Click here to access the old Backgammon Galaxy Version 1 calculator.


UPDATE: New Calculator for Backgammon Galaxy Version 2 (September 5, 2023): Use the first (leftmost) calculator below

  Backgammon Galaxy Version 2 (September 5, 2023) Ratings Calculator     Backgammon Studio Heroes Ratings Calculator     FIBS Ratings Calculator  
Player 1 Rating (before match):
Player 2 Rating (before match):
Match Length:

  
Enter beginning-of-match rating and experience
Player 1 Rating:
Player 1 Experience:
Player 2 Rating:
Player 2 Experience:
Match Length:
Enter beginning-of-match rating and experience
Player 1 Rating:
Player 1 Experience:
Player 2 Rating:
Player 2 Experience:
Match Length:
Player 1 Corrected Expected:%
K:
Pr(Player 1 Wins):%
K1:
K2:
Pr(Player 1 Wins):%
K1:
K2:
Player 1 Galaxy Rating Change Scenarios
(New ratings in parentheses)
Win both match and PR: +  ()
Win match, lose PR: +  ()
Lose match, win PR: -  ()
Lose both match and PR: -  ()
Heroes Rating Changes if P1 Wins
Player 1:
Player 2:
Heroes Rating Changes if P2 Wins
Player 1:
Player 2:
FIBS Rating Changes if P1 Wins
Player 1:
Player 2:
FIBS Rating Changes if P2 Wins
Player 1:
Player 2:

Calculator Instructions

1. Choose a calculator to run (leftmost calculator = Galaxy, middle calculator = Heroes, rightmost calculator = FIBS).

2. Enter beginning-of-match (not end-of-match) ratings in the Ratings boxes. Note that the Backgammon Galaxy end-of-match screen shows end-of-match ratings, so for testing purposes, if you use this screen, you will have to back into the beginning-of-match ratings (calculate them by hand).

3. If using the Heroes or FIBS calculator, enter beginning-of-match experience in the Experience boxes. For a player's very first FIBS/Heroes match, entering "0" (zero) will currently return an error. As a temporary workaround, enter "0.0" or "0.00" (without the quotes).

4. Enter the match length in the Match Length box.

5. Click the "Calculate" button.

For the Galaxy calculator, the output (Player 1 Galaxy Rating Change Scenarios) are Player 1's rating changes for the four different scenarios from Player 1's perspective. Player 2's rating moves in the opposite direction (e.g. if Player 1 gains 10 rating points, Player 2 will lose 10 rating points).

Note that the Backgammon Galaxy web calculator purposely limits rating differences to 700 points since the rating formula wasn't tested on any matches with rating differences larger than 700 points. You can enter larger rating differences in the Excel calculator though.

Galaxy Notes

On September 5, 2023 Version 2 began using a new ratings formula. This calculator is an attempt to replicate the formula. Although this calculator isn’t 100% accurate, it is arguably more than 99.99% accurate. See the Accuracy section below for details. No errors larger than 0.01 were observed during testing.

Description of new Version 2 Galaxy formula

Accuracy

The coefficients were optimized based on a representative sample of matches (273 matches) collected between September 5, 2023 and September 23, 2023. The 273-match sample consists of 88 1-point matches, 94 3-point matches, 40 5-point matches, and 51 7-point matches. The sample contains samples of small rating differences (18 matches with rating differences of 4-20 rating points), medium rating differences, and large rating differences (28 matches with rating differences of 400-700 rating points). In all 273 matches, the actual rating change was within 0.01 points of the predicted rating change:

1-point matches (88 matches)
Exact match: 87 occurrences
0.01 error: 1 occurrence

3-point matches (94 matches)
Exact match: 88 occurrences
0.01 error: 6 occurrences

5-point matches (40 matches)
Exact match: 40 occurrences

7-point matches (51 matches)
Exact match: 47 occurrences
0.01 error: 4 occurrences

Overall summary (273 matches)
Exact match: 262 occurrences
0.01 error: 11 occurrences

While it’s possible that new data won’t match as nicely as the old data, based on my observations (collecting the data in several batches and adjusting the coefficients after each batch), I feel that it’s likely that the calculator will output the exact rating change more than 90% of the time (and possibly 95%+ of the time) and that all (or almost all) of the errors will be 0.01 rating point errors. Note that a 0.01 error is usually a small fraction of the actual rating change (e.g. 0.01 is 0.2% of 5.00, 0.1% of 10.00, and 0.05% of 20.00). The calculator is arguably 99.99%+ accurate. The sum of actual rating changes over these 273 matches was 2665.19 ratings points and 0.11 / 2665.19 is only 0.004%.

The calculator matches 22 out of 24 data points in Marc Olsen's original chart (posted on Facebook on September 5, 2023) after correcting for a typo in the chart (a 1400-player defeating a 1700-player in a 1-point match wins 7.87 points, not 7.78 points). The two errors were (1) 2100 defeats 1600 in a 3-point match (Marc's chart: 6.35, my calculator: 6.3586 (rounds to 6.36)) and (2) 1700 defeats 1400 in a 3-point match (Marc's chart: 10.09, my calculator: 10.0831 (rounds to 10.08)). Later, I discovered coefficients that correctly matched all 24 of Marc's data points, but it came at the cost of an apparent systematic 0.01 error for the X = 570-700 range in 3-point matches, which I deemed unacceptable, so I didn't change the coefficients.

If the calculator is ever wrong by more than 0.01 rating points, I'd like to know about it so that I can work on improving it. Please email me.

Heroes/FIBS Notes

1. The Heroes rating system is identical to the FIBS rating system for experience greater than or equal to 400. For experience less than 400, there is only a tiny difference in the formula (in the calculation of K1 and K2).

2. Some FIBS calculators on the Internet instead require the user to enter the end-of-match experience. This calculator requires the user to enter the beginning-of-match experience.

Credits

Formulas, Excel files, web coding: Chris Yep

Match data was provided by Joseph Heled, Travis Roberts, and Marc Olsen. I'd like to especially thank Joseph Heled for reviewing this work, providing valuable feedback on this topic (and backgammon ratings in general), and encouraging me to release the formula even though it's not quite 100% accurate yet. If you have time, I encourage you to check out his YouTube channel.

If you notice any calculator errors larger than 0.01, please contact Chris Yep.

Excel files (calculators)

Backgammon Galaxy Ratings Calculator
Backgammon Studio Heroes ratings calculator
FIBS ratings calculator
All ratings calculators (both old and new) in one file

Last Update: September 27, 2023