QELO = Raw Score * Completeness * Competitiveness * Scaling factor (100)
Raw Score: Your Owns + bonus points(BPs)
Completeness is one of two game level characteristics. A game with 64 out of 64 questions answered correctly is assigned a completeness of 1.0. This number ranges between 0 and 1 and shows the percentage of questions answered in a match.
Competitiveness is the other game level characteristic.
Competitiveness measures the level to which a match’s scores are clustered. The higher the level of clustering, the higher the number. It is a weighted ratio of the 2nd score and 1st score, the 3rd and the 2nd and the 4th and the 3rd.
For a 4 player game
Competitiveness: 0.33*2nd /1st +0.33*3rd/2nd +0.33*4th/3rd
For a 3 player game
Competitiveness: 0.4*2nd /1st +0.4*3rd/2nd
The lack of a fourth competitor reduces the competitiveness in the game by around 20% assuming that a median competitor is in the 4th seat. Therefore the coefficients here add up to 0.8 and not 1.0
For a 2 player game
The lack of two competitors reduces the competitiveness in the game by around 40% assuming that two median competitors are in the 3rd and 4th empty seats. Therefore the coefficient here is 0.6 and not 1.0
Note: We have added a 0.05 constant to the Competitiveness number as an insurance against terribly one sided games resulting in very large coefficients that make the formula useless. From our experience with running the data over the last 3 seasons of FLQL through the QELO system, such games do not occur in leagues that offer something for everyone.