Calculation of scores and results

The goal of this chapter is to be easily understood by the wider community of our sport as well as being clear and accurate as to leave no questions on how the calculations will be implemented. To meet both goals, some sections will be accompanied by an expansion panel containing examples and simplified explanations using less math formulas.

Averaging

If there are two judges of a type the two scores are averaged.

Example

Judge	Score
Judge 1	112
Judge 2	114

Gives an average of $\frac{112 + 114}{2} = 113$

If there are three judges of a type the two closest scores are averaged, if the scores are equally spaced the benefit goes to the athlete and the two higher scores are averaged.

Example

Judge	Score
Judge 1	112
Judge 2	114
Judge 3	118

Since judges 1 and 2 are closer (2 clicks) than judges 2 and 3 (4 clicks), scores from judges 1 and 2 are averaged for a total score of 113.

A similar situation:

Judge	Score
Judge 1	112
Judge 2	115
Judge 3	118

Since judges 1 and 2 are apart by 3 clicks and judges 2 and 3 are also apart by 3 clicks, the higher pair of scores (judges 2 and 3) are used. Those two scores are averaged for a score of 116.5.

If there are four or more judges of a type the highest and lowest scores are dropped, and the remaining scores are averaged.

$$\frac{\text{Judge}_1 + \text{Judge}_2 + \text{Judge}_3 + \text{Judge}_4 - \text{Judge}_{max} - \text{Judge}_{min}}{4 - 2}$$

Example

Judge	Score
Judge 1	112
Judge 2	115
Judge 3	118
Judge 4	119
Judge 4	121

Judge 1 and Judge 5 who has the lowest and highest scores are dropped leaving judge 2, 3 and 4 which are then averaged $\frac{115 + 118 + 119}{3} = 117.33$

Rounding

All variables are calculated without applied roudning, except for Capital Letter Variables and functions (duch as $R$, $D$, $P$, $M$, $F_p$, $L(x)$) which is roundee to two decimal places

Example, If the variable is $R$, then $R = \frac{\lfloor R * 100 \rceil}{100}$