# Rating System

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### Nath Krismaratala

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Nov 29, 2005, 2:56:53 AM11/29/05
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I'm looking for a rating system for Riichi Mahjong. I guess something
like http://www.daimi.au.dk/~mahjong/system.html (I can't read Danish)

If you have any suggestion (or a translation) , you would make me
happy.

Best regards,
Nath

### Tina Christensen

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Nov 29, 2005, 3:38:25 AM11/29/05
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That's the rating system of Mahjong Denmark.
It's described on our English website: http://uk.mahjong.dk/rating/

Tina Christensen

### Nath Krismaratala

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Nov 29, 2005, 10:31:00 AM11/29/05
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> It's described on our English website: http://uk.mahjong.dk/rating/

(^_^ #) Shame on me. I didn't find the English page. Thank you Tina.

> Each players score is multiplied by two if only half a game is completed.
> (Half a game is one wind in Riichi, two winds in International).
>
> Gamefactor = 40 (*2 if three players) (*2 if only half a game is played).
>
> Difficulty = average of all the participating players' ratings.
>
> RatingNew = RatingOld + [ (Score + Difficulty - RatingOld ) / Gamefactor + 1 ]

How did you come up with this formula?

Best regards,
Nath

### Tina Christensen

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Dec 6, 2005, 11:25:39 AM12/6/05
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Nath Krismaratala wrote:

> > Each players score is multiplied by two if only half a game is completed.
> > (Half a game is one wind in Riichi, two winds in International).
> >
> > Gamefactor = 40 (*2 if three players) (*2 if only half a game is played).
> >
> > Difficulty = average of all the participating players' ratings.
> >
> > RatingNew = RatingOld + [ (Score + Difficulty - RatingOld ) / Gamefactor + 1 ]
>
> How did you come up with this formula?

The formula was made by Anders Labich and Thomas Kragh.

The purpose is to compare the strength of players. So what parameters
are useful in determining a player's strength? Your score in the game,
obviously, but the rating earned should depend not just on your score,
but also whether your score was achieved against players more or less
skilled than you. When four players sit down at the mahjong table, you
would expect the guy with the highest rating to be the most likely
winner. If I have a rating of 2000, and the average rating of the four
players is 1000, then I am expected to score 1000 points (on average,
if we play 40 games). The expected score is the player's rating minus
the average rating of the players. If I gain more than 1000 in the game
I will increase my rating, if I score less than 1000, I will decrease
my rating. Since luck is important in mahjong, you will have to average
over a number of games. 40 I guess is a somewhat arbitrary choice of
how many games it takes to even out the luck. (The "+1" is an artefact
of the thought process leading to the formula, and is unnecessary,
actually, it was just never weeded out).

Your question is very broad, and I do not know whether I have answered
it.

Tina

### Nath Krismaratala

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Dec 7, 2005, 12:21:04 AM12/7/05
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Hi,

> 40 I guess is a somewhat arbitrary choice of
> how many games it takes to even out the luck.

So 40 is an arbitrary smoothing factor or way of introducing damping in
the formula. Now, I understand.

Are you happy with a value of 40? For instance, if a new player joins
the league, does it take him a long time before his ranking stabilises.
Does the ranking players with a lot of games out of reach for newcomers
or the relative rankings change fast.

> (The "+1" is an artefact of the thought process leading to the formula,
> and is unnecessary, actually, it was just never weeded out).

This was for me the most mysterious part. Once removed, everything make
sense for me.

> Your question is very broad, and I do not know whether I
> have answered it.

Actually, you did very well. Thank you very much, Tina.

Best wishes to you,

Nath.

### Tina Christensen

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Dec 12, 2005, 5:39:20 AM12/12/05
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Nath Krismaratala wrote:

> So 40 is an arbitrary smoothing factor or way of introducing damping in
> the formula. Now, I understand.
>
> Are you happy with a value of 40? For instance, if a new player joins
> the league, does it take him a long time before his ranking stabilises.
> Does the ranking players with a lot of games out of reach for newcomers
> or the relative rankings change fast.

We are quite happy with the value of 40. It's a reasonable dampening.
It doesn't matter much for your ranking that you have many games. Your
old results fade, and what happened in a game 100 games ago is
virtually unimportant for your current ranking. If a newcomer plays
consistently well, he will soon approach the top. But it does take a
little while, as also it should.

Tina

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