Rating lists
Mahjong Denmark has two rating lists: one for Riichi (modern Japanese mahjong), which was started in August 2001, and one for the Mahjong Competition Rules, which was started in February 2004.
The same rating system is used for both lists. The basic idea is to compare the skill of players. There is no denying that luck is an important element in mahjong so it is crucial to average over many games. For players with at least some 40 games, the rating indicates that if a player has 1000 rating points more than another player that means the former will on average win 1000 points more than the latter, no matter who they play against.
Description of the elements in the rating tables
The side menu links will lead you to pages with the rating lists in Danish. Therefore this explanation. The lists show: overall rank, name, rating, average expected score (per wind), average point score (per wind), number of winds played, number of games played. A game can be 1 or 2 winds in riichi or 1-4 winds in MCR. Each name links to a page of statistics for that player. The side menu allows you to access specialized lists e.g. to show only Copenhagen players (København), only Aarhus players, the standard list (inactive players removed; this is the default list) or the complete list. You can also access the complete list of all games played: spilliste.
The mathematical details of our rating system
| RatingNew = RatingOld + |
|
Difficulty = average of all the participating players' ratings.
Gamefactor = 40 * Modifier (*2 if three players) + 1
If less than a full game is played, each players score is multiplied by a Modifier. The Modifier also affects the Gamefactor.
For a full game the Modifier = 1. For half a game the Modifier = 2.
Half a game is one wind in Riichi, two winds in Mahjong Competition Rules.
| Number of winds | Modifier, MCR | Modifier, Riichi |
|---|---|---|
| 4 | 1 | - |
| 3 | 4/3 | - |
| 2 | 2 | 1 |
| 1 | 4 | 2 |
Further description of the rating system
given in rec.games.mahjong December 6 2005:
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 artifact of the thought process leading to the formula, and is unnecessary, actually, it was just never weeded out).
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[?] [Are] the ranking players with a lot of games out of reach for newcomers or [do] 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.