Background

The Alberta rating system was devised around 1970 by Dr. C. J. Elliott to measure ranks of players in the University of Alberta Go Club. It has been continually updated and used since then. Players using readily accept the ratings computed. It has not gone beyond use in Edmonton mostly because of communication difficulties. Currently, the Calgary Go Club is using a separate copy but of course when Calgary and Edmonton players meet there is no single system. (2005)

Goals of the Rating System

• To be accessible on the internet by fall 2006.
• To handle tournament games between any 2 individuals in Canada.
• To allow processing of club games (non tournament)
• To handle processing by a local club level.
• To also serve as a membership tracking system.
• To handle multiple organizations and membership in more than one organization by an individual.
• To allow manual adjustments
• To allow access by security level only by authorized users.

Considerations

• Beginners progress rapidly compared to stronger players>
• Stronger players are more consistent in their strength
• Stronger players should not get dragged down in rating by losing handicap games to weaker players who are stronger than their current rating.
• A rating system cannot determine absolute rank or rating, only relative strength.
• Any rating system requires a reference or anchor.
• A beginner who loses is not ever weaker. ie. a 30 kyu can't become 31 kyu because he/she loses games.
• The system needs to easily allow for growth in strength not be a zero sum system.
• The rating system in related to the probability of a player winning an even game when he is exactly 1 rank weaker than the opponent. This must be known and incorporated into the mathematics.

Rating and Rank

Rank is the kyu or dan level of an amateur player.

Rating is a more precise number. Each rank is assigned a rating value 100 points in width.

For example:

	Rank		Rating Range		Average
	6 dan		500 - 599		550
	5 dan		400 - 499		450
	4 dan		300 - 399		350
	3 dan		200 - 299		250
	2 dan		100 - 199		150
	1 dan		0 - 99		50
	1 kyu		-100 - -1		-150
	2 kyu		-200 - -101		-250
	3 kyu		-300 - -201		-350
	4 kyu		-400 - -301		-450
	5 kyu		-500 - -401		-550
	6 kyu		-600 - -501		-650
	7 kyu		-700 - -601		-750
	8 kyu		-800 - -701		-850
	9 kyu		-900 - -801		-950
	10 kyu		-1000 - -901		-1050

For ranks lower such as 13 kyu just subtract 1000 from the 3 kyu rating.

Players are initialized at the average rating  believed to match their rank.

Principles

• The system must not wander up or down.
• The system must not punish stronger players who lose to weaker players because they are stronger than their rating suggests.
• The system should encourage one to compete.
• The computed ratings must reflect the number of handicap stones required between two players.

Considerations for a local Club

• Club games must be anchored by their strongest players.
• Assume the strongest player's rating is fixed unless he/she competes in provincial, national or outside events.

National Considerations

• The top players must be ranked and recognized to promote competition and acceptance of the system.

Features

Fixed Freeze levels

These rating levels are set by the system administrator. For example, if a level is set at a rating of 500 then in a game between a player above that line and one below the rating of the player above is not changed. ie. the stronger player serves as an anchor. It is good to set a freeze level below the rating of the strongest player in a club. If another player crosses the line then the stronger player's rating can be affected.

If a freeze level is set just below 1 dan then dan players as a group are unaffected by losing (or winning) against kyu players. Kyu players are allowed to move up withour dragging dan players down. Each club can set its own freeze levels.

Rating Protection Band

This band is like a moving freeze level. If the band is set to say 400 points then in a game between two players separated by more than 400 points the rating adjustment of the stronger player is unaffected.

Mathematical Formula

The probabilty of player A winning an even game is 50-50 or 0.5 if the relative strengths are equal. If player A is N stones stronger than player B then lets assume the probability is exponential.

If the probability is P then

                      P = 1 - (exp(-alpha*N))/2

so that when N=0 P=1/2

Since P is known to be about 2/3 or 0.667 when N=1 we can solve for alpha.

Alpha = log(2/3)  natural logarithm to base e

         = 0.4 approximately.

To calculate points based on a rating difference of 100 pts = 1 rank then it is natural to award a percent of the maximum for an even game. The adjustment for unbalanced games must use the above probabilty.

Points awarded = Amplitude * (1 - exp(-alpha*N))/2

Now there a similar calculation if the stronger player loses and the weaker player wins but I leave that as an exercise or contact the author for more details.

Rating Game Amplitude

Typically set to 10 points (10% of a rank). This means in an even game between two equal players of same rating the winner gets 10 points and the loser loses 10. It determines the speed of progression. 10 seems to work well.

Alpha

Alpha is related to the probability of player A winning against player B in an even game when B is 1 stone stronger. The probability has been measured statistically and is about 1/3.

To test the correctness of any rating system one should set two players to the same rating. It doesn't matter what. Then enter many game results between the 2 players so that A wins 2 out of 3. ie. A, A, B, A, A, B, A, A, B, A, A, B, ...................

The ratings of the 2 players should level out to A being 1 rank stronger. If this is not the case then the rating system fails the most basic test.

Also, the average rating of A and B should not continually increase or decrease.

Bonus Points Level

This setting will inject bonus points for beginners who are below the level. 9 or 10 kyu is typical. What this does is award bonus points to both players so one gets a bonus for simply playing. This seems reasonable and seems to help the system keep up with the rapid progression of beginners.

Exponential Probability

Rating points are awarded according to an exponential curve. This means that if a 5 kyu winns against a 3 kyu in an even game then the rating points is calculated on the curve and would be around 15 points instead of 10.

Similarily, If the 5 kyu lost as would be expected the number of points is much less than the alpha value. Perhaps the winner gain 3 and the loser lose 3.