Wednesday, October 18, 2006

Working with what we know.

The market for 2nd elimination is already open and The MacDonald Brothers and Dionne are favourites to go. How can anyone sensibly speculate as to who will leave this week without knowing how they will sing on the night?

Dionne and The Unconventionals combining to form the bottom two on Saturday night taught us two things: 1) An act relatively popular in the polls can find themselves in the bottom two by performing diabolically on the night (and subsequently exit), and 2) An act unpopular in the polls can perform well and still fail to attract votes, and hence attract the wrath of the judges.

When things appear uncertain, it is often rewarding to remind ourselves of certainties, because they can sometimes be overlooked. At the risk of stating the obvious, here are four of them:

Certainty #1

Firstly, we know for certain how the opinion polls have adjusted after last week’s show. To summarise, here is an update of the data posted last week. Only incremental votes post show have been included where possible, and as yet there is no data for (however, I have added a new internet poll, which is rather confusingly called Reality TV Polls.)

And in picture form, the above manifests itself as follows:

Certainties #2 and 3

We also know for certain that 2 of the remaining 11 contestants will come bottom and face the judges. Combine this with the certainty of knowing which contestants are in which judge’s group, then we can deduce, for each possible bottom pairing, which judge it will be to cast the deciding vote on Saturday night. (note – pairings from the same group will be marked as “open”)

Certainty #4

Our final certainty is how the judges received the contestants last time out. To quantify this, for each remark a judge made to a contestant, I have allocated a score of one to three. A score of one represents adulation, two represents less excited remarks, and three represents comments of a non-complementary nature (of which there were surprisingly few).

Putting together certainties 2,3 & 4 gives some clues as to how the deciding judge will vote assuming that the performances on Saturday night are on a par with those last week. For example, if the final two last week had been Ray and Dionne, who would have gone?

Well, the table above shows us that Louis would have had the deciding vote. Of Ray, Louis said “You’ve got a big smile and a great personality, but you’re gonna have to work hard on your voice.” Of Dionne (the very next act), Louis said “I think you’re the best act so far”. On the basis of these two comments a “Louis” score of 3 for Ray and 1 for Dionne has been allocated. And on that basis, if Ray and Dionne make up the bottom two on Saturday, assuming their performances are on a par with last week, then Ray should leave.

Many pairs are too close to call, and these have been left blank, but filling in the gaps that we can gives the following:

The two burning questions at this stage are – 1) How do we fill in the rest of the table above, and allocate likelihoods to each pairing finishing bottom? And 2) How do we adjust this for variance in the quality of performance in acts from last week?

These are two questions that I am going to spend the next couple of days pondering and attempt to answer before the weekend. A kind of “half-certainty” at this stage is that a contestant that performed well last week but badly this week will have more chance of survival than a repeat offender, and that for some contestants the likelihood of performing badly is greater than that of others. But we are now moving from a deterministic world of certainty into a stochastic one.

Suggestions (polite ones only please!) and discussion would be more than welcome!



Anonymous Nick Edwards said...

It is interesting to see you say that you think Louis would have chosen Dionne to stay over Ray. I 100% disagree, DESPITE the fact that he said she gave a better performance.

All 3 of Simon, Sharon and Louis (particularly Simon) have a vested interest in who the final acts are - and not just so that they win for themselves, but to ensure that the show is a success.

Ray has been quite a well-known character throughout the audition process, whereas Dionne has been an unknown quantity - to lose Dionne in week 1 would have been no big loss to the show in the eyes of the judges, but to lose Ray would have.

Louis would have found some excuse like 'Ray has more potential in the long-run' or something along those lines, to ensure Dionne went out and Ray stayed in.

I'm a big fan of Dionne!!

1:37 AM  
Anonymous Nick Edwards said...

Incidentally, that was supposed to be a suggestion in effect... I think you need to take into account the marketability of these acts on the programme. Kerry's disability; Nikkita's mum... other 'storylines' that have developed, because the judges won't want to lose these so early on.

1:39 AM  
Anonymous Alf Garnett's PR Guru said...

Nick - Louis deciding between Ray or Dionne (after her top-rated performance and his dire out of tune dirge about Jacko's pet rat) would always be tough -'cos in fairness we know how much Mr. Walsh likes young male singers - a real heart vs head battle! ;) Nice charts Statman - this is why reality TV betting needs you - some original thought and presentation...keep it up.

9:25 PM  
Blogger Statman said...

Thanks for the comments guys.

Nick - you are absolutely right to evoke discussion about the assumptions behind the model I'm trying to develop. Fortunately, in the next stage you will be able to factor in your subjective opinions using personal inputs to account for the factors such as those you mentioned.

At this stage I'm just trying to use information we know for certain, (this necessarily doesn't mean I personally think Louis would boot out ray over Dionne, as you suggested).

Stay tuned for an update..

11:54 PM  
Anonymous Maloolaboo said...

Like death and taxes there are no certainties but it is the art of gambling that allow us to look at both sides of the coin before the flip. As you are aware, Statman, over at the Forum (Mals Place) I started a similar grid based on last weeks comments. But there are certain assumptions that a gambler has to make and has to make quickly to benefit in the market place. Whilst it is not a certainty, it is reasonable to assume that quite a number of contestants can be removed from the grid thus reducing the number of "blanks". The biggest assumption in Reality shows is that, in general, voters decide who they will support at an early stage in any contest (and they sometimes back accordingly).

Reducing the size of the field is the "art" to which I refer. Supporters committed to a contestant WILL forgive a bad performance but not perhaps several, so its fairly safe to assume that given our knowledge of the polls/voting so far, the likelihood of Ben, Leona, Nikitta etc ever getting near a "decision" this coming Saturday correctly warrants the current "rag" odds.

An exercise that I am currently conducting is the potential effect of a contestant making a complete hash of Live appearance 2, and this throws up some interesting data. For example, Ray can afford to completely mess up his act and still get enough votes from both his supporters AND from sympathy votes to ascend the bottom 2 whereas McDonald Bros will only have to make one small mistake to ensure a bottom 2 place. (more)

Further, the complexity of the inter relationships between the Judges does not allow us a simple assessment either, but on a case-case basis it is perfectly possible to do what you are attempting. I used the illustration of Ray above to demonstrate why he is highly unlikely to be in the bottom 2 but for the sake of argument, lets assume he is up against Dionne, as you suggest….

Louis has the casting vote and despite his public comments, has been known to reverse those in a vote (as have Sharon and Simon in the past). Louis motivations are both personal and professional and he both prefers young boys to black girls on a personal level and has a tendency to support Simon rather than Sharon from a professional survival perspective. His other considerations are “competition” and his own popularity with the public. Sacking Ray would lose him more respect from the UK mums than eliminating Dionne and also Dionne competes for the “black singer” role that his own group, 4 Sure aspires to.

My own view, and I know many others will have other opinions, is that Louis would have rejected Dionne and kept Ray. Which only goes to prove that in Reality, we gamble on opinion.

Keep up the good work, the debate is fascinating.

12:10 AM  
Blogger Statman said...

Your comments as always are insightful and much appreciated Mal.

There are two methods that I am currently working on that will capture the "distance away from the bottom two" of a contestant that you describe. One way is to use Bayesian theory to allocate conditional probability. That way we can capture and use the fact that we know P(Ben makes bottom 2 given he makes a hash of his song) << P(Macdonald Brothers make bottom 2 given they make a hash of their song). Combining this with a probability that each contestant will actually make a hash of their song in the first place can lead us to the probability that they actually do make the bottom 2. The problem I am having at the moment is to easily and intuitively partition the probability space so that readers can “do it themselves”. This involves having to input a value for P(they sang badly given they are in the bottom two) which is not a very intuitive measure. For instance, what would you say the value of this figure would be for Dionne?

The other method is one that can always be relied upon when more elegant and abstract methods prove elusive, and that is brute force simulation. I’m concentrating on this for the time being, and will post something before the show tomorrow night.

7:52 PM  
Anonymous maloolaboo said...

Thanks Statman. Separating the elements of subjective v objective probabilities in a contest like X Factor may not be really all that difficult if we are prepared to rely on the polling evidence. The component parts of the probabilities are personality (likeability), talent, taste and performance and the first of these is interpretive from the poll evidence whether you regard that element as subjective or objective. Viz “Ben is liked” is objectively evidenced from his poll rating. Talent is another objective element about which we have some real and some anecdotal evidence via the polls and judges comments. Taste is a very subjective element and is personal to each viewer and the closest measurement we can ever get is through popularity evidence. The final element of performance is the only variable that is both subjective and immeasurable before the event and only subjectively guessable afterwards.

Where am I going with this?. Well, I believe that we can reasonably accurately assess the elements of likeability and talent through interpreting the polls. Taste, although subjective already forms a significant portion of the poll rating but we must constantly remeasure it through weekly performances. Performance, whilst an important element of the equation is not actually very significant until there are repeated good/bad performances ie Contestants who are in the current top 6 are there because they were at the top even before last weeks live show and some of their performances were indeed dubious.

It is possible, through performance to move UP the scale but those at the top need several bad performances to dislodge their positions. Acts who are at the middle/ bottom of the polls are the ones most vulnerable to bad Live performances. For that reason I discount Ben, Leona, Ray, Eton Road, Nikitta and probably Ashley from losing sufficient support through a bad performance to reach the bottom 2 this week.

Kerry and Robert are almost direct opposites, Kerry is liked, Robert not. Kerry has limited but polished talent, Robert has untamed talent. Kerry’s style appeals to enough people to stay a while yet, Robert’s doesn’t suit everyones taste. Kerry is more likely than Robert to give a good performance. From these 2, Kerry must be favoured to avoid a bottom 4 position (this being a subjective judgement by me).

Dionne, 4 Sure and MacDonalds appear 1. Not to be Liked and/or 2. Have lesser talent and/or 3. Do not appeal to the taste of sufficient public to vote for them.

This assessment infers that all of the 3 above Acts need to give exceptional performances to encourage public support and based on last weeks performances, they have their work cut out for them.

So, where does all this leave us?. The first named 6 are unlikely to lose their heretofore popular support (even with a bad performance) and the bottom 4 must give excellent performances to roust a few votes. NOW we can look at the probabilities of a reduced field and re-measure the 3 variables before applying the 5th element in the guise of Simon/Louis and Sharon. So here is my own take:

It is fortunate this week that each of Dionne, 4Sure, McDs and Robert are all within a few % of each other in the polls (as we know them*), so the live performance will form a large percentage (say 90%) of the voting content (the other 10% being a mixture of Dionnes talent, Roberts tears, 4Sures looks and McD’s groupie vote). In later weeks we may well have to interrelate disparate poll positions with the effects of bad performances and that may require some probability theories, but not this week. If we assume that all 4 of the above got joint bottom votes, then how would the judges vote?

Simon has the casting vote no matter what happens!.

Of Dionne, Simon said: Not the best singer but vocally incredible
Of Robert, Simon said: Fantastic, one of the best we have heard
Of 4Sure, Simon said: Tuning issues, but I like you (had to ask their names)
OfMcD’s, Simon said: Boring, Dull just like painting by numbers

So, whether we use complex mathematics to address the eviction issue or use clear thinking and logical subjective measurement, the conclusion is that Simon’s verdict will eliminate either McDonalds or 4Sure (unless they BOTH give exceptional performances). I would resist the urge to bet if the bottom two are Dionne and Robert.

Sorry, I just realised how long this post is! And I will now answer your question. Dionne’s performance last week was heavily over masked by the proximity of her backing singers and whilst she has talent, she has an untamed voice that puts her at severe risk of a “bad’N”. Her propensity to over sing (and over estimate her own singing ability) doesn’t endear her to the public and her macho stance is sometimes, well, unladylike. With a sub 10% poll rating and a 60% risk of a bad performance, Dionne may well find herself at the bottom again and in need of saving.

*Recent evidence suggests that both Eton Road and Dionne have improved their poll positions.

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3:23 AM  

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