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Proposed Backgammon World Ranking Points

What points system should be used in a World Ranking System?  I originally believed that the U.S.'s American Backgammon Tour (ABT) system was best, but I've changed my mind.  I believe it unfairly skews points towards those who win a tournament or finish second.  I believe it would be best that a more equitable system be created.

By way of example, let's assume we have a 64 player tournament.  Under the current ABT system, only the top 8 would receive ABT points.  The distribution would be:

  1. 32

  2. 16

  3. 8

  4. 4

  5. 2

  6. 1

  7. 0.5

  8. 0.5

The other 56 people would get nothing.  A world ranking system based on ABT points would be skewed towards tournament winners.  That's too top heavy.  A person could win one major tournament, sit out several years and still be near the top of the world ranking.  We need to encourage participation, not discourage it. 

The golf world ranking system has a more level distribution of points.  The top 60 in a tournament (typically 120 entrants) are awarded points, and the distribution begins:

  1. 100

  2. 60

  3. 40

  4. 30

  5. 24

  6. 23

  7. 22

  8. 21

  9. 20

  10. 19 

The US Backgammon Federation (USBGF) awards points to "ranked positions" according to this scheme:

  1. 1.0

  2. 0.7

  3. 0.5 = 1/(rank-1) = 1/(3-1) = 1/2

  4. 0.333 = 1/(rank-1) = 1/(4-1) = 1/3

  5. 0.250 = 1/(rank-1) = 1/(5-1) = 1/4

If we normalize this to our 64 player backgammon example, and award points to the top 50% of the field (32), the distribution would be:

# Unnormalized Proposed points
(normalized for 64 players) 		ABT points
1 1.0 13.5385 32
2 0.7 9.4770 16
3 0.5 6.7693 8
4 0.3333 4.5128 4
5 0.2500 3.3846 2
6 0.2000 2.7077 1
7 0.1667 2.2564 0.5
8 0.1429 1.9341 0.5
9 0.1250 1.6923  
10 0.1111 1.5043  
11 0.1000 1.3539  
12 0.0909 1.2308  
13 0.0833 1.1282  
14 0.0769 1.0414  
15 0.0714 0.9670  
16 0.0667 0.9026  
17 0.0625 0.8462  
18 0.0588 0.7964  
19 0.0556 0.7521  
20 0.0526 0.7126  
21 0.0500 0.6769  
22 0.0476 0.6447  
23 0.0455 0.6154  
24 0.0435 0.5886  
25 0.0417 0.5641  
26 0.0400 0.5415  
27 0.0385 0.5207  
28 0.0370 0.5014  
29 0.0357 0.4835  
30 0.0345 0.4668  
31 0.0333 0.4513  
32 0.0323 0.4367  
totals 4.7272 64 64

The proposed system spreads the points across more players and is more level.  The ABT system heavily weights the top two finishers.

Money vs Points - No need for them to align

It should be noted that the ABT Point System is used both to award points and cash prizes.  The ratio of ABT points is the same ratio used to award ABT cash.  There is no reason why they have to be aligned.  The ABT system could be used disperse the cash.  The flatter/deeper USBGF system could used to award points. 

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