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At the heart of the rating system used to rate Scrabble players in Australia is a rule which models the probability that a higher rated player will beat a lower rated player. The curve is a function of the difference in ratings. Prior to Dec 1, 2006, Australia used a logistic curve with a slope parameter of 172. The formula (expressed in spreadsheet language) is 1/(1 + EXP(-x/172)). However checking the actual win rates using many games shows that the curve is wrong.
For instance when the ratings difference is 300, the logistic formula gives the higher rated player an 85% chance of winning, but the data show that they win only 74% of such games.

We now use a straight line rule which better accords with the prior data. Your percent chance of winning is fifty plus one twelfth of the rating difference (but capped at 95%).

The practical consequences are that the higher rated players in a section will find it fairer in maintaining their rating, or being able to progress to the next higher sectionif they can prove their worth.

Ratings will slowly change as the result of the change, and it is possible that we may again get a mismatch between the observed win proportions and the modelled probability. Monitoring will occur from time to time by a working party assigned to CASPA.

Quick rating check

Here’s an example of how you can calculate your rating change.

Example: You are rated 1453. You win 5 out of 7 games against opponents whose average rating is 1393.

  1. You are 60 points higher on average.
  2. Your probability of winning a game is on average = 50 + 1/12 of 60 = 55%.
  3. You would be expected to win 55% of the 7 games, ie 3.85 games.
  4. You actually won 5 games, which is +1.15 games better than
  5. A multiplier of 20 usually applies. Your rating gain is 1.15 x 20 = 23 points
The source code in Perl can be downloaded by right clicking here.

Enquiries regarding the National Rating System may be sent to the National Ratings Officer, Martin Waterworth, at nro@scrabble.org.au.

Australian Scrabble® Players Association (ASPA)
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