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I was put in charge of coming up with a normalization/scaling scheme for a competition in which competitors are scored 0-100 by 6 judges and then the high and the low are dropped before the cumulative score is calculated. In past years we have found scores from judge to judge are not consistent on an average and range basis and thus the request to implement some sort of normalization.

My first instinct was to go with a straight normalization to z-scores and then re-scale those to an arbitrary mean and standard deviation. A colleague of mine suggested the following equation:

[("normalized score") = (raw - low)/(high - low) * X ] where X is the arbitrary top score (i.e. top score is converted to 100 if X=100) and the lowest raw score would convert to 0.

I'm struggling with determining which would be the better way to go about this as well as explaining one vs the other to the executive board of the competition.

Do you guys have insight as to the differences/pros/cons to each method?

Thanks for all your help

bigredhockey