 December at 2000.

Sign up for the podcast on the programme website.

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