MG/ELO

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MuwuM's Concept of ELO ranking in MG

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.

$R_{team}\leq 2100$	$k_{team}=32*n$
$R_{team}\leq 2400$	$k_{team}=24*n$
$R_{team}>2400$	$k_{team}=16*n$

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:

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

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:

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