Calculating freestyle scores

Freestyle scores are based on a cumulative Difficulty model where Presentation, Required Elements, and Deductions can affect the score.

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

Presentation increases or decreases the score by a percentage calculated from the presentation marks (+, ✓, or -).

Deductions take off a percentage for misses, and time and space violations.

Each missed required element will also take off a percentage from the total score.

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

$R = D \times P \times M \times Q$

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 sum of the total points for each skill performed in a routine. Every time a skill is successfully performed, the value of that skill is added to the difficulty score.

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 $d_j$ , where $j$ is the judge number. This means judge 1 is called $d_1$, judge 2 is called $d_2$, etc.) For example:

$\begin{aligned} s_1 &= L(1) \times n_1 \\ s_2 &= L(2) \times n_2 \\ d_1 &= \sum_{n = 1}^{x} = s_1 + s_2 + ... + s_x \end{aligned}$

All difficulty judges’ scores are then averaged together according to the averaging rules, the result is called $D$

Example

A difficulty score will be calculated by multiplying the number of times the athlete(s) completes a skill by the point value of the corresponding skill level. (For example, if an athlete completes 10 level 1 skills, they will get 1.5 points, as $10 \times 0.15 = 1.5$).

Then, the total points for each level are added together to get a total difficulty score for that judge. For example, if an athlete completes 10 level 1 skill, 10 level 2 skills and 10 level 3 skills they will get 7.2 points ($10 \times 0.15 + 10 \times 0.23 + 10 \times 0.34 = 1.5 + 2.3 + 3.4 = 7.2 \text{ points}$).

Presentation

The presentation score may impact the difficulty score by a total factor of $F_p = 60 \% = 0.60$​
Where the Form and Execution category may impact the score by a factor of $F_{p,F} = \frac{1}{2} F_p$,
the Entertainment category may impact the score by a factor of $F_{p,E} = \frac{1}{4} F_p$,
the Musicality category may impact the score by a factor of $F_{p,M} = \frac{1}{4} F_p$

In events where tournament organisers have decided music won’t be used the following factors are used

Form and Execution category may impact the score by a factor of $F_{p,F} = \frac{1}{2} F_p$,
the Entertainment category may impact the score by a factor of $F_{p,E} = \frac{1}{2} F_p$,
the Musicality category may impact the score by a factor of $F_{p,M} = 0$

The total presentation score may be outside $1 \pm F_p$

The scores of each category (Form and Execution, Entertainment, Musicality) for each judge is calculated on a scale from −3 to 3 as $j_F$​, $j_E$​, $j_M$​ by averaging the marks the judge has given in that category where "–" is worth -3, (the amount of negative marks given by a judge for a specific category is called $n_{\text{x,minus}}$​ where $x$ is $F$, $E$ or $M$, for the category) "✓" is worth 0 (despite this, the marks are important as they are part of the average and brings the score closer to the average; the amount of checkmarks given by a judge is called $n_{\text{x,check}}$​) and "+" is worth 3. (the amount of positive marks given by a judge is called $n_{\text{x,plus}}$)

$j_x = \frac{ -3 \times n_{\text{x,minus}} + 0 \times n_{\text{x,check}} + 3 \times n_{\text{x,plus}} }{ n_{\text{x,minus}} + n_{\text{x,check}} + n_{\text{x,plus}} } = \frac{ 3\left(n_{\text{x,plus}} - n_{\text{x,minus}}\right) }{ n_{\text{x,minus}} + n_{\text{x,check}} + n_{\text{x,plus}} }$

The averages of all judges’ scores for each category is then averaged as $a_F$, $a_E$ and $a_M$ by averaging $j_x$​ according to the averaging rules for all judges who judged that category.

To calculate the multiplication factor that will be used to calculate the final score, the averages $a_x$ are multiplied by their respective factor $F_{p,x}$ and added to 1, this is called $P$.

$P = 1 + \left( a_F \times F_{p,F} + a_E \times F_{p,E} + a_M \times F_{p,M} \right)$

Simplified

The Presentation score will be multiplied by the difficulty score, which can raise or lower the total score. The presentation score can impact the routine in a range of $+180\%$ to $-180\%$. The presentation score is broken down into three categories at weights as follows:

• Form/Execution: $50\%$ of the $180\%$
• Entertainment: $25\%$ of the $180\%$
• Musicality: $25\%$ of the $180\%$​

The range of $\pm 180\%$ can in other words be broken down into three ranges of:

• Form/Execution: $\pm 90\%$
• Entertainment: $\pm 45\%$
• Musicality: $\pm 45\%$​​

To calculate the presentation score, the marks of each judge are given a value, with the check being 0, the minus being the negative value of that category and the plus being the positive value of that category. Within each category, the average mark values for all judges are averaged according to the averaging rules. Then the categories are all added together for the final presentation adjustment value.

Deductions

Each deduction (miss, time violation, space violation) may impact the score with a factor of $F_d = 2.5\% = 0.025$​

The average number of misses recorded by the Required Element and Athlete Presentation judges are calculated according to the averaging rules. This average is called $a_m$​ and is rounded to a whole number, the factor $F_d$​ is then multiplied with $a_m$​, the result is called $m$​. ($m = F_d \times \lfloor a_m \rceil$​)

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

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

Simplified

The Required Element judges and Athlete Presentation judges count misses. These are averaged to get the number of misses. Each miss will take 2.5% off the total routine score.

The Required Element judges count some additional deductions which are time and space violations, those are calculated and averaged separately and added to the average amount of misses to determine the final deduction value.

Required elements

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

The average number of missing required elements recorded by the required element judges are calculated and called $a_q$​ this average is rounded to a whole number, the factor $F_q$​ is then multiplied by $a_q$​, the result is called $q$​. ($q = F_q \times \lfloor a_q \rceil$​) (Note that required elements are counted per instance of each required element, not per group of required elements, for example, if the required elements are 4 basic jumps and 4 double unders and the athlete performs 2 basic jumps and 3 double unders this corresponds to $2 + 1 = 3$ missed required elements)

The required elements ($q$) are subtracted from 1 to be converted into a factor, the result is called $Q$ ($Q = 1 - q$​)

Simplified

Each missing execution of a required element contributes a 2.5% deduction. For example, in an individual Single Rope freestyle routine:

	Number required	Number performed	Missing required elements	deduction
Multiples	4	4	0	0
Gymnastics/Power	4	3	1	2.5%
Wraps/Releases	4	1	3	7.5%
Total required element deduction:				10%

Result

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

$R = D \times P \times M \times Q$