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How to Calculate Your Rating

NOTE: The Scrabble® FAQ Ratings Calculator has pretty much made this document obsolete; the latter is now useful only to explain how the former works. Also, there are certain unusual situations that the Ratings Calculator cannot handle where manual calculation will be necessary.

This rating calculation guide is based on a web page explaining the rating system by John Chew, a member of the NSA Ratings Committee. See the bottom of this document for a link to his page.

This guide is intended as a step-by-step guide to help Scrabble® players find their approximate rating after a tournament. It was originally written for club #374 members by Paul Sidorsky. This updated and expanded web version is intended to benefit all NSA players.

This guide may not give exact ratings. There are many nuances to the ratings formula that just cannot be included in a simple guide. However, careful application of the instructions will generally allow you to approximate your rating within 5 points almost all of the time. The more time you invest, the more accurate your approximation will be.

1. Subtract each of your opponent's ratings from your own and note the difference for each. For example, if your rating is 1304 and an opponent's is 1231, the difference would be 73. The difference can be negative or positive.
2. For each opponent, determine the expected probability of winning by consulting the tables below. If a difference falls between two values in a table, you will have to approximate the probability. (Unless you are mathematically inclined and want to compute it exactly, in which case see John Chew's page which is linked below.) For example, if a difference in ratings is 175, you can approximate the expected probability of winning to be about 0.73. Using two decimal places is adequate.

3. Add all of the probabilites together to get the expected number of wins. If you played an opponent more than once, add the probability of winning against that opponent once for each time that you played him/her. For example, if you played an opponent three times and the probability of winning was 0.24, you would add a total of 0.72 for that opponent.
4. Subtract the expected number of wins from the number of games you actually won. For example, if you were expected to win 4.87 games and you won 6, you would end up with 1.13. This number can be negative or positive.
5. Multiply the number from step 4 with the proper constant from the table below to get the approximate change in rating. Round the result to the nearest whole number. Games Played refers to the number of sanctioned tournament games you have played in during your lifetime.

NOTE: For simplicity, use the constant that applies at the start of the tournament only. For precision, calculate your rating in multiple sections split at the point where the constant changes. (This will likely require some trial and error.)

6. Add the value obtained in step 5 to your current rating. This gives you an estimation of your new rating. Obviously, if the value from step 5 is a negative number, your rating will decrease when the value is added.
7. Multiply the number of rounds in the tournament by 5. If the number obtained in step 5 is greater than this number, subtract this number from that in step 5 and add the difference to your rating. This gives you what are called "accelleration points" to help compensate for underrated players whose performance far exceeded expectations based on their current rating. For example, if there were 8 games in the tournament, and the number obtained in step 5 was 51, you would get 51-40=11 extra points for a total of 51+11=62 points.
8. For added precision, determine if any other players that you played received any "accelleration points". Normally, this will only happen with the top two or three finishers, but may happen with low-rated players who win half or more of their games. Divide the number of accelleration points received by 20 and add that total to your rating. if you played the same person more than once, add this amount once for each game you played with that person. These are called "feedback points" and are given to compensate players for playing underrated players. For example, if a player's rating went up 94 points after an 8 game tournament and you played them twice, you can calculate the player received (94-(5*8))/2)=27 "accelleration points". This works out to 27/20=1.35 "feedback points". Since you played the person twice, you will receive 2.7 extra rating points, which will likely be rounded to 3. NOTE: "Feedback points" are not all that common and only affect your rating by a few points. The only time you would probably want to compute them is if you are attempting to ascertain your exact rating, e.g. for the purpose of meeting a predetermined cut-off.

Try practicing using tournaments for which you have already received your ratings from the NSA. Your result should equal or come close to the "New Rating" shown. The actual rating formula is very complicated so do not expect a perfect match every time. These instructions are intended to allow members to simply form an educated hypothesis as to what their rating will be like after a tournament. In my personal experience, I was able to get a perfect match about 2/3 of the time, and came within 2-3 points the rest of the time.

The procedure for calculations involving first time (unrated) tournament players is rather a mystery. It is known that if you play an unrated player, it does not count towards your rating, so you must ignore any games played against unrated players. If you are a new player trying to work out your first rating, the easiest way to guess is to simply assume a rating of 500. You will not likely achive an accurate result for your first rating, but you should be close enough to have a general idea (eg. within 50 points) of where you will be. Note that your initial rating can never fall below 500 - it will be raised to 500 if it would have been lower.

NOTE: Long tournaments (17+ rounds) are calculated in two separate halves (9 and 8 games for 17 rounds), so perform steps 1-8 once for each half. Very long tournaments (33+ rounds) are split in three sections.

Other sources for NSA ratings calculation information are as follows:

• The Base Document for this page. (Formerly part of the Unofficial Ratings Committee page, it was seperated from this page when the Official Ratings Comittee page was created.) This document is the file by John Chew from which this page was derived. It explains the ratings system from a more technical (mathematical) standpoint. Most of the information from this document is contained in this page in a more simplified and/or diluted form.
• The NSA Director's Manual. This is only available to sanctioned NSA directors (at least currently - maybe they'll provide an online version soon?) If you can get your hands on a copy, however, it does have additional tips on working out ratings. Try asking your club director. However, the tips in the manual are somewhat oversimplified and not very accurate.