# MG/ELO

## MuwuM's Concept of ELO ranking in MG[edit]

Every (human) player starts with an ELO ranking of 1000. Winning will increase and loosing decrease a players ELO. CPU-Players have fixed/static ELO ranking:

CPU (Easy) | 400 |

CPU | 600 |

CPU (Ultra) | 800 |

CPU (Mega) | 1000 |

On each match a ranking for each team is calculated:

$ R_{team} = Round(\sqrt{\frac{\sum_{i=1}^{n} R_i^2}{n^2}}*2) $

Where $ R_{team} $ is the ranking of the team, $ n $ is the number of players of the largest team (if one team has 2 players and the other team 3 it is 3), $ i $ is the index of the player of the team (1 is the first player of the team) , and $ R_i $ is the ranking of the player $ i $, if no player is found at the team with the position $ i $ use $ R_i = 0 $.

Afterwards a $ k $-factor for the team is calculated.

$ R_{team} \le 2100 $ | $ k_{team} = 32*n $ |

$ R_{team} \le 2400 $ | $ k_{team} = 24*n $ |

$ R_{team} > 2400 $ | $ k_{team} = 16*n $ |

based on the $ k $-factor for the team the $ k $-factor of each player is calculated:

$ k_{player} = Round(\frac{k_{team}*R_{player}}{\sum_{i=1}^{n} R_i}) $

Now the ELO-difference between the teams is calculated:

$ Diff_{team} = max( min( R_{enemy team} - R_{team}; 400);-400) $

Now the expected score is calculated:

$ E_{team} = \frac{1}{1 + 10^{Diff_{team}/400}} $

Now set $ S_{team} = 1 $ for the winning team and $ S_{team} = 0 $ for the loosing team

And finally the ranking of each player is changed:

$ R'_{player} = R_{player} + Round( k_{player} * ( S_{team} - E_{team} ) ) $