Changing Magic's Ratings System

by Alex West | posted at 2010-02-20 22:55:00
tagged: MTG, Magic, Magic the Gathering, Alex West, Ratings, ELO, Change

(The ELO ratings system, used to determine a player's Magic rating and based off a similar system from the world of competitive Chess, has been used moderately successfully to track players' abilities as competitors throughout the game's history. It is not without faults, and throughout Magic's existence, there have been talks of revamping it or creating an entirely new system altogether. Today, Alex West offers up an analysis of a new system he thinks would do a better job more accurately reflecting a player's true value as a competitor, while shoring up the weaknesses in the present system.)

I propose the following system to allocate ratings points:

1. Each player joins the rating system with 1000 rating points.

2.Each tournament is given a rating based on the mean average of ratings of all players at the tournament.

3. A ratio, "R", is assigned to each player by dividing their rating by the average tournament rating.  Thus, a player with a higher rating will have an R greater than 1, and with a lower rating they will have an R less than 1.

4. A weight "W", is assigned to each tournament.  This determines the relative importance of the tournament in question.  (This value would be set by WoTC, similar to the current "k" value.)

5. At the beginning of each tournament, each player will pay a number of ratings points into a tournament purse, "P".  The number of points paid in will be # of Swiss Rounds * R * W.

6. At the end of each tournament, the total standings points for the aggregate of players are added together, "S".  Players who drop from the tournament will be scored 1 standing point for each round they did not play, as if they had drawn in each of those rounds.  Standings points from the Top 8 should be included.  Divide P by S to determine how many ratings points to award for each standings point.  Each player gains ratings points equal to their final standings points times this number (P/S).

Example: A tournament with 8 players will go 3 rounds, and has a W value of 3.  Each player (we'll assume they all have R values of 1 for simplicity) pays in 9 ratings points (3*3*1), resulting in a tournament pool of 72 ratings points.  In the course of the tournament, there are 1 3-0, 3 2-1, 3 1-2, and 1 0-3 records.  The total record of all players is 12-12.  10 wins is 36 standing points, so 72 divided by 36 means that each standing point is worth 2 ratings points.  Thus, the records are paid out as follows: 3-0 gets 18 points (9*2), 2-1 gets 12 points (6*2), 1-2 gets 6 (3*2) points, and 0-3 gets 0 points.  Given the initial outlays of 9 points each, that means the net results for each player would be 3-0 +9, 2-1 +3, 1-2, -3, 0-3 -9.

Analysis of Consequences:

* Players effectively compete against "the field" or tournament, rather than each individual opponent.

* Tournaments with high numbers of draws will award slightly more points to players with wins.

* Players would be more likely to complete all tournament rounds in order to maximize/maintain their rating.

* Ratings will be more stable, as individual wins or losses will not cause spiked gains or losses as under ELO.

* As R moves from 1 to 2, a player will have to go from earning even records (4-4) to dominating records (8-0) to break even on points.  Effectively, the higher a player is rated relative to the tournament, the better the record they will need to keep or improve their rating.

* Players will need to seek more difficult tournaments to increase their ratings past certain levels.

* There will still be some rating protection done by professionals who have increased a rating at a GP or PT level event.  However, since the system does not heavily punish individual losses to low ranked players, this behavior will become less pronounced.

* Players who have not increased their rating through GP or PT level of competition have a high incentive to play many tournaments in order to gain ratings points.

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