Here are the probabilities for the 4 Couple Week

4 Couple Week
Judge Rank: A (first), B, C and D (last)
Percentage Chance in Dance Off (fair 50.0%): A = 25.0%, B = 41.2%, C = 58.3%, D = 75.0%.
Percentage Chance Eliminated (fair 25.0%): A = 0.0%, B = 4.2%, C = 20.8%, D = 75.0%.

Percentage chance of one of judges' bottom 2 eliminated: 95.8%

As the probabilities above show, the Strictly vote is a laughably biased vote in favour of the judges' opinions. It is also a system that can penalize a voter's favourite if they split their votes in some ways. A voter could possibly be assisting in eliminating one of their favourites from the show if they are not careful how they vote. Please see my advice for this week at the bottom.

As normal we only assume unique judge ranking for inclusion in the dance off. We also assume the overwhelming historical case that judges eliminate the couple they ranked lower in the earlier show. The latter has occurred so far in this year's Strictly. (Note be wary though, as some on this forum have suggested the judges always reverse at least one decision in the dance off to try to justify its existence. I do not know if that is true.)

These are the odds the lowest ranked couple will face:

Couple at the Bottom of the Leaderboard:
Will be in dance off in 1 in 6 cases when they are 1st with the public.
Will be in dance off in 5 in 6 cases when they are 2nd with the public.
Will be in dance off in 6 in 6 cases when they are 3rd with the public.
Will be in dance off in 6 in 6 cases when they are 4th with the public.

In contrast, look how easy it is for the judges' favourite:

Couple at the Top of the Leaderboard:
Will be in dance off in 0 in 6 cases when they are 1st with the public.
Will be in dance off in 0 in 6 cases when they are 2nd with the public.
Will be in dance off in 1 in 6 cases when they are 3rd with the public.
Will be in dance off in 5 in 6 cases when they are 4th with the public.

To make it a little clearer, the last placed couple on the leaderboard will almost certainly leave if they are 2nd or below with the public. There is even a chance (1 in 6) they will leave if they are the public favourite. Remember, if they are in the dance off, then the judges will have to reverse their decision of just a few hours earlier to avoid elimination.

The judges' favourite will almost certainly avoid the dance off in all cases except when they are last with the public. However, even if they are last and do appear in the dance off then the judges have already told them they are their favourite just a few hours earlier, so they are likely to survive.

These facts show you just how massively biased this vote is in favour of the judges' opinions.

We only have four couples left, so there should not realistically be any draws, but considering the massive number of draws we have seen through this entire series, I will try to explain the probabilities for all 7 possible draw scenarios later in this thread if I have time. However, I am very concerned why we have been seeing so many draws this year.

What we can say is there are a sufficiently wide spread of marks available to the judges that draws should be uncommon, especially in these latter weeks and especially when there is a clear distinction in the couples' dances that do not justify the same mark. If the judges are choosing to limit themselves to a narrow range of marks then there is an argument that they are choosing to create draws. If so, why?

We have heard nonsense from a few individuals on this forum trying to defend this heavily biased and mathematically rigged vote. They have unsuccessfully tried to claim that these probabilities are wrong because not every event has an equal chance. What they have failed to say is nobody knows how the public are going to vote, even the illustrious BBC or the naysayers on this forum. The BBC might like to tell us how we are going to vote, but they cannot, they do not know. Will we vote for the most technically perfect dance, the most entertaining or the person who has made most progress? From what I have read on these forums many people's vote changes every week between these and other categories. There is one simple fact:

Until the public vote we must assume every public voting eventuality is possible and carries equal weight. We must assume this until the public have told us otherwise.

What we can say with absolute certainty is this voting system makes it possible for a couple who is very popular with the public, getting thousands more votes than other couples combined, to be thrown off the show against mass public opinion. Look at the probabilities above. Look how biased it is for the bottom of the leaderboard couple even when they are second with the public. It is also shameful that the public favourite can be thrown off the show against the public will.

The presenters in 2015 and the celebrities (in prerecorded edits) in 2016 were telling the public that nobody was safe. What we saw in my posts in the early weeks was that some couples could get ZERO public votes and only appear in the dance off in an incredibly small 1 in 100,000 of all the voting possibilities where they were last with the public. That is an extraordinary level of safety with no public support.

Even though some couples were ridiculously safe, the BBC wrote on their website, 'No couple is guaranteed to be safe on judges' votes alone however, and the viewers' votes can always influence the outcome. This means each week any couple can face or be saved from the dance off with the public vote.'

Up until early 2016 the BBC were on written record with the provably untrue statement that it was impossible for the public favourite to be eliminated in a 5 Couple Week. The truth is the public favourite that is at odds with the judges' ranks can be eliminated in every week, and the chance of them being eliminated increases through the season.

Even though the BBC were unaware before 2016 that the public favourite could be eliminated, they have changed their statement about this issue and are now on public written record as saying, 'Overall, the rules of the vote were well-explained to the viewers and they would understand the significant role the judges had in eliminating any couple in the dance-off (even if that couple had been the audience's favourite)'. I guess we should take a positive from that and be glad that the BBC consider all of us viewers a lot smarter than them.

I absolutely love this show, as we all do on this forum. However, through my posts I have come to realize that like me, many of you are also unhappy with the mathematical bias this voting system gives to the judges, and how difficult it is for us to save some of our favourite couples even when they are getting mass public support.

Sadly this voting system mainly populates the final with judges' favourites irrespective of whether they are popular with the public. It is also a system that can remove public favourites before the final. Additionally, it is a system that can penalize a viewer's lower judge-ranked favourite if that viewer decides to split their votes in certain ways.

Thank you again for everyone who has taken the time to read my posts.

So what is my advice to everyone this week? I am afraid, the percentages are way to hectic at this stage of the season. My advice is to pick just one couple that you absolutely must see in the final and give all your votes to them. I really think splitting your votes in any way this week could have a major detrimental effect for your lower ranked favourite. Hopefully we will be lucky and the public favourites will make it though. Best wishes to everyone.

Paracetamol

It's Friday night, my brain is fried.

tl;dr

I always do !

Its good to see you back again daveGold. I see you are not trying to mislead everyone this week at least.

It would have nice of you to finally admit the vote is massively mathematically biased in the judges' favour, even though you have tried to falsely convince everyone it is not for weeks with Mickey Mouse arguments.

I don't think you ever answered my question. Are you connected or know anyone working for the show?

Well, personally I don't want the "people's favourites" in the final. Not when those choices are made on the basis of who looks a bit shifty or full of themselves, who may have done a bit of ballet dancing when they were at school etc.
I think the judges (in the main) are reasonably objective in their views and marking. Yes, I've disagreed with them in the past, but more often than not they get it right. In the end, I want the best dancer to win, even if I don't happen to like them. Besides, in the final Joe Public does get to decide. That's how we have ended up with one or two duffers taking the prize.

Fair enough. This is not BB so the dancing should count for something. We get the last word in the final which is good enough for me.

Thanks.

I am not a pro-dancer myself, but I do know some and have watched the show with them. I do not know about all the toe and heel leads, but sometimes the pros I know have said the judges have got it wrong. They do not praise or highly mark some couples for doing the difficult stuff, and also praise other couples when they do it wrong or badly.

Either way, what we can say is IF there is a phone vote, then it must be fair to the public and the public cannot be misled. That is an obligation of the BBC Editorial Guidelines and Ofcom regulations.

That,I would agree with.

The problem with this voting system is the final is mainly populated with the judges' favourites, even if the public are not impressed with what they have done the entire series.

This is all I ever do. Pick my favourite couple and vote every week regardless of whether they slip up in a routine or face the dance - off. Apart from one time ( supporting Pixie Lott ) my favourites have either won or come second, so I feel I'm pretty good at picking !

If the BBC run public votes then there are BBC Editorial Guidelines to adhere to (eg all contestants must have a fair chance, which does not appear to be happening in this vote as seen by the probabilities above). Also Ofcom regulations say viewers must not be misled (which also does not appear to be happening by the comments made by presenters claiming nobody is safe, when there are some couples that can get ZERO public votes and will only appear in the dance off in a 1 in 100,000 chance).

Ah, the tyranny of the majority

Do they have "favourites" based on anything other than dancing though ? I've heard that accusation thrown around in every series, but is there any real evidence to show that it's true.
I know they can go overboard in their praise of certain dancers occasionally, but doesn't that usually even itself out ? Those favourites appear to change depending on who does best in any particular week. And I certainly don't think the BBC has any "agenda" about who wins, which is another accusation that was frequently heard in the past.

Just out of interest, how would you change things ? I presume you would still want a panel of judges giving marks, and you are not suggesting turning Strictly into purely a popularity contest ?

They are the viewer favourites too. We get to decide who avoids the dance off up til now. I doubt the judges give a toss.

Sadly vald, the maths shows that may not be the case.

The week Ed Balls left he could have been second with the public. Remember that week many seemed to be wowed by Danny's dance and they also generally felt Claudia was massively undermarked. Could one of these things (or both) put Ed in a critically unsafe rank while still getting massive public support?

Ed Balls could have still been getting massive public support, but been pipped to the 1st with the public slot and been eliminated as a result.

Some of the ones who survived could have been getting minimal public votes.

Firstly you need to get the vote conforming to regulation.

You can get a fair vote, but roughly the same percentages as present by letting the judges give free passes (ie not put to the public vote) to the top half (round down) of the leaderboard. Then make only the bottom half be subject to the public vote, but ignoring judges' scores at this stage. The bottom two in the public vote appear in the dance off.

Since there is presently a 97% chance every week that one of the bottom half will be eliminated, you will get almost exactly the same result as with the present system, but the vote conforms to regulation, and the presenters can then encourage you to vote for any of the bottom half in the public vote without breaking Ofcom code.

However, as I say this still gives the judges too much influence.

The mathematician who suggested this solution said it would be fairer to both public and judges if only the top third were to be given free passes and the bottom two-thirds are then put to the public vote. (Or possibly somewhere between one third and one half is optimal.)

The judges keep their favourites. The public are guaranteed to keep their favourites. Only those couples who are indifferent to both judges and public will ever find themselves in the dance off.

If the judges got to keep a third of the leaderboard safe the cries of favouritism and unfairness in the scoring would probably be ten times what they are now. How is it better to go from their favourites having a tiny chance of being in the DO to having no chance? People kept safe by the judges until the final would build up no voting base to help them in the final but probably a resentful 'anti vote' from fans of other couples.

This is true....though tbh It would have meant someone like danny or louise being in the last two in the public vote, but still beating him overall. Improbable, but possible!
As for this week, those stats are mind-numbing. Suffice to say that the jooodges will do their utmost to stuff up claudia by placing her last 2moro.

[quote=Ellie1967;84843596]If the judges got to keep a third of the leaderboard safe the cries of favouritism and unfairness in the scoring would probably be ten times what they are now. How is it better to go from their favourites having a tiny chance of being in the DO to having no chance? People kept safe by the judges until the final would build up no voting base to help them in the final but probably a resentful 'anti vote' from fans of other couples.[/QUOTE]

thats happened a number of times over the years, no names mentioned...

I think you may be taking this show a bit seriously!

But the public are then guarantee to keep their favourites. This present system means your favourites at the bottom of the leaderboard can be given the boot even when they are getting massive public support.

The couples at the top do not need your vote to survive with the present system. In many ways you could say the public are being conned into voting for already extraordinarily safe couples. Telling the public not to waste their votes on already safe couples by not even putting them to the public vote is an honest thing to do.

This also focuses the public's attention on the couples that actually need your vote.

I think there should be a test based on the OP and a prize awarded for anyone who can show that they actually read all of it!

I am worried about Claudia as well.