Calculating Double Dutch freestyle scores

Double Dutch freestyle scores are based on an average routine difficulty level where presentation, required elements, and deductions can affect the score.

Difficult ($D$) is calculated as two separate components, the jumper difficulty and the turner difficulty. The turner difficulty is the average skill level of the 20 most difficult turner skills of the routine. The jumper difficulty is the average difficulty of all the skill sequences in the routine. These are added together with a little higher weight given to the jumper score.

Presentation ($P$) increases the score by a percentage of the difficulty score calculated from the presentation marks (+, and -).

Deductions ($M$) take off a percentage for misses, and time and space violations.

The result/routine score (called $R$) is obtained by multiplying the difficulty score ($D$) with the presentation score plus 1 ($P$), and the deduction score ($M$). The result cannot be lower than 0.

$$R = D \times (1 + P) \times M$$

The calculation for each of these scores is described in the following sections.

Difficulty

The difficulty score is the average of the average of skills per difficulty judge type.

The points per level can be calculated with the following formulas where $x$ is the level of the skill $L\left(x\right) = 1.5^x$ rounded to two decimal places.¹ However, a level 0 skill is always worth 0 points.

A "plus"-level (such as level 3+) is calculated as the level plus 0.5 (for example $L\left(3 + 0.5\right) = L\left(3.5\right)$), whereas a "minus"-level is calculated as the level minus 0.25 (for example $L\left(3 -0.25\right) = L\left(2.75\right)$).

Jumper Difficulty

The score for each Jumper Difficulty judge is calculated by first converting all plus- and minus-level marks into their numeric representation (for example, Level 3+ becomes level 3.5, level 2- becomes level 1.75, etc.). Break marks are counted as level 0 marks.

The amount of marks for each level (0, 0.75, 1, 1.5, 1.75, 2, 2.5, etc., called $n_x$, where $x$ is the level) is then multiplied by $L\left(x\right)$. The sum of all the points per level is then divided by the total number of marks to get the average difficulty level, called $d_{J,j}$ where $j$ is the judge number.

All the Jumper Difficulty judges' scores are then averaged together according to the averaging rules, the result is called $D_J$.

Turner Difficulty

The score for each Turner Difficulty judge is calculated by first converting all plus- and minus-level marks into their numeric representation (for example, Level 3+ becomes level 3.5, level 2- becomes level 1.75, etc.), then all the level marks are ordered from highest to lowest level, and the highest 20 marks are taken into consideration for the next step. If there are less than 20 marks the list of marks are filled with Break (Level 0) marks until there are 20 level marks.

Each of these 20 marks are then converted into their point value using $L\left(x\right)$, their point value is summed together and divided by 20 to get the average difficulty level, called $d_{T,j}$ where $j$ is the judge number.

Example

Given these marks:

1. 1
2. 1
3. 2
4. 2+ = 2.5
5. 3
6. 2- = 1.75
7. 3
8. 3
9. 5
10. 5+ = 5.5
11. 5+ = 5.5
12. 4- = 3.75
13. 3
14. 3+ = 3.5
15. 4- = 3.75
16. 3
17. 3
18. 4- = 3.75
19. 3
20. 3
21. 4
22. 3
23. 4

They would be ordered and converted into points as follows, with the lower marks beyond the highest 20 removed

1. 5.5 = 9.3
2. 5.5 = 9.3
3. 5 = 7.6
4. 4 = 5.06
5. 4 = 5.06
6. 3.75 = 4.57
7. 3.75 = 4.57
8. 3.75 = 4.57
9. 3.5 = 4.13
10. 3 = 3.38
11. 3 = 3.38
12. 3 = 3.38
13. 3 = 3.38
14. 3 = 3.38
15. 3 = 3.38
16. 3 = 3.38
17. 3 = 3.38
18. 3 = 3.38
19. 2.5 = 2.76
20. 2 = 2.25

Which would then be averaged into a score of 4.48

All the Turner Difficulty judges' scores are then averaged together according to the averaging rules, the result is called $D_T$.

Total Difficulty

With the aim of making the jumper score have an impact of 35 % of the total score, and the turner score have an impact of 25 % of the total score, the jumper difficulty score $D_S$ is multiplied by a factor of $\frac{35}{25} = 1.4$ before the turner difficulty score and the jumper difficulty scores are summed together to get the difficulty result $D$:

$$D = (D_J * 1.4) + D_T$$

Because of the averaging, the total difficulty score is between 0 and $L\left(5.5\right) + \left(1.4 \times L\left(5.5\right)\right) = 22.32$

Presentation

The presentation score is calculated in the same way as the Single Rope Presentation score, but with the factor the presentation score may impact the score being $F_p = 40 \% = 0.40$, which means the scaling factor to get the final score is $\frac{2F_p}{24} = 0.03\overline{3}$

Deductions

The deductions score is calculated similar to the Single Rope Deduction score with that no deduction is given for breaks.

Result

The result/routine score (called $R$) is obtained by multiplying the difficulty score ($D$) with the presentation score plus 1 ($P$), and the deduction score ($M$). The result cannot be lower than 0.

$$R = D \times (1 + P) \times M$$

Footnotes

1. Note that compared to Single Rope the points per level is not multiplied by $0.1$. ↩