Ok, there's been a change to the format (due to their being too much of a spread of points when the category is bunched up). Rather than equalise the scores on the category by the range (max-min), instead, it'll be done as a % of the max score in that category. It seems a bit fairer, there'll be less 0s, and it's got one less set of calculations. :D
(I highlighted the main change in red):
CCC - Categorized Chimp Challenge
All teams compete in a number of categories (performance measures). Lets assume there are three categories and let's call them CAT1, CAT2 and CAT3.
At the end of the competition, each team gets their scores in all categories, and the team with the best overall performance is crowned "King of the Chimps" and receives this year's jaded monkey.
I will now explain how to come up with that "overall performance". Let's work on a 4-Team example:
CAT1 CAT2 CAT3
Team A: 140 Team A: 50 Team A: 30
Team B: 60 Team B: 70 Team B: 60
Team C: 100 Team C: 90 Team C: 10
Team D: 80 Team D: 80 Team D: 40
At this point, the scale of scores in each category is completely different, and this poses a serious concern when you want to put them together in a single score by adding them. For example, in CAT1, Team A has an 80 point advantage over Team B and this spread is impossible to close whatever no matter how well Team B does in other categories.
To remedy this, we will bring all categories to the same scale from 0 (zero) to 100, such that the best team in each category will receive a 100, and the other teams' scores will be scaled accordingly. This way, no single category will have a dominance in the overall score and the categories will be completely balanced.
To this end, first, determine the maximum score within each category:
CAT1 CAT2 CAT3
MAX. 140. 90. 60
Let's call these values MAX1, MAX2, MAX3.
Then, multiply the scores in CAT1 by 100/MAX1, scores in CAT2 by 100/MAX2, and scores in CAT3 by 100/MAX3. This is what you get:
CAT1 CAT2 CAT3
Team A: 100 . Team A: 55.6 Team A: 50
Team B: 42.9 Team B: 77.8 Team B: 100
Team C: 71.4 Team C: 100 Team C: 16.7
Team D: 57.1 Team D: 88.9 Team D: 66.7
The scores can easily be interpreted as "given the best team is 100, how well Team X did in this category". A score of 50, for example means that that team did exactly half as well as the best team.
As a final step, all you have to do is sum up the scores for each team:
Team A: 205.6
Team B: 220.7
Team C: 188.1
Team D: 212.7
Team B wins.
To summarize, what this system does is adjusting the category scores such that each category is between zero and 100. Let's call this adjusted categories ACAT1, ACAT2, and ACAT3.
For a shorthand notation, I will use ACATi, CATi and MAXi for category i, and ACATij, CATij for Team j's scores in category i. Finally, let's call Team j's final score, SCOREj.
The formula can be written as:
SCOREj = ACAT1j + ACAT2j + ACAT3j
ACATij = CATij x 100 / MAXi