# Strictly Come Dancing – the weird maths

My father in law pointed out something very odd regarding the recent controversy about the BBC letting all three contestants go through without any having to face a dance off.

Normally, if there are three contestants, they get 3, 2 and 1 points for being ranked 1st 2nd and 3rd by the judges. They then get the same depending on how they are ranked by the public. The bottom two then face the dance off and the couple ranked lowest in the dance off by the judges is eliminated.

This time, the judges scored the top two equally, so the scoring was two threes and a one.

But it then became clear that there was no point in the public voting to “save” the bottom contestant from the dance off, as they would inevitably face the dance off.

This is the reason why the BBC said all three should go through (and the votes carried over to next week).

But here is the oddity: even if each couple gets either 3,2 or 1 from the judges, the bottom couple cannot avoid the dance off anyway. Do the maths and you’ll see. So the reason the BBC gave for letting all three couples through would have applied anyway, whether or not the top two couples tied. That the top two couples tied in the judges’ vote is irrelevant. No one seems to have noticed this (or have they)?

S

As I understand it if the top two are tied on points, it goes by the actual number of public votes. So the bottom couple could be saved if they got the most public votes, and the pair second with the judges got the second most public votes.

In particular, if the judges gave A/B/C points 3/2/1, but the public completely reversed that with 1/2/3, then they’d all be tied on 4 points. Since ties are broken by using the public votes, couple C would be safe.So, yes, it’s theoretically possible for the last placed couple to be saved in these circumstances.Apparently they’ll be talking about this on Radio 4’s “More or Less” this afternoon (always a good listen).

The tied couples should have a dance-off and be awarded first and second accordingly. The third placed couple would remain in third place.

just testing

I have been working out the maths too and have found the following. With 3 people left there are 6 combinations of results and 2 of these are not definite with who will be in the dance off as in one two have the same score and in the other all 3 have the same score. I got a bit carried away and looked further. With 4 people left there are 12 combinations and 5 of these are also a problem with two or more people having the same marks. With 5 people left there are 20 combinations and 10 of these are a problem. With 6 people left there are 30 combinations and 17 are a problem! That is 50%or around 50%. With these statistics these problem scores must have arisen before, especially as there have been 6 series. If the dance off contained the 2 people with the least viewers votes than this is ok. With this marking system it is easy for the judges to manipulate if they wish to do so. I am a dancer myself and the judges marks seem to be a bit ODD at times: in this series and series 5. I think that the final should have at least 4 people in it to make it fair for each contestant and also with just viewers votes. jane o

Actually, with three contestants, it could be a 3 way tie after the public vote, and then the largest public vote settles a tie, I think. So the lowest scoring contestant after the judges have scored could, in theory, avoid the dance off. I was wrong about that.