This is written to help people maximize the usefulness of their votes to help ensure public favourites survive. Some couples are so extraordinarily safe without a single public vote, this is to help you know which ones so you can vote wisely.

The stats for a 10 couple week can be found below.

This has been proven by mathematicians. Any half-decent mathematician can easily calculate this themselves. I did not know it until I was told. Did you?

As you will see, there is a 90% certainty that one of the bottom three judges' ranks will be eliminated each week, even when they are getting high public support. The middle ranks only start to become vulnerable when the judges create a significant number of tied couples in their rankings. For example, Laura and Tameka only found themselves in the dance off together because there was a staggering 8 of the 14 couples that shared a judge-score with at least one other couple that week.

Surprisingly, from the 8 couple week onward through to the semi-final, the favourite in the public vote that week can be eliminated in that week. I am not kidding, it is a provable mathematical fact. Things are much worse for the public second favourite.

The judges' favourite in many weeks can get ZERO public votes and still will be 99.9% certain of avoiding the dance off in all public voting possibilities where they get ZERO public votes.

Let A, B, C, etc denote the couples, with A the judge favourite and J the judge least favourite. We will assume unique judges' ranks in this example. That is the only assumption being made for the chance of being in the DANCE-OFF.

We have assumed the lower judge rank will leave in the dance off for the Elimination percentages, as that is the overwhelming historical precedent.

10-Couple Week (Results to 1 decimal place)
--------------
Judge Rank: A (first), B, C, D, E, F, G, H, I and J (last).
Percentage Chance in Dance Off (fair 20.0%): A = 0.0%, B = 0.3%, C = 1.8%, D = 5.7%, E = 12.0%, F = 19.7%, G = 27.9%, H = 36.1%, I = 44.3%, J = 52.2%.
Percentage Chance Eliminated (fair 10.0%): A = 0.0%, B = 0.0%, C = 0.0%, D = 0.1%, E = 0.4%, F = 1.6%, G = 5.1%, H = 12.9%, I = 27.7%, J = 52.2%.
Percentage chance of one of judge bottom 3 eliminated: 92.8%

See how the judges' favourite has greater than 99.9% chance of avoiding the dance off. Even in the very rare cases where a top-half-of-the-leader-board couple finds themselves in the dance off, it is almost certain they will be paired with one of the bottom three, meaning they are almost certain of avoiding elimination.

Only two more weeks to go and the massive mathematical skew in the vote means that even the public favourite in a week can be eliminated in that week. It is much worse for the public second favourite. Due to the secrecy of the results of the public vote we will never know when the judges eliminate one of the public favourites.

I hope this helps everyone understand the vote a little better.

Unlikely.

How can I make it easier to understand? I want to help people not waste their votes on safe couples, and make sure their favourites survive.

As maths were my worst and least favourite subject, I can't begin to understand your post at all ! A shutter comes down and anything more difficult than primary school maths is beyond me.

All I know is that my favourite will get my 3 free votes every week and they will get to the Final. Apart from Pixie Lott, I've never had a favourite who didn't get to the Final, and three of them even won it ! I should really place a bet on at the bookies

I wouldn't bother, to be honest.

Just enjoy the dancing.

Isn't the answer to vote for your favourite? We can't influence other folk. (The show does that )

the only sure fire way to help your favourite is to vote for them - if your favourite is mid table and you have a habit of throwing a sympathy vote for a couple near the bottom as well then dont

Exactly.

Juggling with who you vote for based on stats, could see your middle ranked favourite out because people vote in greater numbers for the poor but entertaining.

Personally I don't vote for anyone in the top half of the leaderboard before December. There's just no point. If they're eliminated that early from that high up, they were on a hiding to nothing anyway.

I stopped there, appreciate your work but I vote for who I like - currently Judge Rinder, Greg, and Danny or Daisy

I vote for who I like or enjoy watching, regardless of whether they are top of the leader board or at the bottom

I dont consider my vote "a waste" if I have enjoyed the dance and tbh, no couple is "safe"

my 3 free votes are currently going to Ed, Robert and whoever else impresses me on the night

As a scientist and mathematician, I'd like to know how the people providing these figures derived the percentage chance (probability). Was this by using previous series as a statistical sample? This sample is quite small. Or was it by looking at all the theoretical mathematical possibilities? I think from the way you've written this up it is probably the latter?

I think in reality, certain things can confound the theory. For example, if you have someone who is always likely to be in the top of the judges scoreboard and who is also assured a high viewer vote (like Jay say), then that has a different effect on the middle and bottom half of the scoreboard than someone who is not so popular but always scores well with the judges (Simon Webbe say). So in the end the actual public appeal of the top half dancers makes a lot of difference.

(Also the couple lower on the leaderboard is saved in a dance-off about 15% of the time. If you're constructing a statistical model that you want to be convincing, then that has to be factored in, and can't just be written off as this one does, because it's not an insignificant number)

BIB If a voter's favourite also happens to be what you are referring to as a safe couple, then that voter is going to vote for them. and would not consider it a wasted vote.

Also, the remainder of the info is, dare I say it, basic common sense.
Anyone who has followed Strictly for a few years or more ( as the vast majority on this board have ) knows that, in the early weeks, the top Judges Leaderboard couples cannot end up in the DO, simply due to the number of contestants.
Once the numbers reduce, then they can.

Plus all the figures in the world mean diddly squat when the judges scores result in lots of tied places.

There is no such things as a 90% certainty.

It is your conjecture that Laura and Tameka found themselves in the dance off only because of ties on the leader board. It is not a fact.

When talking about future predictions you could tighten up your language. You can talk about possible voting outcomes (ranking of the public votes), and perhaps say that 99% of all outcomes will result in someone going through. Each outcome is not equally likely though. Without knowing the likelihood of these outcomes you cannot talk about chance and probability of couples being eliminated.

On a more general note, I think Strictly works best if people do just vote for their favourites. Changing a vote because of mathematics will only lead to disappointment, for one or for many.

Pretentious Pratt.
Will vote for whomever I want, no matter where they happen to be on leaderboard.

Steady on! That's a bit off.

I think the OP was simply trying to offer a mathematical method of voting for anyone who likes that sort of thing.

Of course you can vote for whoever you like. Nowhere was anyone suggesting otherwise.

S'ppose a safe couple, is your favourite?

People are still going to vote for them.

People tend to vote for their favourites anyway.

For me it's a "must record" entertaining TV variety programme.
I don't care who wins and I've never voted.

Same here.

This ^^ pretty much. You cannot influence anyone else's opinion so the only way to make your vote count is to cast it for the ones who you like best (generic yous all round).

Owww my head hurts

facts and figures are all mubo jumbo to me, I just vote for my favorites

Excuse me, not waste you're vote.

Yeah Pretentious.

Pardon?

This is the point I am trying to make. The upper half of the leaderboard are so safe, it is a wasted vote.


This is not true. 'No one is safe' is an illusion that has built up over many years and everyone is starting to believe it. For example, in the 13 couple week, the judges' favourite when uniquely ranked will only have a 1 in 1.5 Million chance of being eliminated. In that 13 couple week the judge favourite can get ZERO public votes and still only be eliminated in a 1 in 100,000 chance. That is extraordinarily safe.


For the dance off stats I do not use any previous data. I just look at all possible permutations and see what the result would be.

In the 10 couple week there are 10! (10 factorial) possible public voting permutations when there is unique public ranking. Basically, you go through each of those and ask if that couple is in the dance off or not, taking into account the public vote takes precedence in the case of ties. Add up all cases when a couple appears in the dance off and divide by 10!. That is your chance of being in the dance off.

For the elimination percentages I have had to take into account the higher ranked couple for the dance of dance overwhelmingly stays (note sometimes there are multi-dances in a week). I think it might be about 5-10% for the lower rank staying, but that will not make too much difference to the results given above.


The actual difference it makes is voting for a judge favourite makes it more likely a bottom three couple will leave, but the problem is it becomes more likely the bottom three couple will leave when they are still popular with the public.


I think that is a bit high. Remember when there are two dances, the eliminated couple is only judged on one of those dances in the dance off. Sometimes in the cases you mention, the couple with the higher joint score had a lower score in the dance off dance.


This is true. For example if the judges gave every contestant exactly the same score, then everyone has an even chance. (Note my Laura and Tameka comment.)


I think the point I am trying to make is say your favourite couple is 99.9% safe without a single public vote. So they do not need your vote. Then, say your second favourite (perhaps Ed) is really unsafe. By voting for the top of the leaderboard you are making it more likely the bottom person will go, even if you vote for the bottom person as well.


Someone has pointed out that it can also happen every week. I have checked this and it appears to be true.


But what happens when your second favourite leaves the show because you gave a vote to your favourite who was already safe and did not need your vote, and this denied your second favourite a public-rank score that was needed to save them? The crazy thing is a public second favourite who is unpopular with the judges can leave the show, especially when one or a few of the judges' favourites rank well with the public.