I have no private messages in my inbox.

As I have explained over the weeks, the BBC cannot say they know how the public will vote. What if they thought contrary to the way in which you and the BBC think the public will be voting?

All we can say is these are all the permutations how the public can vote. There is a massive bias in the number of permutations that allow certain couples to avoid the dance off. A similar thing is true in Eurovision where many songs have literally no chance of winning the contest, prior to the public vote. Until the public actually vote we cannot make any assumptions as to whether some of those permutations are more likely or not. If you truly understand mathematics you would understand that.

All but one week this year has conformed to model as I have predicted. The only week that did not conform to model was the week where 8 of the 14 couples were tied with at least one other person. This should be a very rare situation, and I must admit I am very concerned about the number of draws we have seen this year.

I know people who called the US election and the Brexit vote because they did not get muddled by your way of thinking. The BBC and every other major UK and US news network called both those votes incorrectly because they believed they knew how people would vote.

davegold, I am sure you are a nice guy, but you are wrong.

BBC Editorial Guidelines state every entry must have a fair chance of winning. That is not true under this system.

Ofcom regulations say the BBC must ENSURE the public are not misled. Unfortunately due to things the presenters and celebs are saying and not saying, that is also not true.

If the BBC are saying the same thing as you with regard to them knowing how people will vote, then I am afraid they are misleading as a result. That is a breach of Ofcom regulation as far as I can see.

Baz_James has started another thread, but sadly at this time all his probabilities are wrong. All my callculations are correct and take into account the public vote trumps any ties.

Also daveGold makes exactly the same flaws in his arguments as he has on this thread. However, I hope my explanation above helps daveGold see where he is going wrong. DaveGold, what you are saying is just not how probability works.

And many people, including professional dancers, totally agreed with the judges marks for Claudia's AT and thought she was unfairly ranked higher than she should be given the distinct lack of many elements of AT in the show dance version performed that night.

People are told to vote for their favourite couple and that, at the end of the day, is all that anyone needs to do. If their favourite happens to be someone who isn't a particularly good dancer well it's just hard cheddar in a light entertainment show which is based around an element of learning how to dance.

And lots of people including Argentine Tango teachers and regular Argentine Tango dancers agreed with the judges or thought they were very generous. There was very little At and mostly because her feet were barely on the floor long enough to execute any AT steps. ( and it does have steps)

Hehe expressed slightly more eloquently than my reply AT

Are you watching the voting by the judges so far tonight?

It looks like Ore will be saved by the judges. At the moment, unless Claudia is first with the public, she is gone. Even if she is second with the public she is almost certainly gone.

I have talked with some pro dancers so far tonight on the phone and their ranks for the first half are:

1. Danny
2. Claudia
2= Louise
4 Ore

They cannot see why the judges are marking Ore so high. They say Claudia and Louise were both good but made a few mistakes, eg Louise was a bit too skippy.

Nope, I don't watch the show live. I'll catch up on iPlayer later.

OK, after all of them the pros I have phone have the following:

1. Danny
2. Claudia
3. Louise
4. Ore

They have not got a clue what the judges are seeing in Ore's two dances. Claudia pipped Louise on her second dance to get her just above Louise.

The judges ranked:

1. Ore
2. Danny
3 Louise
3= Claudia

As there was a draw at the bottom I will post the new probabilities.

4 Couple Week with a Draw at the Bottom
Judge Rank: Ore (first), Danny, Louise and Claudia (joint last)
Percentage Chance in Dance Off (fair 50.0%): Ore = 33.3%, Danny = 50.0%, Louise = 58.3%, Claudia = 58.3%.
Percentage Chance Eliminated (fair 25.0%): Ore = 0.0%, Danny = 8.3%, Louise = 45.8%, Claudia = 45.8%.

Percentage chance of one of judges' bottom 2 eliminated: 91.6%

I think it is almost odds-on that one of Louise or Claudia will be eliminated.

If you want one of these to get through you need to vote like mad.

Whoever you like just vote for one. Splitting your votes is a very bad idea.

I explained this to you before. This is one of the most well known 'surprising' bits of probability - the birthday problem. Why are you unwilling to listen to people?

https://en.wikipedia.org/wiki/Birthday_problem

As usual, you have not responded to a mathematical argument with a mathematical response. The Eurovision song contest and US elections are not relevant to my argument i.e. - the public vote on Strictly cannot be assumed to have equally likely outcomes. Please show the mathematical basis on which you make the assumption that all outcomes of the public vote are equally likely, whether it is Ed Balls dancing Gangnam or Anastacia dancing Bat out of Hell.

Thanks for responding. I can now see where you are going wrong. This is a little long, so I have bolded a key point at the bottom.

The Birthday Problem you quote is one where there is statistical evidence over a long period of time that the events do not occur with equal likelihood. Such things as winter holidays and summer periods tend to cluster birth dates. (However, the thing I would like to point out is this phenomenon was unknown until credible statistical analysis had been done.)

We cannot assume that to be the case in Strictly voting. Let us use the Gangman example you have suggested on two occasions. You, me and the BBC have no concept of what effect such a dance will have on the voting public. That is what the public vote is for. It is a vote based in opinion.

You believe that people will vote for it with mass public support. When I saw it I thought it was the worst dance Ed had done and might have reduced his rank to one where it was more likely to be in the dance off, and almost certain elimination as a result. It was totally out of context of the ballroom/Latin nature of the show and could possibly annoy the people that typically vote on these shows. From a snapshot social media opinion on these forums there were very diverse opinions. However, the important point is, when I formed my opinion of what the public might do, I understood I could not say for sure, I did not know.

The simple fact is that every week people's opinions will change (as can be seen on these forums). You, me and the BBC cannot call these things, however clever we all think we are. As I say, I know people who correctly called both US and Brexit votes because their sampling and understanding of the key issues of the vote was a million times better than the news networks and opinion polls. The BBC and all other major UK and US news networks all got it wrong.

I find it very difficult to believe that you or the BBC are doing sufficiently credible sampling between the completion of all dances and the point where the voting lines close to make any accurate statistical argument that one public voting permutation is more likely than another. We all may have opinions, but until those votes are cast none of us actually know. The public ultimately decide.

Therefore, since we do not know how the public will vote, and since it is impossible to do any credible sampling in the short period between the end of the show and the lines closing, we must assign an equal weight to each possible event. To do otherwise based solely on a few people's opinion is a very dangerous and mathematically incorrect thing to do.

As I have repeatedly said, the only sure thing we can say is there are so many possible voting permutations and some contestants will find themselves in the dance off even when they are doing very well with the public, getting mass public support, even getting significantly more votes than others below them.

For example in the unique voting case in the 4 Couple semi final, the lowest ranked person would still find themselves in the dance-off when coming 2nd with the public in 5 of 6 eventualities. That is not acceptable and does not adhere to BBC Editorial Guidelines that say every contestant must have a fair chance of winning.

To finally put your argument to bed, clearly coming 2nd with the public and being eliminated in 5 of the 6 occassions with unique judge ranking is wrong. How can you or anyone else say that the 1 in 6 chance that they are not in the dance off when coming 2nd with the public is more likely to happen than the other 5. You cannot.

Also in the early weeks the judges' favourite can get ZERO public votes and only find themselves in the dance off in 1 in 100,000 of the permutations where they are getting zero public votes. How can the BBC presenters who have said no one is safe claim that they believe those 1 in 100,000 permutations are more likely than the other 99,999? They cannot. Therefore, their comments are possibly misleading the public contrary to Ofcom regulation.

So sadly you are wrong.

On a brighter note, I did think your individual judges' rankings of the semi final couples to be very enlightening. It is a shame we do not know which would be everyone's dance off dance, as we could pinpoint possible judge intention with a little more accuracy.

I have B_OR on my ignore list. Sadly - very sadly - that doesn't stop his/her rantings showing when someone replies to his/her absolute drivel. Why doesn't anyone tell B_OR to disappear up his/her own orifice? Everyone else has a valid opinion. B_OR just talks absolute, undiluted carp!

B-ORE

For future reference- the longer the post, the less likely I am to read it.

If there was anything relevant in there I'll never know.

Yet again the anger and intimidation.

If you look at the two posts before my last one, daveGold (someone who is at least reasonably polite) asked a question about why the Birthday Problem did or did not apply. He politely asked me to explain, which I did. As daveGold is clearly confused on this issue, that post was a little long.

If you do not want to read it, then don't.

However, do not use bullying and intimidation just because your arguments are flawed. The Jaz_something member did exactly the same and then produced a post with clear basic mathematical errors to try and undermine my posts. Others pointed out those errors, which he then had to withdraw.

You, me, daveGold and the BBC do not know that 1 in 6 event that lets a person avoid the dance off when 2nd with the public is any more or less likely than the other 5 in 6 events that means they are in the dance off when 2nd with the public.

You might not like the idea that this vote is massively biased against mass public opinion, but the simple fact is it is.

Must? There is no must. We don't have to make that assumption at all. It is dangerous to calculate probabilities based on opinion, however I am not the one assigning probabilities to anything. I am saying that these figures are unknown. You are using your opinion to say that all results are equally likely! If we do make an assumption of equality we should acknowledge it and reduce the certainty of our predictions.

It is still a fundamentally flawed assumption that the public cannot spot a popular dance when they see it. As a consequence of your assumption

- the vote is not changed by any quality of the dance
- the vote is not changed by any part of the Strictly show at all
- the vote in previous weeks has no impact on the current week
- none of the couples are more popular than any others
- the voters have no pattern to their voting, i.e. they do not vote for people in trouble

Specifically, let's look at the Ed Balls phenomenon, or Judy Murray, or Anne Widdicombe, or John Sergeant, or lets just call it the survivor phenomenon. How do these people keep defying the odds and keep in the show? If your model was correct it would predict that these people would stay around until Halloween since they always do. The strength of your model has to determined by its failures as well as its successes,

The answer is straightforward. These celebs have popular support. By escaping the dance off at the expense of someone in mid table we know that they have a high popular vote that they carry from week to week. They are not likely to be bottom of the public vote after having been ahead of four or five couples the week before. This survivor phenomenon happens every series because a model that acknowledges their popularity will suggest it will happen each and every series!

I do not understand why you feel you are capable of spotting a popular dance on behalf of the entire voting public on Strictly. You cannot.

Also it is a very dangerous assumption that popularity one week can result in popularity the next. Again, you are not the self appointed spokesperson of the entire voting public.

I have made it clear throughout. I do not know how people will vote. Consequently I must assume equal probability. No one, including you and the BBC do not either. That is what the public vote is there to find out.

The fact is the model I have presented over the weeks has accurately predicted one of the bottom three will be eliminated in the early weeks and one of the bottom two will be eliminated in the latter weeks, as the model said it would happen with a 90%+ probability. The only week it did not conform to this basic model was in the week when a staggering 8 of the 14 couples shared a rank with at least one other couple. But even then it conformed to the modified model.

I have found over the years your type of approach is a problem with the BBC and other news outlets. They all appear to feel they understand the public and can speak for them. You and they cannot.

For example, one week I noticed on these boards they felt Claudia had been massively undermarked. Did that sentiment on this forum spread across all voters, or was it unique to this board? I do not know, and nor do you. DaveGold, you are very wrong to say you know.

As for Ed Balls staying until midish season, this model does predict that. The bottom of the leaderboard has to be middle to upper rank with the public in the early weeks to survive. Then as the season progresses, it becomes more and more unlikely for them to stay unless they are the favourite with the public. (Look at the 5 in 6 chance of being in the dance off when second with the public in the 4 Couple Week.) Just one event like Claudia being undermarked or Danny wowing with a Samba as reported on these boards can drop him to an uncertain second or criticaly terminal third when still receiving mass public support. I do not want to predict what that actual event might be, but such an event can happen. I listen rather than tell people what those events might be.

If you truly believe you fully understand the voting public's every motivation, you need to phone up the BBC, declare your all seeing, all knowing status, and tell them to stop wasting License Fee Payer's money on running this vote, and just let you tell them the results of public opinion instead. Giving you 100 notes and a slap-up meal in the BBC canteen will be a massive saving to the public.

I think using the basis theory of everyone having a fair share of the votes is possibly the best way of using the OPs theory, which seems to work well. However, I think Davegold is right when he says that it is possible to predict someone getting more than their fair share of the vote. Maybe not to 100% accuracy, but the fair share strategy isn't 100% accurate either. When Ed danced to Gangnam Style, his fair share would have been 12.5%. If any bookmaker had offered reasonable odds on Ed getting more than 12.5% of the votes, he would have been knocked over in the rush.

Anyway, what I'd like to ask the OP is whether he/she could produce one of his/her percentage suggestions to show what the chances of the last four would have been had Danny and Ore tied for the lead, and Louise and Claudia tied for last place in the judges scoring? Would there have been a significant change? And actually, if it is easy to do, another one with Danny and Ore tied at the top, Claudia in third, and Louise in last place. Don't worry if it takes too much time, it is after all, academic.

I want a mathematical discussion please, so don't being me personally into it. Defend the model and its assumptions!

If you do not know how people will vote then the model shouldn't assign a precise probability to each and every outcome of the vote. There is no reason why the model 'must' do that. Unknown is not the same as equally likely. It is possible to use your figures as count of possible outcomes, indicative values, rather than hard probabilities.

The model doesn't predict the survivor (Ed this year) at all. The model assumes that the bottom of the leader board is in an entirely random position on the leader board every week. The model predicts that the bottom of the leader board is the most likely to go each week, and the chance of the bottom of the leader board surviving for a few weeks is 50% each week, so 6% after four weeks. However this happens every year. As I said before, the model should accommodate this regular feature of the strictly results.

Until you can model this, you shouldn't be telling people that the survivor has a 50%+ chance of going out each week and that their voting should change accordingly.

Firstly, what I have said is not bringing you personally into it. It is demonstrating what you are saying is absurb. You cannot say these things and make these assumptions. You do not know how people will vote. Nothing is obvious.

I believe you are presently claiming this because you know I have been subjected to a significant amount of abuse by about 5 members of the 2 to 3 thousands viewers of my weekly posts, and you are trying to deflect attention away from that and pretend it is me doing it. I am the one that that has been abused and bullied over these past weeks for trying to explain something that the BBC should have been telling the public themselves. You are not the one being bullied.

As for the mathematical point, if you do not know how people will vote, which you do not and neither do I, then you must assume equal probability and see how good that model is. The truth is it has been a frighteningly accurate model. It has been for years.


What this model shows, extremely well, is someone like Ed at the bottom will be facing incredible odds every week just to survive which is the result of so comparitively few permutations allowing him to survive. Those number of permutations (as a percentage) which will give him the boot will increase week by week to a ridiculous level in the semi when he will be thrown off the show in 5 of the 6 occassions when he is still very popular with the public when he is second with the public. He will even be given the boot in 1 in 6 occassions when he is first with the public. That is wrong.

From that point of view this model has been very accurate this year, and for many years previously.

This model shows the dangers of the public splitting votes between the top and bottom of the leaderboard favourites, something the show has failed to tell the public through its entire joint public/judge voting history. There have been people on this board claiming they have purchased extra votes by phone just to do this.

This model also shows the extraordinary safety of certain couples in the early weeks, so safe they do not need a single public vote to survive in any realistic scenario. This is contrary to the illusion presenters and Strictly have cultivated over the years.

You have spent many weeks arguing over a minor technicallity that you do not like my use of the phrase 'percentage chance', while completely ignoring the massive bias towards the judges in this vote.

To quote a doctor of mathematics friend of mine who is also reading these posts, you are doing the equivalent of standing in a crockery shop watching the plates flying everywhere and pointing an accusing finger at a butterfly, while ignoring the red-eyed raging bull.

I have a few minutes. I am on a break and its only 4 couples. I will see if I can post it up quickly.

4 Couple Week with a Draw at the Top and Bottom
Judge Rank: Ore and Danny (tied first), Louise and Claudia (tied last)
Percentage Chance in Dance Off (fair 50.0%): Ore = 50.0%, Danny = 50.0%, Louise = 50.0%, Claudia = 50.0%.
Percentage Chance Eliminated (fair 25.0%): Ore = 8.3%, Danny = 8.3%, Louise = 41.7%, Claudia = 41.7%.

Percentage chance of one of judges' bottom 2 eliminated: 83.4%

The dance off percentages really surprises me. I am sure I have them right though.

I don't really care. I wish some people would just get a life.

Sorry, I am looking at the latest TV news about civilians (including children) being killed wholesale in Aleppo.

4 Couple Week with a Draw at the Top
Judge Rank: Ore and Danny (tied first), Claudia and then Louise (last on own)
Percentage Chance in Dance Off (fair 50.0%): Ore = 41.7%, Danny = 41.7%, Claudia = 50.0%, Louise = 66.7%.
Percentage Chance Eliminated (fair 25.0%): Ore = 4.2%, Danny = 4.2%, Claudia = 25.0%, Louise = 66.7%.

Percentage chance of one of judges' bottom 2 eliminated: 91.7%