The probabilities. Please look at my 'What does this all mean?' section below:

6 Couple Week
Judge Rank: A (first), B, C, D, E and F (last)
Percentage Chance in Dance Off (fair 33.3%): A = 3.9%, B = 13.6%, C = 26.4%, D = 39.4%, E = 52.2%, F = 64.4%.
Percentage Chance Eliminated (fair 16.7%): A = 0.0%, B = 0.1%, C = 1.5%, D = 7.9%, E = 26.0%, F = 64.4%.

Percentage chance of one of judges' bottom 3 eliminated: 98.3%

Percentage chance of one of judges' bottom 2 eliminated: 90.4%

I have previously reported how splitting your votes between multiple couples, especially at opposite ends of the leaderboard, could have a serious negative impact on your favourite with the lower judge-rank. Now, due to the low numbers of couples, this effect is even more exaggerated than before. So be very careful. Splitting your votes in this way could be the nail in the coffin for your favourite with the lower judge ranking.

If Ed is most popular with the public as many quarters are suggesting, then it is almost mathematically certain we will see either the 4th or 5th in the judges' ranks leaving this week. I am sad to say I think we will see one of my favourites, JudgeR or Claudia leave this week. This crazy voting system means both of JudgeR and Claudia could be getting notable public support compared with other couples, but still leave. Crazy, but true.

I think the next few weeks up to and including the semis are my least favourite weeks due to the bias this voting system gives to the judges against the public vote. This is due to the low numbers of couples at this stage.

Others on this forum have speculated the judges occasionally sacrifice a higher ranking couple in the dance off to justify its existence. If this is true, we have not seen one yet this year so far. If Claudia and JudgeR are the two in the dance off, then do not be surprised if the judges eliminate the higher placed couple on the leaderboard.

If Ed drops to 3rd (or below) with the public he is almost certainly gone. It is even reasonably risky he could be eliminated if he is as high as 2nd with the public.

As normal, ignore the angry people who are trying to convince you these probabilities are wrong or being misinterpreted. The naysayers are wrong. Some of their arguments are laughable. We have got to the stages where the bias against the public vote has gone from absurd to insane. I remember when my favourite (and it seemed many other people's favourite) Austin Healey was eliminated.

Notes on the 6 Couple Week:

There are just 720 possible ways the public can uniquely rank the couples in the 6 Couple Week. Each one has been checked to see which couples would be placed in the dance off as a result, taking into account the public vote will break ties. The only assumption made for the dance off percentages is there is unique judge ranking. The additional assumption made for the elimination percentages is the judges' least favourite of the two will be eliminated. The latter is the overwhelming historical case.

The judges' favourite will avoid the dance off in 96% of all public voting permutations.

The judges' favourite can get ZERO public votes and will still avoid the dance off in 78% of all the voting possibilities when they are getting zero public votes.

If there are any draws (and we have had a ridiculous number this year) then the middle and upper ranks will become vulnerable.

Even the public favourite can be eliminated, however it is still rare at this stage.

What does this all mean?

1. I think we have got to the stage where splitting votes between multiple couples is a critically bad idea, especially if they are at opposite ends of the leaderboard. Your vote for the higher ranked couple could deny your lower ranked couple the public rank they need to avoid the dance off.

You might need to consider just giving all your votes for the lower ranked of your favourites in this case, especially if there are no ties and your other favourite is rank 1 or 2 on the leaderboard.

2. However, if you want to split your votes between two low ranking couples (4th and below), then I believe that can still be considered a mathematically valid idea.

3. Splitting your votes between two high ranking couples (3rd and above), is also a reasonably safe voting idea, but possibly will not have a major impact on the result.

4. If the judges create many ties, like they have been doing this entire series even though they have a full range of scores, then the middle or upper ranks become more vulnerable to appearing in the dance off with other middle or upper ranks. When they flash the leaderboard, quickly count up as many tied scores as you can. The more ties, the more help the middle ranks need. If there are loads of ties, just pick one (or two max) favourites anywhere on the leaderboard and just vote for them.

Just so people know, the maths is based on all couples having an equal chance of being in every position in the public vote. If you think differently then it changes the maths.

For example: If you think that Ed will not be in the bottom 2 of the public vote, which seems like a reasonable assumption after last weeks results, then 33% of the outcomes counted above will not happen.

Remember, Pixie Lott went out from 2nd= on the leader board in a week with 6 couples.

I suspect you're right and we will see Claudia or Rob go out this week. Apart from Ed (who could still go) they are the right ones to go. Of course they could surprise me and pull off some great dances tonight for the first time.

So I honestly can't see Danny being eliminated this week. I would be very very surprised if he were in the bottom 2 of the public vote. I suspect he is one of the top 2.

I wouldn't be surprised if one of the females is put top by the judges, simply because an all male final is not desirable.

It will be interesting to see if there are any ties on the scoreboard.

So if the judges favourite has a 96% of avoiding the dance off, does that mean that the public favourite has a more than 96% chance of avoiding the dance off? (Sorry, being lazy and haven't done the maths).

Deleted.

If Ed comes top of the public vote (not a foregone conclusion) but bottom of the judges' vote, as expected, is this the only situation in which he'd be eliminated? If this were the case and the judges wanted him gone (entirely theoretical I might say; they probably don't care) they would have to mark the least popular down and the next least popular high (a choice between Claudia and Ore I suspect)

Ed 1+6=7
Celeb1 2+1=3
Celeb2 3+5=8
Celeb3 4+4=8
Celeb4 5+3=8
Celeb5 6+2=8

Very interesting. Thank you for all your work on this !
Was last week's result - Ed last in the judges vote and avoiding bottom two - a real statistical anomaly ? Or was there still a reasonable chance of it happening ?

And that is how probability works. You and I cannot say that Ed will be public favourite. That is for the public to decide. All we can say is the vote has been mathematically rigged against contestants that are at odds with the judges' opinions.

Again I refer you to the 4 Couple Semi Final. If Ed is second with the public then there are 5 of the 6 cases where he is second where he will still leave. That is insane and unfair. What if he had been second with the public all the way through the competition getting loads of public votes. The judges are saying we are going to ignore that, write those thousands of votes off and chuck him out. That is a public vote where the strength of support Ed is getting (number of votes) will not determine whether he stays, but instead the order of the minor rankings that people are comparitively indifferent to.

Dave, you claim to be an Oxford Maths Grad. Please start acting like one and for once admit the vote is massively rigged against the public.

If you are truthful, you will be compelled to admit this voting system is such that the judges' predominantly decide the majority of the contestants that get to the final, even potentially eliminating public favourites along the way. In the 4 Couple Semi, Ed will even leave if he is public favourite in a 1 in 6 chance. That is fundamentally wrong.


At a time when the BBC was getting a lot of flack about the rigged nature of this vote.

See my comment about other people's comments about sacrifices.

Yes it is. Top of the public vote is a pretty safe position for anyone. Top of the public vote is guaranteed to go through if there are any ties on the leader board.

Great stuff. That is exactly correct. This pattern you have here can be applied to every single week throughout the contest.

The worst week is the Semis when there are 4 Couples which is a 1 in 6 chance.

I do not want to say that the judges are rigging the vote in the way you describe, as I believe they are honest people, but this voting system does lend itself to this type of activity.

Think of Eurovision. That system can make it almost impossible for certain songs to win. Look at last year. Austria was a very popular song with the public, but did not stand a hope in hell of winning the contest, even if it was public favourite in the vote of millions, as the 200 jury members across Europe had marked it so low. (I really liked the Austrian song; it was very sweet.)

For the past two years the public favourite song in a vote of millions (Italy 2015 a landslide favourite, Russia 2016) were both relegated to 3rd by just 200 jurors.

It is going to be interesting.

I think Danny is in the top 3 of the Public vote, so I don't think that if he was top of judges as well, he'd be in the dance off.

I am worried about Ore and Claudia.

Ed was reasonably safe if public favourite last week.

In the semis it is a 1 in 6 chance of elimination for Ed.
In the quarters it is a 1 in 24 (I think).

I think the formula is 1 in (n-1)! where n is the number of couples and ! means factorial. You might find it on your calculator (scientific) on the button labelled [n!].

n! = n x (n-1) x (n-2) x .... x 2 x 1

Eg 4! = 4 x 3 x 2 x 1 = 24.

Wow .... now I must find my calculator.

Have any of the eliminations this year surprised you ?

There have been an extraordinary number of ties this year. I know the BBC are aware that ties make the system fairer. I hope these many ties have not been manufactured just to make the vote fairer.

Also, are you saying a roll of the dice 1 in 6 chance of being eliminated is fair to someone that has won a public vote of thousands or 10s of thousands? I do not. I think it is a disgrace having any voting system that allows for public favourites to be eliminated.

All but one of the eliminations have conformed to expected mathematical pattern. Namely there is a 90% probability or above that one of the bottom three will be eliminated in litterally every week.

The only one that did not conform to pattern was the Tameka/Laura week where Tameka left. However, the mathematics did predict her vulnerability as there were a staggering 8 couples of the 14 that week that shared a score with at least one other couple. As I explain in my OP, the more ties there are the more vulnerable middle ranks will find themselves to appearing in the dance off with another middle rank.

Every lower or equal rank has always left in the dance off this year. Elsewhere on this forum others have speculated the judges might eliminate the higher rank at some point, otherwise the dance off appears a little stupid.

Thank you.

Hmmm, if, as some speculate, that Danny, Louise and Ore are the judges / producers favourites, and ed is the publics firm fave, it's au revoir judge or Claudia ....if only I were brave enough to place a bet !

Random thought, I'm a fan of the X factor too, and I am pondering what difference it might make if that show used the strictly voting system.

I guess we would not still be watching honey G !

No, the way the show is scored it is quite likely for there to be a tie. If eight couples are scoring between 27 and 39, say, it is more likely that they have a tie than they do not. This even ignores Darcy, Len, and Bruno typically marking the same as each other.

The dance tonight had 100% entertainment value, while the judges marked it for what it was. So will the public vote, or lack of, put them in the bottom 2 to give Ed a chance to get it right the whole way through?

The only thing I see insane here is trying to apply statistics to Strictly Come Dancing. It's like a nerd at the bus station noting down all the arrival and departure times. Be better if people applied statistics to something useful like third world crop yields or sumfink

Yet again, no you are wrong DaveGold. The judges have a wide range of scores, even if they chose to have a bottom score of 5. Individual judges choose to give couples of clearly different ability the same scores. That is why there are so many ties. Your 27 bottom limit is assuming a typical bottom of about a 7 from each individual judge. The ties are generated because the judges choose to have a very narrow range of scores.

Also if Craig ever marks a teacher's pet couple on the low side, we invariable joke that someone else will overmark to compensate. Sadly we are almost always proved right.

Can I ask you something DaveGold? You seem to be defending the indefensible. I have heard exactly the same incorrect and flawed arguments you have used over the weeks from people connected with the show. Are you connected to the show in any way?

I'm sure most people are fed up with this mathematical feuding, so please accept some standard maths with humility for a change!

Most people have seen this phenomenon of shared scores before as the Birthday problem https://en.wikipedia.org/wiki/Birthday_problem. Let's assume this time that 8 couples are scoring from 24 to 39, with each score at equal probability, the chance of the 8 couples having different scores would be 12%. If you assume any patterns in the marking then the chances will drop further.

B_OR...

Please answer this question: How can you claim to draw sound/valid conclusions from any of this hoo-ha, when you use basic probability + some misinterpreted statistics, to analyse what you openly accept to be a flawed/fixed system, of which (and here's the vital bit) certain vital aspects & parameters lie outside your realm of understanding?
I don't mean that in a nasty way, I mean that in a very true sense - there quite literally are factors at work in the mechanism you're trying to analyse, which simply defy logical examination or explanation. To put it another way - there's a ghost in the machine, and it is undermining your attempts to understand the system (not to mention adversely affecting your abilities to coherently relay your findings to others) by virtue of its very presence, which you appear to both simultaneously acknowledge yet reject...?

Hmm... It's difficult to know where to start. You're on the right track...ish, sort-of, but you're not only heading in the wrong direction, you're also barking up the wrong kettle of ball-ganes. To make matters worse, you are dressed inappropriately for the weather, and the guide book you think you hold in your hand is actually a copy of Women's Weekly (with several pages missing, and others scribbled on). Do you see what I mean? No!? OK...

Think of a loaded dice. Do the laws of probability apply to it? How about statistics? How would you set about 'analysing' it? Would it matter if certain sides were obscured from your view? Or if you were blind? Or how about if the person throwing the dice, 'knows' the dice far better than you ever could, and is an expert at making it look like it's loaded a particular way, when in reality, it's actually loaded rather differently? (oh, and the thrower is variable too - sometimes they can & do roll it the way they want, other times they're less willing/able to do so, but you can never be sure - and besides you're in a different room to the one you thought you were walking into, and to further complicate matters, all results are being passed onto you by a small Korean woman who can speak neither your language nor that of their master). What then? Hey?

Sigh.... Look, here's the thang: Often, your "maths" is correct... (almost)... Oh BUT, and it is a big but, you consistently misuse/ill-appply it, in a variety of vague, ambiguous & semi-amusing ways. Some examples, for instance: making basic category errors, trying to lever "statistics" into equations where they don't belong, using false assumptions/best guesses/leaps-of-faith/etc, which (despite having their place somewhere in the natural order of things) you insist on wielding like some sort of mad-eyed-egg-head, in order to present your resulting vacuous inferences as cold-hard-FACTS. Perhaps most devastating of all, you choose to either ignore, or perhaps unknowningly fail to take into account, numerous vital aspects of the system, which ultimately render your cherished data unstable, at best, inedible, at worst, and more-often-than-not-so, essentially meaningless.

Lo! Now, hear this:

Despite all I have said, reverse-engineering SCD is possible... to some extent, and indeed, I myself have made many untold thousands of dollars from doing exactly that. Successfuly, and for many many years now. How? How do!

I can't tell you how (you know why not), but I CAN tell you this:

Your system is woefully incomplete & entirely inadequate for the task at hand. Sorry to burst your balloons, old chum. But you must admit, they were getting a bit bloated.
I suspect the problem lies with your ingredients. You've tried to bake a cake, using parts of a rusty old bicycle, and it just hasn't quite turned out right. Eek! What will the guests think? Will they notice? Or perhaps they'll be too polite to say anything? Don't worry. Dry your tears, spare your blushes, save your kisses, stop tbe press - we've all been there, trust me - we've ALL been THERE. Now then, where was I? Ah yes...

On the other hand, MY patented Strictly-Come-Dancing analysis-system uses a precise combination of the following essential ingredients: mathematics, probability, statistics, LOGIC (formal & modal), set theory, semiotics, game-theory, sociology, psychology, mis-direction, showmanship, magic, deconstruction, philosophy, anti-philosophy, complete isolation, insanity, sanity, a good memory, clean trousers, a pocket calculator, stopwatch, pen, pencils, paper (plain, ruled & graph), NO computer, blood, sweat, tears, insomnia, dedication, determination, discipline, fluid-sense-of-self, zero-dance-knowledge, flatulence, code-breaking, snacks (lots of), money (lots of), no alcohol (none of), a passion for knowledge, a thirst for understanding, a little something for the weekend, swimming trunks & overnight bag (just in case), time, time & more time, time & time again, INTUITION, fully-unblocked drains, a cat (one is ideal, two plenty, but any more could potentially distract), a sharp mind, the ability to devine authenticity at a distance of at least one mile, focus, patience, TIME, empathy, energy, entropy, wizardry, concentration, skillz, Vernon Kaye on speed-dial, god-like powers of doublethink, full-head-of-hair, huge amounts of will-power, massive amounts of paper-mache, the ability to withstand pressure so intense it makes your pips squeak, ludicrous quantities of peanut-butter, 23 additional Top Secret ingredients, and finally... above all else - balls the size of Wales.
Whale-sized balls, even.

That's how I roll. Take me as you find me. Sevverrrn! (7)
Sorry to be so brief this time out, I'm in a rush. Nature's calling, and I simply must go. Peace out, y'all...

Dr