Country rankings are based on an aggregation of the TopCoder members within a particular
country that have competed within the last 180 days, in other words, those that are "active".
The formula below has the property that if all the coders from a particular country have
the same rating, then that country's rating would be the same as the individual ratings.
When coder ratings differ, the country rating is based mostly on the top rated coders.
The intent is to provide a better way to rank countries than a simple average.
When generating the country rankings we take the individual ratings for active coders
from a particular country, sorted in decreasing order. These ratings are given
by rating_{1} ... rating_{M}, where M is the total number
of active coders from a country.
Where:
M is the number of active coders from a particular country
i is a 1 based index of active coders from a
particular country when sorted by rating in descending order, in other words,
their rank within their country
rating_{i }is the rating of the coder
with index i
R is a constant that will dictate the weighting of the different ranks
One may determine the weighting (R) using the
following equation.
Where X is the fraction of a country's rating
that will be based on the top K coders within that country.
We have chosen an R of .87, this means that
the top 10 coders contribute about 75% of a country's rating.
