Backgammon Ratings
What They Are, How They Work, and Are They Useful

Kent A. Goulding, 1984

From Backgammon Times, Volume 4, Number 1, Spring 1984.

Ranking Players

One of the most common questions I have been asked over the years has to do with who the best backgammon players are. Time and again I am asked: "Who are the top ten (or twenty) backgammon players in the world or in the U.S.?" I can give my opinion, but it is often clouded by my personal feelings about some players or my lack of knowledge about others.

Often an expert's top ten list is a list of good players who are his friends or players against whom he often plays. Ask a player in New York and you will find nine of the top ten players are from that city. Ask a player in Los Angeles and there will be few New Yorkers on the list. A good rating system will compare players all over the country, and without bias.

Master Points and Ratings

Ratings and master points are two commonly used methods of ranking players of games of skill. For many years the American Contract Bridge League has supplied master points to hundreds of thousands of tournament bridge players, while the U.S. Chess Federation has provided all of its members with ratings.

Master points are cumulative: you can only win them, you can never lose them. Master points are awarded when a bridge player wins a bridge event or places near the top. The more players that are in the event, the more master points that can be won. Also, certain events are considered more prestigious or difficult to win, and more master points are awarded for placing in these events than in less prestigious events. While a player who plays frequently will win more master points than an equal player who seldom plays, there is more to master points than just attendance. There is plenty of skill in duplicate bridge, so the better players win with surprising regularity and therefore garner most of the master points.

Ratings are something altogether different. A chess player earns a rating as soon as he has played in his first tournament. His first rating is determined by how many games he won and lost and by the ratings of his opponents. Once he has a rating, it will be subject to change (down as well as up) after every tournament he attends. Playing frequently will do nothing to advance a player's rating (other than add to his experience, and probably his skill). A high rating must be earned again and again, otherwise the rating will drop. Likewise, a player must do poorly to achieve a low rating, and must continue to play poorly to keep his rating low. By itself, a chess rating tells you little, but by comparing it to other ratings it can be quite meaningful. Chess ratings range from somewhat below 1000 to as high as around 2800. The vast bulk of tournament chess players fall in the 1200 to 1600 range.

Years ago Prince Alexis Obolensky and his World Backgammon Club attempted to institute a master points system for backgammon. Local clubs were contacted and master points were awarded at some tournaments. The system was never fully implemented and quickly flopped.

Today, many local or regional clubs and associations award master points. The master points of a given club are in no way related to master points of other clubs. These master points are a reflection of both skill and attendance and are useful to promote the weekly or monthly tournaments of their respective groups. In most cases each player's master point total is started at zero each year. Often there are prizes and honors bestowed upon the player with the highest total at the end of each month or at the end of each year.

I have no objection to these master point systems. They are well received in many areas and serve a valuable purpose. One of the objectives of master points, presumably, is to determine who the better players are. Even if a nationwide master point system were to be implemented, attendance could be rewarded along with skill. To best determine who the best players are, ratings are far superior to master points.

How Ratings Work

There are several factors which go into any rating formula. If a player wins a match he will gain rating points, if he loses he will lose rating points. How many points are won or lost depends on several factors.

There are three factors used in my system (the system was actually devised by Lawrence Kaufman, who is one of the world's leading authorities on rating games of skill and is currently the rating advisor to the U.S. Chess Federation). The difference between your rating and your opponent's rating is a key factor. You will gain fewer points beating a lower rated player than you will by beating a higher rated player. Likewise, you will lose more points if you lose to a lower rated player than you will lose if you are beaten by a higher rated player.

In fact, you are "giving odds" when you play anyone with a rating different than your own. In such cases, you will stand to win or lose different amounts. For example, if a player rated 1500 plays a player rated 1600 in a 15 point match, the 1500 player will gain 46 rating points if he wins, but will only lose 29 points if he loses. (The 1600 player faces opposite odds, he will either win 29 points or lose 46 points.)

The second factor in determining the number of points won or lost is the length of the match. Backgammon is at least partly a game of chance. It makes sense that the longer the match, the more likely the better player is to win. This is taken into consideration in the rating formula. A short match gives the weaker player a better chance of winning, so the weaker player will not be rewarded as much as he would if he won a longer match against a tough opponent.

In the above example, if the players played a five point match, the 1600 player would stand to win 11 points or lose 14 points (making him a 56–44 favorite, compared to 61–39 in the 15 point match). Notice also that there are fewer points up for grabs in the five point match. The longer the match, the more points are up for grabs and the bigger the odds the higher rated player is giving.

At present, the highest rated player is rated about 1800, while the lowest rated player is rated around 1300. If these two players were to play a 15 point match, the expert would stand to gain only 7 points if he won while he would lose 68 points if he lost.

The Experience Factor

The third factor is the experience factor. The computer keeps track of the total length of all matches each player plays. A player who has played three matches, all to 15 points, will have experience of 45. The computer looks at each player's experience and then multiplies the number of points he wins or loses by either 1, 2, 3, 4, or 5. Five is used for players with experience of less than 100, four for experience of 100–199, three for 200–299, two for 300–399, and one for 400 and up.

The above examples were all calculated assuming players with less than 100 match points of experience. Had the players been seasoned veterans with experiences of over 400, the number of points won or lost would be 1/5 as large.

The rating formula is quite complex, but simplifies greatly if the players have identical ratings. In that case, you can easily calculate how many points will be won or lost: the length of the match divided by two, then multiplied by the appropriate experience factor. Two brand new players (both rated 1500) play a 15 point match. The winner will gain 37.5 points and the loser will lose 37.5 points (15/2 × 5 = 37.5). Equal players with over 400 points of experience would only win or lose 7.5 rating points for the same 15 point match.

Unlike master points, a rating can go down just as easily as it can go up. In fact, the higher a player's rating gets, the harder it is to keep it high. The experience factor allows players with little or no experience to rapidly reach a rating indicative of their true strength. The rating of any player with less than 100 experience points should not be given a great deal of weight. Ratings of players with experience over 400 should be considered fairly accurate. The computer also keeps track of the total number of matches a player has won and lost. These numbers are not used to calculate ratings, but are there to add a little extra information about how a player has performed.

Initial Rating

There are a number of possible ways to start up a rating system. One way is to attempt to assign each player the rating you think he/she deserves. Another way is to start all players with the same rating. The most accurate methods all involve using tournament results to determine a starting rating for each player.

Due to several factors, I decided to start almost all players with a rating of 1500 (the number 1500 has no significance other than to give backgammon players ratings somewhat comparable to chess players). A few well-known experts were started at either 1550 or 1600. This "head start" given to some strong players will have almost no significance after only 20–30 matches. The reason for it is not to reward these players, but to make it fair to the players they play in their first matches. It simply didn't seem right to have losing a match to a player like Paul Magriel have the same effect as losing a match to an average player.

How to Use Ratings

Okay, now we have a rating system. So what? Some players think it is wonderful, some object that they will lose their "pigeons" because they will be exposed as experts (hitherto unknown), and some just plain don't care. It is my belief that a reasonable rating system, supported by all tournament organizers, can only help backgammon. It is human nature to want to know how you stand among others in your field.

The vast majority of backgammon players are by nature competitive and want to win (even though they also enjoy playing). A rating system would help to identify those players who are playing well and deserve the recognition of their fellows. A rating system would also help to unify backgammon in the United States. Players will be able to play in tournaments far from home and have some idea of the strength of the players they encounter.

A central rating system is the first step toward a national federation of some type. If there is ever to be growth of our game and corporate sponsorship of events, there must be something which shows there is some sort of national unity and cooperation. Besides, even if many players don't particularly care for ratings, I think enough like the idea that the project should be continued.

I do not believe that the rating system should be used in place of master points. I strongly believe that master points are a good idea on a local or regional basis. Promoters must have some way of boosting attendance and honoring those who attend often and play well.

Once ratings can be shown to be fairly accurate, there is then the possibility of class tournaments. That is, tournaments with limits on the ratings of players who enter. For years the American Backgammon Championships, Inc. has tried to find ways of determining who is eligible to play in the annual Plimpton Cup Tournament. One guideline could be a player's rating. The idea of having tournaments open only to players of certain ratings presents a variety of possibilities, including a "U.S. Invitational Championship" where only the top 16 or 32 players are invited to play.

Collecting Data

I started collecting the results of the championship division of major backgammon tournaments in early 1983. Several organizers sent me some results of tournaments held in 1982. Every tournament I have received has been rated. By the time this article is published over 50 tournaments will have been fed to my computer. Close to 1,000 backgammon players, nationwide, will have backgammon ratings.

I need help. I have the computer resources to handle the rating of tournaments and I have enough spare time to punch in the results. What is needed is feedback from backgammon players and tournament results. So far, almost every organizer I have contacted has responded by sending me the results of the championship division of his/her tournament. I have failed to obtain results from some tournaments because I didn't know they existed or because the organizers threw away the draw sheets. It doesn't take much time to stuff a few draw sheets in an envelope and stick them in the mail. I would prefer to be able to mark them up and keep them, but will gladly return any draw sheets that an organizer wishes to keep.

There are already a couple of players in my computer with identical first and last names. There will be more. It is therefore helpful to have at least partial addresses for each player. I would like the full name of each player and their address (home town and state, at least). As soon as possible after the tournament is completed results (draw sheets showing the length of each match, the name and date of the tournament, and the full names of all players) should be sent to:

Kent Goulding
P.O. Box B
Kensington, Maryland 10895

Any player wishing to know more about the rating system or wishing to know his/her rating can write to me at the above address. Please include a stamped, self-addressed, return envelope.

I would also like to hear players' opinions about the rating system in general. Do you like the idea? Would you like to see the full rating list published, or just the top 50 or 100? If you have a low rating, would it bother you to have it published along with all the others?

I have spent literally thousands of dollars and months of work to get the project this far. I need at least some encouragement from players, readers, and organizers to keep it going. Please take a minute to drop me a line and let me know what you think.

Author, instructor, and world-class backgammon player, Kent Goulding is a contributing editor of Backgammon Times.

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