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  1. 2014.12.22 [개발/랭킹] The AQB Ratings System Formulae


The AQB Ratings System Formulae 




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The AQB Ratings System Formulae 

The ratings system uses the formulae presented below to calculate the new rating for both teams after each game. The parameter values are also given, and are currently the same for all sports.


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For games that are non-drawn (non-tied):

Rn = Ro + R * (B + H + D * K)

Where:

Rn is the teams new rating

Ro is the teams old rating

R is the result variable:

R = +1 if the team won
R = -1 if the team lost

B is the base ratings change for any result:

B = 20

H is the home advantage variable:

H = -4 if the home team wins
H = 4 if the away team wins
H = 0 for a game played on neutral ground

D is the difference in ratings of the two teams, as follows:

D = Ro of losing team - Ro of winning team

K is the weighting applied to the ratings difference:

K = 0.05



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For games that are drawn (tied):

Rn = Ro + Rd * (B + H + Dd * K)

Where:

Rd is the result variable:

Rd = 0.25 if the team was the lower rated before the game
Rd = -0.25 if the team was the higher rated before the game
Rd = 0 if both teams had the same rating before the game

Dd is the difference in ratings of the two teams, as follows:

Dd = Ro of higher rated team - Ro of lower rated team



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The following general rules also apply:

A winning teams rating will never decrease. A losing teams rating will never increase. 
In the case of a drawn (tied) result, the lower rated team will never gain a higher home-advantage-adjusted rating as a result of the game. If this would happen, both teams final home-advantage-adjusted rating (Rn) is equal to the average of the two home-advantage-adjusted ratings before the game. 
The base rating for all teams is generally 1000. Exceptions are listed in the database notes for each rating. 
Any specific alterations to the above rating system are listed in the database notes for each rating. 


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The AQB (Active, Quality-Based) Rating System uses historical data to assign relative performance ratings to each team in the chosen sport. The base for the rating system is the first game in that sport, and ratings begin from that date. Ratings are recalculated after every game using the ratings function, and the new ratings are used for that teams next game.

The ratings function is a linear function represented as follows:

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The home-advantage-adjusted ratings differential is the difference between the rating of the winning team and the rating of the losing team, adjusted for home advantage. The ratings change is the increase [decrease] in the winning [losing] team's rating.

This means that if the winning team's home-advantage-adjusted rating is 320 or more greater than the losing team, the two teams' ratings will not change; if the ratings are equal the winning team's rating will increase by 20 (and the losing team's rating will decrease by 20).

Posted by SB패밀리