The first judge is far more generous in scoring than the second judge, who gives much lower scores. If your application was rated by the first judge, it would earn a much higher total score than if it was assigned to the second judge.
We have a way to address this issue. We ensure that no matter which judges are assigned to you, each application will be treated fairly. To do this, we utilize a mathematical technique relying on two measures of distribution, the mean and the standard deviation.
The mean takes all the scores assigned by a judge, adds them up, and divides them by the number of scores assigned, giving an average score.
Formally, we denote the mean like this:
The standard deviation measures the “spread” of a judge’s scores. As an example, imagine that two judges both give the same mean (average) score, but one gives many zeros and fives, while the other gives more ones and fours. It wouldn't be fair, if we didn’t consider this difference.
Formally, we denote the standard deviation like this:
To ensure that the judging process is fair, we rescale all the scores to match the judging population. In order to do this, we measure the mean and the standard deviation of all scores across all judges. Then, we change the mean score and the standard deviation of each judge to reflect the range of typical distributions.
We rescale the standard deviation like this:
Then, we rescale mean like this:
Basically, we are finding the difference between both distributions for a single judge and those for all of the judges combined, then adjusting each score so that no one is treated unfairly according to which judges they are assigned.
If we apply this rescaling process to the same two judges in the example above, we can see the outcome of the final resolved scores. They appear more similar, because they are now aligned with typical distributions across the total judging population.
