### The Starting Round

There will be times when the points awarded will differ from what you might think they should be. Here we'll explain an important difference between the Starting Round from a Points point of view and the Starting Round as it is physically implemented on the day of the competition.

### Example

Let's say Level 2 Freestyle started with 34 couples, this is closer to the 'ideal' quantity of 24 for a quarter-final than it is to the 'ideal' quantity of 48 for a pre-quarter-final.

We could run this category from a quarter-final with 4 heats of 9, 9, 8, 8 couples respectively. However we sometimes like to have fewer couples on the floor to give them better exposure to the audience and judges and to keep the attrition rate at or below 50%.

So physically we can run this like an incomplete pre-quarter-final but from a points point of view in terms of number of competition couples it is more like a quarter-final.

### DWAS

In the case of DWAS we often have Sash Dancers to make up for any imbalance between leads and follows.

It is possible that the follows have a different Points Starting Round from the that of the leads however both would begin at the same physical round with Sash Dancers making up the difference.

For a deeper explanation have a look below. At the very end is a mathematical approach with an equation that allows to calculate the Points Starting Round.

### Competition Rounds

A standard competition comprises one or more stages or rounds. There will always be at least one round - the final round - called the Final. Then if numbers are sufficient there will be Semi-finals, Quarter-finals, Pre-quarters-finals and preliminary rounds and so on.

Each competition round is made up of one or more heats. The final always has just the one heat and then in theory a semi-final has two heats (semi meaning "half"), a quarter-final has four (quarter meaning "four") and so on.

Notation used:

 F = Final SF = Semi Final QF = Quarter Final PQF = Pre-quarter Final

Most Modern Jive competitions have 6 couples (or triples) in the final. In the case of Dance With a Stranger (DWAS) there are two competitions being run side by side within the same heat, so the final of DWAS has 6 individuals of each role in the final. We have 6 because any more then it's harder for the audience to watch a final with too many couples and also because the final then becomes too diluted and it's not such a great experience for the competitors.

Notation:

 6 = Heat of 6 competitors 8 = Heat of 8 competitors

### Example

If a final has 6 couples then each preceding round would have twice that number as shown in the table below.

PQFQFSFF
 66666666 or 888888

6

6

6

6

6

6

6

4824126

Once we get to 8 heats of 6 couples we may be inclined to have 6 heats of 8 couples to save time (other options include running a split floor).

So the earlier the round a category starts the greater the achievement to progress to the final and then place. This is why the MJPI has Progression points.

### The Competitors' Perspective - Attrition Rate

In the ideal situation of starting with 48, 24 or 12 entries, 50% of the entries do not make it through to the next round so the attrition rate is 50%. But what if the numbers are different?

Round ARound BAttrition Rate
482450%
241250%
12650%
481275%
322425%
321262.5%
161225%
16662.5%

An attrition rate greater than 50% tends to be bad news, it's like a mass sacking, it's brutal and heavy-handed especially where competitors have put in hours of practice. Even if there is a repechage, the fact remains that in going from one round to the next over half the entries do not get through.

Attrition RateCompetitors' Face
> 50%
= 50%
< 50%

### Which Categories / Tiers?

As you may have picked up, a key factor is how much time and resources competitors put into preparing for their categories. Freestyle is a Tier 1 category where couples comprise a fixed partnership and is the one that competitors (usually) put in the most preparation.

Other categories require less investment and so competitors are more accepting of a greater than 50% attrition rate. For example, Lucky Dip would be more likely to go from 4 heats of 7 or 8 down to 2 semi-finals.

### Theory vs Practice

The real world seldom adheres to the ideal world, and we rarely get the number of entries in a cateory being either 6, 12, 24 or 48. We've seen how an attrition rate of more than 50% does not go down well with the competitors so how do we treat the numbers in between?

### Example 1

If we had 17 entries, is that closer to a semi-final or quarter-final?

17 is closer to 12 than it is to 24 implying that based solely on the total number of entries then we should consider the Starting Round as being a Semi-Final.

SFF

9

8

6

176
76%
QFSFF

6

6

5

6

6

6

17126
29% 50%

Looking at the attrition rate then it would be better to have the Starting Round at the Quarter-Final.

There are TWO different Starting Rounds

1. The Points System Starting Round.
2. The Physical Starting Round.

So in the preceding example the Points awarded would come the column headed "Semis" (see earning points) even though the actual category would start at the Quarter-Finals.

### Example 2 - Chch Champs 2018

Level 2 Freestyle had 34 entries, looking at the Points System, 34 is closer to being a Quarter-Final than a Pre-Quarter-Final.

 Standard round starts at: Last round you danced Pre-quarters Quarters Semis Finals Pre-quarters 10 - - - Quarters 20 10 - - Semis 35 20 10 - Finals - no placing 55 35 20 10 3rd Place 85 60 40 25 2nd Place 90 65 45 30 1st Place 100 75 55 40

Physically, this category started with Pre-Quarter-Finals on the day (there was also a repechage).

QFSFF

9

9

8

8

6

6

6

34126
65% 50%
PQFQFSFF

7

7

7

7

6

6

6

6

6

6

6

6

3424126
29% 50%50%

If we had more than 6 entries in the semi-final heats (e.g. 2 heats of 7) to even out the attrition rate we would still be left with two attrition rates > 50% (59% and 57% going from Quarters to Semis and Semis to Finals respectively).

### By The Numbers

Finally, if you've made this far then you may be thinking at what point does the number of competitors change the Starting Round from Semi-Final to Quarter-Final and Quarter-Final to Pre-Quarter-Final?

Here we go:

 C = Number of Competitors a = Attrition Rate s = Success Rate = (1 - a) r = Number of Rounds excluding the Final F = Number of Finalists

A fraction (s) of competitors succeed in going through to the next round. So the number of Finalists (F) remaining from an original pool of Competitors (C) going through a number of rounds (r) with a success rate of (s) is given by:

F = C x a^r

The number of Competitors at the start of a competition is therefore:

C = F / (a^r)

For many Modern Jive competitions F = 6 and our preferred Attrition Rate is 50% and so the Success Rate s = 0.5.

C = 6 / (0.5^r) which can be written as, C = 6 x 2^r

r3 (PQF)2 (QF)1 (SF)0 (F)
C4824126

To get the maximum number of competitors for each round we can see what the number would be for half round values. This is a better indicator than just taking the average because there is a power relationship between the number of competitors in each round.

r3.52.51.50.5
C6834178

This also tells us that we shouldn't have more than 8 entries in a final.

For interest we can determine the attrition / success rate from the number of rounds and number of competitors:

s in terms of C, F and r,

s = (F/C) ^ (1/r) or, root(r)(F/C)

a = 1 - s = 1 - (F/C) ^ (1/r) or, 1 - root(r)(F/C)

### Calculating the Points Starting Round

Right from the start we wanted to know what the starting round r should be for a given number of competitors, finalists and rate of attrition / success.

r = ln(F/C) / ln(s) = ln(C/F) / ln(1/s)

If F = 6 and s = 0.5 then this can be written as:

r = ln(C/6) / ln(1/0.5)

r = ln(C/6) / ln(2), for all C >= 6.

If C < 6 then r = 0 as we can't have a negative number of rounds (well we can in theory just like we have fractional rounds but we wouldn't or couldn't have them in practice.

### Was All This Necessary?

This may seem overly complicated at first but hopefully what it does achieve is a sense of finality in that can this be analysed or taken further? By providing a nice mathematical approach (which even includes logs - and you can't argue with logs) then it shows that this whole problem / challenge has been thought out thoroughly as our dancers have come to expect of us.