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How Marathon Match ratings are calculated
New ratings are calculated as follows:
After each competition, each coder who attended the competition is re-rated according to
the following algorithm. A coder is considered to have attended the event is they make a submission of any kind (example or full). Only registering for the event will not cause the coder to be rated. The average rating of everyone in the competition is calculated:
Where NumCoders is the number of coders in the competition and Rating is the
rating without the volatility of the coder in the competition before the competition.
The competition factor is calculated:
Where Volatility is the volatility of the coder in the competition before the competition.
Win Probability Estimation Algorithm:
Where Rating1 & Vol1 are the rating and volatility of the coder being compared to, and Rating2 & Vol2 are the rating and volatility of the coder whose win probability is being calculated. Erf is the "error function".
The probability of the coder getting a higher score than another coder in the
competition (WPi for i from 1 to NumCoders) is estimated.
The expected rank of the coder is calculated:
The expected performance of the coder is calculated:
Where 
is the inverse of the standard normal function.
The actual performance of each coder is calculated:
Where ARank is the actual rank of the coder in the competition based on score
(1 for first place, NumCoders forlast). If the coder tied with another coder,
the rank is the average of the positions covered by the tied coders.
The performed as rating of the coder is calculated:
The weight of the competition for the coder is calculated:
Where TimesPlayed is the number of times the coder has been rated before.
To stabilize the higher rated members, the Weight of members whose rating is
between 2000 and 2500 is decreased 10% and the Weight of members whose rating
is over 2500 is decreased 20%.
A cap is calculated:
The new volatility of the coder is calculated:
The new rating of the coder is calculated:
If |NewRating - Rating| > Cap the NewRating is adjusted so it is at most Cap different than Rating.
<In some cases, the algorithms above would lead to a decline in rating, even though a competitor has placed (or tied) for the first place position. In this event, the ratings will be run as normally, and subsequently, any competitors tied for first place will then have their ratings adjusted so that: newRating = oldRating + 1 in the event that newRating <= oldRating .
This will not effect the new volatility of the competitors, which will still be calculated as above.
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