Calculating Single Rope freestyle scores

Single Rope freestyle scores are based on a cumulative difficulty model where presentation, required elements, and deductions can affect the score.

Difficulty ($D$) is calculated by adding the points from each skill performed. There is no limit on the total difficulty score.

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

Required elements ($Q$) will take off a percentage from the total score.

Deductions ($M$) take off a percentage for misses, breaks, 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 ($P$), the required elements score ($Q$), and the deduction score ($M$). The result cannot be lower than 0.

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

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

Difficulty

There is no maximum difficulty score. The difficulty score is the average of the sum 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 $L\left(x\right) = 0.1 \times 1.5^x$ rounded to two decimal places. However, a level 0 skill is always worth 0 points.

Example

The point values per level 0-8 skill are:

Level	0	0.5	1	2	3	4	5	6	7	8
Points per skill	0.00	0.12	0.15	0.23	0.34	0.51	0.76	1.14	1.71	2.56

The score of every difficulty judge is calculated by multiplying the amount of skills recorded at that level by that judge (called $n_x$, where $x$ is the level) with $L\left(x\right)$ for each level, and adding the results (called $s_x$) for each level together, (the resulting sum is called $d_{t,j}$ , where $j$ is the judge number and $t$ is the judge type, P, M, or R. This means multiples judge 1 is called $d_M,1$, rope manipulation judge 2 is called $d_R,2$, etc.)

Example

$$\begin{aligned} s_1 &= L(1) \times n_1 \\ s_2 &= L(2) \times n_2 \\ d_{M,1} &= \sum_{n = 1}^{x} = s_1 + s_2 + ... + s_x \end{aligned}$$

All difficulty judge' scores for each type of difficulty judge are then averaged together according to the averaging rules, the result for each judge type is called $d_t$ where $t$ is the judge type, P, M, or R.

After this, $d_P$, $D_M$, and $d_R$ is averaged together to get the difficulty result $D$:

$$D = \frac{d_P + d_M + d_R}{3}$$

Presentation

The presentation score may impact the difficulty score by a total factor of $F_p = 60 \% = 0.60$​

The scores from the first step for each of the five categories (Musicality, Form/Execution, Creativity, Entertainment, and Variety/Repetitiveness) are collected from each judge and for each category the number of plus marks (called $n_{t,j,\text{plus}}$) is added to 12 after which the number of minus marks (called $n_{t,j,\text{minus}}$) and misses recorded by that judge (called $m_{j}$) are subtracted, the result (called $j_{t,j}$ where $j$ is the judge number and $t$ is the category) is rounded to an integer larger or equal to 0 and smaller or equal to 24. For example:

$$\begin{aligned} j_{M,1} &= \begin{cases} 0 & 12 + n_{M,1,\text{plus}} - n_{M,1,\text{minus}} - m_{j} \le 0 \\ 24 & 12 + n_{M,1,\text{plus}} - n_{M,1,\text{minus}} - m_{j} \ge 24 \\ \lfloor n_{M,1,\text{plus}} - n_{M,1,\text{minus}} - m_{j} \rceil & \text{otherwise} \end{cases} \end{aligned}$$

After this, the number of (integer) steps the judge want to adjust the preliminary category score (called $a_{t,j}$ which is a positive or negative integer) is added to $j_{t,j}$ and clamped again. The result of this is called $p_{t,j}$. For example:

$$\begin{aligned} p_{M,1} &= \begin{cases} 0 & j_{M,1} + a_{M,1} \le 0 \\ 24 & j_{M,1} + a_{M,1} \ge 24 \\ \lfloor j_{M,1} + a_{M,1} \rceil & \text{otherwise} \end{cases} \end{aligned}$$

Each of the category scores are then multiplied by the following factors and summed together for each judge to get a total score between 0 and 24, the result of which is called $p_{j}$.

• Entertainment: $0.25$
• Form/Execution: $0.25$
• Musicality: $0.20$
• Creativity: $0.15$
• Variety/Repetitiveness: $0.15$

All the judges' $p$ scores are then averaged according to the averaging rules and scaled to a number between $0$ and $2F_p$ by multiplying it by $\frac{2F_p}{24} = 0.05$, the result is the final presentation score called $P$.

Required elements

Each missed required element may impact the score by a factor of $F_q = 2.5\% = 0.025$

For each difficulty judge, the number of missing required elements for their judge type is calculated by subtracting the number of skills performed at a level 3 or higher (called $n_{3+}$), and 0.5 times the number of skills performed at a level 2 or lower (called $n_{2-}$) from the number of required elements for that judge type (called $N_{q,t}$ where $t$ is the judge type), with a minimum result of 0. This number is called $a_{q,t}$ where $t$ is the judge type, P, M, or R. For example

$$a_{q,M} = min\left( N_{q,M} - n_{3+} - 0.5n_{2-}, 0 \right)$$

For competition events with pairs interactions, the number of missing required elements are calculated by subtraction the number of marks recorded by each technical judge (with difficulty level playing no part) (called $n$) from the number of required pairs interactions (called $N_{q,t}$ where $t$ is I for interactions), with a minimum of 0. The number is called $a_{q,t}$ where $t$ is the required element type: I. For example

$$a_{q,I} = min\left( N_{q,I} - n, 0 \right)$$

For each judge type/required element, the $a_{q,t}$ scores are then averaged according to the averaging rules, and rounded to a whole number. The result is called $q_t$.

All the q-scores are summed and multiplied by $F_q$, the result of which is subtracted from 1 to be converted into a factor, the result is called $Q$ ($Q = 1 - F_q \times \left( q_{M} + q_{P} + q_{R} \right)$ or $Q = 1 - F_q \times \left( q_{M} + q_{P} + q_{R} + q_{I} \right)$).

Deductions

Time and space violations will impact the score by a factor of $F_v = 5\% = 0.05$​ each.
Breaks will impact the score by a factor of $F_b = 5\% = 0.05$.
The first miss will impact the score by a factor of $F_{m,1} = 5\% = 0.05$, the second miss by a factor of $F_{m,2} = 7.5\% = 0.075$ and the third miss and onward will impact the score by a factor of $F_{m} = 10\% = 0.1$.

The average number of misses recorded by all judges counting misses are calculated according to the averaging rules. This average is called $a_m$​ and is rounded to a whole number. $a_m$ is then turned into the miss score $m$ as follows: if $a_m$ is 0 then $m$ is $0$, if $a_m = 1$ then $m = F_{m,1}$, if $a_m = 2$ then $m = F_{m,1} + F_{m,2}$, if $a_m > 2$ then $m = F_{m,1} + F_{m,2} + (a_m - 2)\times F_{m}$​.

Or, in one formula:

$$\begin{aligned} m = &\left( F_{m,1} \times max\left( a_m, 1 \right) \right) \\ &+ \left( F_{m,2} \times clamp\left( a_m - 1, 0, 1 \right) \right) \\ &+ \left( F_{m} \times min\left( a_m - 2, 0 \right) \right) \end{aligned}$$

The average number of breaks are calculated and called $a_b$​ this average is also rounded to a whole number, the factor $F_b$​ is then multiplied with $a_b$​, the result is called $b$​. ($b = F_b \times \lfloor a_b \rceil$​)

The average number of additional violations (time and space) are calculated and called $a_v$​ this average is also rounded to a whole number, the factor $F_v$​ is then multiplied with $a_v$​, the result is called $v$​. ($v = F_v \times \lfloor a_v \rceil$​)

The misses ($m$), breaks ($b$) and violations ($v$) are summed together and subtracted from 1, the result is called $M$ and cannot be lower than 0. ($M = 1 - \left( m + b + v \right)$)

Result

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

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