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Background

The tournament system mainly used for go in europe and the usa, McMahon, has for example the shortcoming of being based on the rank of the players, which they usually choose themselves. This can lead to misuse, intended or not.

MacMakko

• relies on the EGFs rating system, which provides a more or less reliable criteria for a players strength.
• uses the EGFs rating system itself as the basis for the rating/ranking system, so the basis is broadly accepted and tested

The current, incomplete, version of a tournament management program that implements MacMakko can be found here.

System

Notation

• $k$ : count of iterations for the guido correction with $i\in \{0,1,..\}$
• $i$ : the $i$-th iteration of the guido correction with $i\in \{0,1,..,k\}$
• $c$ : the current round number with $c\in \{1,2,..\}$
• $r$ : round number of a 'currently processed' round with $r\in \{1,2,..,c\}$
• $a_{x},b_{x}$ : ratings of the players $a$ and $b$ at a given time $x$
• $a_{0},b_{0}$ or $a_{s},b_{s}$ : startratings of the players $a$ and $b$, where $a_{0}=a_{0,n}$ for any $n\in \{0,1,..\}$
• $g_{r}(a_{x},b_{x})$ : returns the new EGF-Rating of the player $a$, that is calculated based on the outcome of the game of $a$ against $b$ in round $r$.

therefore are:

• $a_{r,0}$ or $a_{r}$ : the rating of player $a$ after round $r$ and prior to the guido correction,
• $a_{r,i}$ : the rating of the player $a$ after round $r$ and the $i$-th iteration of the guido correcture.

Rating

The rating of a player is calculated through:

• $a_{c,i}\,:={\begin{cases}g_{c}(a_{c-1,k},b_{c-1,k})&{\mbox{if }}i=0\land c>1\\a_{0}+\sum _{r=1}^{c}(\lambda _{r}(a_{c,i-1})-a_{c,i-1})&{\mbox{if }}i>0\end{cases}}$

$b$ is the opponent of player $a$ in the round $r$.

$\lambda$ is a helper function:

• $\lambda _{r}(a_{x,y})\,:={\begin{cases}g_{1}(a_{x,y},b_{x,y})&{\mbox{if }}r=1\\g_{r}(\lambda _{r-1}(a_{x,y}),\lambda _{r-1}(b_{x,y}))&{\mbox{if }}r>1\end{cases}}$

$b$ is the opponent of player $a$ in the round $r$.

In the first case of the rating calculation by $a_{c,i}$, being $i=0$ (qualitatively: prior to correction), the rating simply results from the definition of the EGFs rating calculation.

In the second case, $i>0$, the rating shall be corrected. Only one iteration is defined here, it is to be repeated $k$ times. For this purpose the rating changes in all rounds, resulting from the assumption that the current rating was the start rating, are added to original start rating. These rating changes are calculated with the help of the function $\lambda$. Therefore $a_{c,k}$ is the last evaluated rating for a round for player $a$.

Background for the correction is the thought, that the start rating of the player, and the rating of his opponent, may not be, or can't be, correct. Instead the last evaluated rating is theoretically nearest to the real strength of the player.

If, for example a player wins a round against an equally strong player we may assume that he is the stronger of the two. If he really is stronger he shouldnt get too much of a boost in his rating; thus the last evaluated rating is assumed to be his strength... wich results finally in the player ranking a bit lower, and his opponent a bit higher, than without the correction.