Did it really not occur to anyone to check the math? There are huge flaws with the calculations because

a) they conveniently forget that ties are broken entirely in favour of the popular vote

b) they look down the wrong end of the telescope

So let's re-examine this from the right end using the actual outcomes. Here ABCD represents the popular vote result, ie. A has the most votes, D the least votes. Taking into account the tiebreaks we find that there are just two possible dance-offs ..

BD 29% CD 71%

Yes that's right, the most popular dancer with the public cannot be in the dance-off and the least popular with the public is always in the dance-off. Not looking so great for those interfering judges now!

This being the case, and assuming that the judges stick to their original marking, there is the following possibility of elimination ...

A 0% B 21% C 42% D 37%

Yes, that does mean that one of the public's bottom two is eliminated 79% of the time, the only anomaly being the slightly better chance of surviving given their least favourite . I fervently hope that this finally puts to bed the nonsense about judges rigging the contest but, sadly, I very much doubt it will.

I wish it would too but unfortunately when you've disproving someone else's maths you need to double check your own too.

The top of the public vote can get eliminated with the combination

4 +2 = 6
3 + 3 = 6
2 + 1 = 3
1 + 4 = 5 (judges score + public score)

I have no idea what you're trying to prove here?

Are you saying that there's no way that the public favourite can fall into the dance off tonight? Or is that only if there's a tied vote?

You speak about using "actual outcomes". What actual outcomes?

Working on my school maths.....

Dave Arch and Claudia Winkleman are in the dance off.

Darn it! Quite right and I'm past editing time limit. So corrected figures ...

Dance-Offs: AD 4% BD 25% CD 71%

Eliminations: A 4% B 21% C 42% D 33%

Basic point still stands though.

It's an assessment of all possible results for the four contestants from adding the judges marks to the public vote. It turns out I made a slight mistake so it is possible for the people's favourite to be eliminated but there is only a 4% chance of it happening. In the vast majority of cases one of the people's bottom two will be eliminated whatever order the judges have them in.

I disagree. I checked B_OR's maths in detail (sorry, I can't post it up since it is too detailed) and came up with the same percentages. I think also you should have posted this on their thread.

I know some people think this topic is boring, but I think it is wrong to suggest they've got their sums wrong. How you then go on to interpret all these numbers and whether it is considered to be an issue or entirely fair is another matter.

I really wish that I had the energy to care, and if I did I'd expend that energy on something more worthwhile.

I'm not suggesting that they got their sums wrong. I am quite sure that the arithmetic is perfect. I'm suggesting, no, proving, that the approach was wrong failing to take all the factors into account. The fact that tiebreaks are decided in favour of the public vote skews the results heavily in favour of the people and away from the judges (as you would expect). It simply is not the case that the judges have the biggest say at all, let alone to the degree suggested on the other post.

It's been a quiet afternoon here in sleepy old Devon! And I am a fan of mathematical puzzles.

They've definitely taken into account the fact that the public vote has precedence if the total score (judges plus public) is the same. They do not account for judges awarding the same scores to two or more celebs, but they have clearly stated that.
Last edited by Ann_Dancer : 10-12-2016 at 18:09

Yes but our friend who likes to makes these long posts with voting advice is not listening. To everyone else the mathematical arguments are just noise.

I'd disagree with the assumption that all outcomes of the vote are equally likely. We wouldn't make that assumption about an election for parliament. What probability did Ed have of going out after seeing his Gangnam dance? Would you advise people to use maths to work that out?

Well, here's my data. On checking it thoroughly I have discovered a couple of mistakes but nothing to change the basic conclusion. You're welcome to check it.

{A, B, C, D} | 2,4,6,8 CD D
{A, B, D, C} | 2,4,7,7 CD C
{A, C, B, D} | 2,4,5,8 BD D
{A, C, D, B} | 2,5,7,7 BD B
{A, D, B, C} | 2,6,5,7 DC C
{A, D, C, B} | 2,6,6,6 DC C
{B, A, C, D} | 3,3,6,8 CD D
{B, A, D, C} | 3,3,7,7 CD C
{B, C, A, D} | 3,5,4,8 CD D
{B, C, D, A} | 3,5,7,5 CD D
{B, D, A, C} | 3,6,4,7 DC C
{B, D, C, A} | 3,6,6,5 DC C
{C, A, B, D} | 4,3,5,8 BD D
{C, A, D, B} | 4,3,7,6 BD B
{C, B, A, D} | 4,4,4,8 CD D
{C, B, D, A} | 4,4,7,5 AD A
{C, D, A, B} | 4,6,4,6 BD B
{C, D, B, A} | 4,6,5,5 BD B
{D, A, B, C} | 5,3,5,7 DC C
{D, A, C, B} | 5,3,6,6 CB B
{D, B, A, C} | 5,4,4,7 DC C
{D, B, C, A} | 5,4,6,5 CD C
{D, C, A, B} | 5,5,4,6 BD B
{D, C, B, A} 5,5,5,5 DC C

AD 1 BC 1 BD 7 CD 15

A 1 B 6 C 10 D 7

AD 4% BC 4% BD 29% CD 63%
A 4% B 25% C 41% D 30%.

As stated A is the vote leader and D the last in the vote. In the first column are all 24 possible judge's positioning (not taking into account ties). First place = 1, 2nd = 2 etc. so the dance-off in column 3 consists of those who have the highest totals. The judge's order is then used to decide on the eliminated contestant.

No, of course all outcomes are not equally likely. For the most part, certainly at this stage, the judges and vote are broadly in agreement (much as that no doubt galls our mutual friend). Complete shocks in the semis (and that applies to both Strictly and DWTS) are very rare indeed.

Ed's 'career' amply illustrates just how much power the vote holds though as he was last in the judge's marks every single time. Naturally as the contest went on he needed to be higher and higher in the public vote to survive but it was still pretty much 50/50 on the day he went out. If he'd led the popular vote he would probably have avoided the dance-off again.

Well the third row looks wrong to start with

{A, C, B, D} | 2,4,5,8 BD D
Should be 2, 5, 5, 8 BC C

Also 2nd and 4th rows should have D going in the dance off on the assumption that the judges will dump whoever they awarded the lowest score to (I think your eliminated is wrong is quite a few instances since the higher letter of the dance off couple would always be assumed to be eliminated.

Sorry, I don't have time to check all this. I've already spent time checking B_OR's maths and am satisfied it is correct. Also it doesn't help that this is the opposite way round to how judges's marks are allocated where highest indicates best.

Loads of mistakes Baz_James, even in your edited posts. My calculations are perfect under the assumptions I have detailed. Thay have also been checked by software.

I take in all cases where draws go in the public favour.

Also daveGold, I explain why you are wrong in my other thread. Please read it. I have explained most weeks why you are wrong.

Just out of interest here, I'm pretty sure that the odds of the public favourite landing in the dance off at this stage are one in six (just short of 17%).

Which one has been knocked out? Dave or Claudia?

Dave, obviously. Despite having the highest viewer vote.