Rating system
Based on the rating system developed by Prof. Árpád Élő
The rating is an integer, the minimum is 0. The starting rate of an unknown player is 0.
Ratings are amended each time you kill someone by adding small amount from your previous rating value. On the other hand, a small amount is subtracted if you've been killed. The amount added or subtracted depends on the ratings of the players.

It is an absolute rating system, i.e. the rating can be used to determine the winning odds of a specific player against another specific player. The system has been worked out according to statistical and probability theory.
Rating differenceProbability of win

The following formula is used:

Rn = Ro + K(W-We)
Rn is the new rating.
Ro the old (pre-event) rating.
K a constant (4 for 0-2099, 3 for 2100-2399, 2 for 2400 and above).
W the outcome: you kill=1; you're killed=0.
We the expected score (Win Expectancy), from the following formula:
We = 1/ (exp10(-dr/1200) + 1)
dr equals the difference in ratings.
This formula has the property that the sum of the rating changes is zero. It turns out that if the rating difference is more then 719 points, then if the strong player kills the weak, there is no change in either rating.

Overall ratings are decreased each day by an amount depending on the current rating.

The following formula is used:
Rn = ( Ro * Ro ) / 125000
Rn is the new rating.
Ro the old (previous day) rating.

Rating Amount subtracted
below 500 1
600 2
800 5
1000 8
1500 18
2000 32

So players with higher rating will see their rating decrease quicker.
A 500 rating will reach zero in approximately 1.5 years without playing.

Series of games
Playing a series of games against the same opponent within a given time interval will adjust the calculation as follows:
The expected score is calculated for the series of games from the pre-match rating-difference of the two players, and the ratings are amended based on the expected score and the actual score of the series of games.
These are basically the extensions of the above calculation for more games played.
However, as more matches will reflect the skill difference more precisely, the amendment is raised based on the number of games played.

Number of games in
a series of games
rating change
1 4
2 10
3 15
4 20
5 24
6 28
7 32
8 35
9 38
10 41
15 50
20 56
infinite 64

In other words the constant K in the above equations is multiplied by a factor of 8*{2-[(9/10)^(n-7)]}, where n is the number of games played.

Note that if you play a 3rd player in between playing the same opponent, it will still be treated as a series of games.

Rating categories:
General of the army
General Above 700
Lieutenant General 600 - 699
Major General 550 - 599
Brigadier General 500 - 549
Colonel 450 - 499
Lieutenant Colonel 400 - 449
Major 350 - 399
Captain 300 - 349
First Lieutenant 250 - 299
Second Lieutenant 200 - 249
Staff Sergeant 150 - 199
Sergeant 100 - 149
Corporal 50 - 99
Private 1st class 0 - 49

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