Ken Larsen's web site

Proposed Backgammon Ranking System

I believe that Backgammon needs to enter the 21st century and develop a real-time computerized world ranking system.  Such a system could provide five benefits:

  1. Provide a world ranking system that's better than the current Giants Voting.  Giants Voting is done only once every two years, takes several months to complete, only includes 64 people, and is in many ways a popularity contest.

  2. Reduce sandbagging at tournaments.  The current practice is for people to enter whatever division (Open, Advanced, Novice) they choose.  Some people play beneath their skill level and cash repeatedly.  This is unfair to other players.

  3. Generate more interest in backgammon.  Tournament attendance will grow, and more people will buy backgammon paraphernalia and lessons.

  4. If I'm correct about generating more interest in backgammon, then tournaments will need more divisions than the traditional Open, Advanced, and Novice.  They will have to follow the lead of Scrabble and name their divisions 1, 2, 3, etc. to accomodate everyone.  A ranking system can greatly simplify the assignment of people to divisions.  I once ran a golf tournament with 308 people and 25 divisions.  It can be done.

  5. It's my assertion that fixing the above problems will enhance the appeal of backgammon to sponsors.  Sponsors can boost the quality and payout of tournaments, resulting in even more benefits to backgammon players.

It likely will take many years for the entire world of backgammon to reach agreement on a unified system, but I thought I'd at least try to get the ball rolling by presenting some ideas.  I'm a proponent of "Ready, Fire, Aim".  If you're trying to solve a problem, generate lots of ideas, and then sift through them to find the good ones.  This web page documents my ideas.  I live in the U.S. and have only played tournaments on the American Backgammon Tour (ABT).  I will focus initially on U.S. issues and data, but I welcome feedback from the rest of the world, because they likely are grappling with similar issues.

My proposed ranking system is based on tournament play for the most recent five years.  The more recent of those five years count more.  Attendance is rewarded to a degree.  The best way to describe my system is to present an example with some real data. 

Larsen-Silliman ranking of U.S. Backgammon Players

This is a spreadsheet that displays data for all people who have won at least a fraction of a point on the American Backgammon Tour (ABT) during the most recent five years.  If you compare it with the latest Giants Voting, you'll find people who have been voted in as a "Giant", but they're incongruously far down on the Larsen-Silliman list. 

All the data came from which is USBGF's section of   A team lead by Patrick Gibson loaded ABT tournament data from 2009 to the present.  Kudos to them for doing that laborious amount of work!

A special thanks goes to Barry Silliman.  He wrote software that successfully scraped data from the aforementioned data base into an Excel spreadsheet.  Because of that contribution, I'm calling the resultant ranking list the "Larsen-Silliman U.S. Backgammon Ranking".  This is to distinguish it from rankings which other people may create.

Thanks also goes to math professor Igor Erovenko for suggesting the various conversion formulas.

CAVEAT 1:  Only main events (Open, Advanced, Novice) are counted.  The ABT does not award points to side events.  [Amusing sidebar:  I personally have won no ABT points, but I've won three side events.  By my proposed system, my rating is zero.]

CAVEAT 2:  The spreadsheet only includes ABT tournaments.  Events in Asia and Europe are not currently counted.  Most notable is that Petko Kostadinov finished tied for 3rd in the 2013 World Championship.  That laudable finish is not counted in the above report.

CAVEAT 3:  It's my assertion that the ABT is parsimonious and top heavy in its allocation of ABT points.  The winner of an Open/Championship Division event gets a lion's share of the points. Second place gets half of first place.  Third and fourth places get half of what second place gets.  Overall, only between 12 and 20% get points, and the allocation is skewed to the top.  A wider, less precipitous allocation would produce a fairer ranking system that would include more people.  Currently a player could win one major tournament and hang around the top of the ranking for several years.  That's not right.  Click here to see an alternative system which is more level and spreads the points across more people.

Explanation of the various columns:

Pts American Backgammon Tour (ABT) points.  These are only awarded for high finishes in the main events (Open, Advanced, Novice).  By design, the average points per entry in an Open Division event is 1.00, the average in the Advanced Division is 0.50, and the average in the Novice Division is 0.25.
E Number of main events that the player entered.  Rebuys are counted as a fractional full entry - from 0.2 to 0.7 depending on the tournament.  This is done, because if a player didn't re-enter, they would still have the consolation bracket to play in.
Weight of Year The most recent 12 month period [chronologically, not calendar] carries a weight equal to the square root of 5.  The next 12 month period carries a weight equal to the square root of 4, the next 12 month period carries a weight equal to the square root of 3, etc.
Weighted Points Grand total of all points for the most recent five years with points in a particular year multiplied by that year's weight.
Weighted Events Grand total of the number of main events entered in the most recent five years with the number of events entered in a particular year multiplied by that year's weight.
Weighted Average Weighted Points / Max(Weighted Events,10)
Note:  If a person's total weighted events is less than 10, 10 is used.
x A number that grows from 0.000 to 1.000 until weighted events = 50.  It's the square root of Weighted Events / 50.
Rating Weighted Average multiplied by x

Philosophy behind this rating system:

  1. I love the simplicity of the points system that Bill Davis has created for the ABT.

  2. Reduce sandbagging.  Tournament Directors can use it to ensure that no one plays below his skill level. 

  3. Poker has implemented a similar scheme in their Global Poker Index.

  4. I'm negative on elo for several reasons.

Next steps:

  1. Tweak the weighting factors.  My original spreadsheet weighted the years 5-4-3-2-1.  Math professor Igor Erovenko suggested SQRT(5), SQRT(4), etc.  Poker uses 3.0, 2.25, 1.2, 0.6, 0.25, and 0.25 where the periods are each just six months.  Similarly, a square root function is currently used for the x (attendance) factor. 

  2. Ensure that ABT tournament directors provide the needed data for future tournaments. 

  3. Learn what points systems are used by Europe and Asia. 

On November 17, 2013 I received the following comment from my fellow club member Mark Woodruff:

Hi Ken,


That is an extremely interesting discussion.  First of all, I'm with you 100% - seems it's beyond time to have an automatic, computerized, data-driven ranking system for BG tournament performance.  The giants list has a nice 'back-room private cigar-club' feel to it, but it would be complimented nicely by a purely data-driven ranking system.


I'm a newcomer to the BG scene obviously, but I'm very surprised to see the reluctance of some to even accept the idea of this new type of ranking system.  Some of the replies I read seem to indicate they want a ranking system that ranks people on pure skill or ability, with all the variance ironed out.  To me the point of a ranking system is to rank people based on results!  It's the same with football, basketball, darts, poker, etc...your performance in competition is what determines where you're ranked...not your theoretical maximum best ability.  So what if the best player in the world is ranked 44 one year, even if everyone knows he's the best.  That is the nature of tournaments, they are not the best measure of skill, especially when evaluated with a small sample size in high-variance games like backgammon, poker, etc.


A group went through this same issue in poker a few years ago, their system is called the 'global poker index', here's a summary article that is somewhat interesting:  It ranks poker players based on tournament results using three main factors: the buyin size (using log), the percent of entrants defeated (more precise than just finishing position since it takes the number of total entrants into consideration) and the aging factor (recent results are more significant than older results).  I believe they explain their algorithm for the aging factor.  I see you are weighting recent results in your system as well.


I know the golf world uses a similar system to the one you proposed:

It uses a golfer's total 'points' divided by number of events to give average per event.  One additional neat thing is that it weights the strength of the field in each event by taking into account the ranking of each participant before the tournament starts.  That gives a 'weighting' to each week's results.  Beating the top 10 is more significant than beating 10 guys ranked 50-100.


I'm sure those are not new ideas, just thought I'd mention them since they are somewhat similar.  Also, since I'm a SAS programmer by trade, I'd be happy to help with any programming support you needed in your research/testing of a ranking system, if it would be of any use.



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