8 Couple Week
Judge Rank: A (first), B, C, D, E, F, G and H (last)
Percentage Chance in Dance Off (fair 25.0%): A = 0.3%, B = 2.7%, C = 8.7%, D = 17.7%, E = 27.7%, F = 37.8%, G = 47.7%, H = 57.4%.
Percentage Chance Eliminated (fair 12.5%): A = 0.0%, B = 0.0%, C = 0.1%, D = 0.7%, E = 3.4%, F = 11.0%, G = 27.4%, H = 57.4%.
Percentage chance of one of judge bottom 3 eliminated: 95.8%

Why is it important to know these probabilities? This is not an inconsequential vote like the Presidential Election. Strictly is an important vote. There is a Glitterball at stake at the end of this, ... a Glitterball. They do not just put artificial glitter on this Glitterball. It is real genuine glitter. Glitter that dreams are made of.

Seriously though, it is important because there is a sizable amount of pre-decision in the vote. As I have mentioned before, there are some contestants who are so extraordinarily safe, they do not need a single public vote to survive. This is contrary to the illusions that have built up over many years, including this year, where presenters or celebrities have misled by saying nobody is safe. Also, this voting system ensures it is likely the final is primarily populated with judges' favourites, even ones that have been unpopular with the public through the entire series

Another issue that many other people discuss on these forums is the extraordinary number of draws we have been seeing. Last week we had 6 of the 9 couples sharing a score with at least one other person. As I have explained before, the more draws you have, then the typically safe middle ranking couples suddenly find themselves on very dangerous ground.

Also, it is important to know that even the winner of the public vote in a week can be eliminated that week. As I showed last week, it becomes ridiculous by the time of the 5 Couple Week. There are rumours due to Will retiring early, we might have a 4 Couple semi final this year. If that is true, those insanely unfair 5 Couple Week probabilities become ridiculous to the point of absurd for a 4 Couple semi final. We have had these 4 Couple semi finals before. Due to the secrecy in the public vote we will never know if our favourites were given the boot by the judges.

In the 4 Couple week, when ranked uniquely, the judges' least favourite will appear in the dance off in all cases when they are 3rd and 4th with the public. They will also appear in the dance off in 5 of the 6 occasions when they are second with the public. That is disgracefully unfair, especially when you consider it is likely they will be eliminated by the judges if they are in the dance off. Also, they will even appear in the dance off on an occasion when they are the public' favourite. That should never happen in a vote of this kind, especially when there are BBC Editorial Guidelines that should be protecting public votes from such results.

In contrast, in the 4 Couple Week the judges' favourite will never appear in the dance off when they are first of second with the public. They will only appear in the dance off in just 1 of the 6 occassions when they are second from last with the public. The only occasion they are likely to appear in the dance off is when they are last with the public, and even then there is an occasion when they will still avoid the dance off when they are last.

As a mathematician I worry these probabilities are too unfairly in favour of people working on the show.

There are a few on this forum who try to belittle or mislead by saying the probabilities are wrong, or the interpretation is incorrect. Ignore them, they are wrong. Every single one of their arguments is not sound or has been countered. One of these cornflake-box geniuses finally admitted last week there may be a problem with the judges' favourite being safe and suggested that could be resolved by just removing him or her from the vote and keeping everything else the same. Many of you will immediately see the problem with that. If you did that in this 8 Couple Week, all that happens then is you will have exactly the same bias and problems as the 7 Couple Week, but just a week earlier.

There are 40,320 possible ways the public can uniquely rank the couples. 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.

There is a 95.8% chance one of the bottom three judges' ranks will be eliminated. Put another way, there is only a laughably small 4.2% chance one of the top 5 will be eliminated.

The judges' favourite will avoid the dance off in all but a 1 in 330 chance.

The judges' favourite can get ZERO public votes and will still avoid the dance off in all but 1 in 42 cases of all the voting possibilities when they are getting zero public votes.

In short, contrary to the illusion that has built up over many years, some contestants are effectively already safe and do not need a single vote from the public.

The middle ranks might find themselves in the dance off, but if they do, then it is likely they will be paired with one of the bottom three from the leaderboard, in which case they are likely to be safe from elimination.

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

What does this all mean?

1. If you are voting for one person and do not care they may already be safe, then that is fine. Please do not reply to this thread with the very intimidating anger that occurred in my 9 and 10 couple week threads.

2. However, if you vote for multiple couples, especially if they are at opposite ends of the leaderboard, be very careful. The bottom ranks on the leaderboard realistically need at least middle or higher public ranks to avoid the dance off at this stage (and even then they are not necessarily safe), while the highest ranks do not really need a single public vote. Your vote for the judges' favourite may be the vote that when combined with other people's votes denies your bottom leaderboard favourite the public rank they need to avoid the dance off.

Your top of the leaderboard favourite does not need your vote to avoid the dance off. Your bottom of the leaderboard favourite not only needs your vote, but also needs your help to ensure as few as possible do not rank above them. The latter is already difficult due to the judges' low rank.

3. If the judges create many ties, like they did last week and unusually for many weeks this year even though they have a full range of scores, then the middle ranks become more vulnerable to appearing in the dance off with other middle ranks, such as the week with Laura and Tameka. When they flash the leaderboard, quickly count up as many tied scores as you can, and do not forget the bottom of the first page might be tied with the top of the second page. The more ties, the more help the middle ranks need.

If you mean me, then I hate to disappoint you but I'm an Oxford University maths graduate.

I find the stats interesting to read OP so thanks.

It has made me think twice about whether to vote for someone at the top of the table when I have firmer faves lower down.

Just so you know Tellymix post the leaderboard just after the show so you can refer to it after the show.

In short- this is the bit that applies to me. Thank you.

"There is a 95.8% chance one of the bottom three judges' ranks will be eliminated. Put another way, there is only a laughably small 4.2% chance one of the top 5 will be eliminated."

Please correct me if I'm wrong,but this is only the case if there are no Leaderboard ties.If there are ties,then this benefits the contestants further down the Leaderboard,and improves their chances of survival.

Of course when calaculating the mathematical odds for survival,you are simply adding up the various voting permutations and expressing these in percentage terms.The problem with this is you take no account of the various contestants popularity,calculating the percentages on the assumption that they all have a probability of the same ilklehood of voting numbers.....this is of course incorrect.

For example,if tonight's programme produces a Leaderboard where Daisy is joint 3rd (for arguments sake with Ore) and there are 2 or 3 Leaderboard ties,she would actually be in grave danger of a Bottom 2 appearance,as in all likelihood she is the least popular contestant left going by previous results.In this case,the quote which I used at the start of my post would be incorrect.

A further point would be that it's no certainty that whoever was further down the Leaderboard among the Bottom 2 contestants,would be certain to go in the elimination.A contestants Leaderboard position may be skewed by making mistakes in the first dance,which can be rectified in the dance off,or skewed by one Judge marking extremely low (usually Craig) but the other 3 judges thinking they were better than their higher Leaderboard rival.

In summary,many thanks for the statistics and they make a fascinating read.However there are many imponderables in the world of RTV and IMO they can not always be accurately assessed by numbers......you have to attempt to factor in the "dark arts"

No offence or anything, but don't you get tired of opening those long winded threads and get shirty when people reply contradicting you?

Me: Top 10 Univ (had 3 As at A-level, Maths, Physics and Chemistry in the early 80s)
Degree: Mathematics, First Class Honours.
Postgrad: PhD

And I am the lowest qualified in the group of people supplying these probabilities. I am the only one in the group who engages in social-media activity.

I am somewhat sceptical you truly are a Maths Grad. It is a triviality to spot the problem still remains if you remove the top ranking celeb from the vote. You just accelerate the end of season problems. I do not know how you would not be able to spot that.

Thanks for the Tellymix heads-up and thanks for the kind words.

I am starting to worry we are getting to the stage where it is likely a very popular couple will leave.

Did you read the 4 Couple Week probabilities (or 5 Couple Week I gave last week)? It is such a crazy system.

Correct. I explain that in the warnings I give. This year has been crazy with the number of tied scores we have been having.

Ties at the bottom are worse than ties at the top for making middle ranks more vulnerable, so be on the look out for that if a favourite of yours is in the middle.


You are right and wrong. This voting system is such that it is possible that even popular contestants at the bottom of the leaderboard can still leave. Look at my 4 Couple Week probabilities (above) to explain more in a simple case.

The whole point of the public vote is to see who the public wants to stay, ie to see who is most popular. The problem with the system is there are very few possible permutations for some to stay, even when they are popular. For example, Ed is very popular, possibly first with the public. What if someone like Danny or Louise wowed the audience one week and Ed dropped to second with the public, but still getting thousands more votes than everyone else. Look at my 4 Couple Week (and 5 Coupe Week given last week) probabilities. Look how dangerous it becomes for a low leaderoard contestant when they are second with the public in those weeks. That is just not a mathematically sound or fair system. The BBC Editorial Guidelines state every contestant must have a fair chance of winning. An average person reading the guidelines would say this system does not comply with those written guidelines.

In the pre-2016 Eurovision the lowest ranked jury song had a 1 in several trillion-trillion chance of winning the 12-UK points in a field of just about 25 songs. Surely that cannot comply with the guidelines. Even in the new system many songs have literally zero chance of winning the overall contest at the point of the public vote due to the jury marks. For two years running the public favourite in a vote of millions, even a landslide favourite in 2015, was relegated to third by just about 200 jury members.

Additionally, in Strictly the person at the top of the leaderboard is so safe they can get zero votes from the public, and still only find themselves in the dance off in less than 1% of the voting permuations where they are getting zero votes. It is so unlikely for that event to happen, because the public have to accidently hit one of those small number of unlikely voting possibilities. The point in this paragraph is important as Strictly have cultivated the false claim that no one is safe, when the truth is some people are to an extraordinary degree of certainty.

I got an A level in Physics (let's not discuss the grade) Doesn't have quite the same burn potential of your response!

Having wonderful qualifications doesn't necessarily make you interesting

One person's wine is another person's poison. I'm quite fascinated in statistics.

What interests me is that bottom of the leaderboard has a 57.4% chance of landing in the Dance Off, and the percentages read in ascending order as you go down the leaderboard. It goes against the grain of the danger zone being the middle of the board, as has been the case of late. Of course the number of ties has weakened the Judges Ranking and strengthened the public vote - it'll be interesting to see if they go down that route tonight or whether every score will be different.

I can't handle maths at all but can just about make sense of the words that come out of them... I kid myself!

My question is: what good does it do to know what masses of people would need to do to achieve an end (supposing they wish to achieve it) when you are just an individual?

The knowledge is insightful but is it useful?

Sorry to be crass and this is in no way meant to discourage the OP. I do read these threads and try to understand them

I'm not casting any aspersions on you personally whatsoever. If you bring a maths statement, or indeed any statement, to a public message board you should expect it to be questioned by your peers. Repeatedly getting angry and denigrating the respondents just gives the impression that you are more interested your own pride than the mathematical correctness of your work.

What I would expect from a maths graduate is the fundamental distinction between counting outcomes and calculating probabilities. This is was correctly mentioned by Bails HolyGrail but you still seem more interested in proving others wrong than improving the accuracy of your mathematics.

Is this geek heaven or hell?

Neither. Too dreary for heaven, too worthy for hell. More like purgatory, perhaps.

I am a complete stratosphere away from being a maths genius and I would need someone to explain this to me in a much simpler format. The minute I see a load of numbers my eyes glaze over !!
Am I being told that I shouldn't bother voting for the top placed couple as it's a wasted vote ? Who therefore should I be prioritising if I'm not sure who to go for and let's say they're number 3 and 8 on the leaderboard ?
Thanks on behalf of a maths thicko