Originally Posted by Sallyforth:
“Maths ain't my strong point so please be gentle...but I see no need to have scores (or votes) converted into points, merely placings.
Even if two or more couples are tied (and even if ties occur in more than one place on the board) what is the likelihood of the public vote in isolation producing any ties as well? Surely then the aggregate of judge and public placings should result in overall rankings without any ties at the bottom, aside from some astoundingly unlikely fluke? (or am I missing something)??? And if it did then it could surely be agreed in advance what method of splitting them?”
Well, you're absolutely right that placings are at the heart of the system, and, if you didn't have to combine a public vote with the judges placings there wouldn't be any need for "points".
But when there
is a public vote to consider, you need to convert the judges' placings and the public placings into "points" in order to be able to aggregate them. And this would be totally straightforward, in the absence of tied judges' scores (you're right, the public vote is highly unlikely to yield a public tie - though the program-makers will no doubt (?!) have plans for this contingency).
Of course, all too often we
do get tied judges'scores, so we need to know how to allocate points in a manner which is fair -
and which preserves the power of the judges' scores.
I'll illustrate two possibilities using an extreme example. Suppose that on Saturday, nine of the ten couples got judges' scores of 30, and the other one got 16 (naming no names!). You could organise the judges' points as follows:
10, 10, 10, 10, 10, 10, 10, 10, 10, 1
or
10, 10, 10, 10, 10, 10, 10, 10, 10, 9
Now, in the first example, the range of judges' points is the full 10, while the second example is 2. Don't forget that the points represent
placings, so in the second example we've reduced the number of placings to 2. I hope you can recognise that this has reduced the power of the judges by a factor of 5, and the result of the aggregation of judges' and public scores will be
almost totally biased in favour of the public.
And all because of tied judges' scores.
Unfortunately, it is the second method which is currently being used (because it's a hangover from when there were dance-offs - but that's another story). They should be using the first method, of course.
I mentioned the DWTS methods, and these don't have the concept of placings, just using the judges' scores and public votes. This sounds great in principle, but only if the judges' marks are as widely differentiated as they should be (i.e. using the full range from 4 to 40). And of course, they're not, and this effectively ends up with reduced judges' influence over the end result, and so would be a recipe for
disahster!
By the way, in the event of a tie
after aggregating judges' and public points (i.e. placings), the public vote wins the day.