By Tim Harford
Presenter, More or Less, BBC Radio 4
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?
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.
LISTEN TO THE PROGRAMME...
More or Less is on BBC Radio 4 on Friday 19 December at 1330
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