Wonder how Chessity's rating system worked?

Sep 22, 2014
StaffCoach 2170

Chessity uses some math and science behind its rating system. This blog is indended to make you understand about how it worked, and the complexity behind it. 

If you are a FIDE rated player, you must be well aware of the K-factors, and how they calculate your rating changes and stuff. In chessity, we use the below formula to make things work!

Chessity rating calculations: 

All rating calculations are based on the formula:
R = Rc + Kf * (Sa - Se)

in which:
• R = the new rating to be calculated
• Rc = the current rating
• Kf = a sensitivity factor
• Sa = the actual score
• Se = the expected score, based on rating difference

The sensitivity factor Kf is a function of the number of rating calculations (N) on which Rc is based: Kf = 500 / sqrt(N) with a minimum of 25 when N is above 400.

The expected score is calculated using a normal distribution (a.k.a. a Gaussian distribution or bell curve). The horizontal axis of the curve is the rating difference (Rd) between the 2 players. Some example values form the bell curve:
Rd = 0 gives Se=0.5 (a draw is expected between 2 equally strong players)
Rd = 200 gives Se = 0.758
Rd = 700 gives Se = 0.993

Of course at the Chessity website your rating is based on your results on the puzzles and not on your score against opponents. But this doesn't change the calculation. When you join Chessity your rating starts at a generous 1600 points and will develop from there.

In games like Castle assault or Chessbox the calcualtion uses the average score on the puzzle set and the average rating of the puzzles you played. For instance if you solve 8 puzzles and fail at 2 others your score will be 0.8 against the average rating of the 10 puzzles. It doesn't matter if you solve the hard ones and fail at the easy ones or the other way around.

In the training part of the websites we have solo exercises like 'Mobile' and 'Chess board' and these use a 'per puzzle' rating calculation. This simply means your result is either 1.0 or 0.0 and that score number is used in the rating calculation. Of course this means there is no 'averaging effect' on the calculation and the results can swing pretty wildly per puzzle. However, in the long run this will not make a difference.

Currently Chessity does not use time usage in the rating calculation. As there usually is far less time pressure in the solo training exercisis most players score better ratings there than in the games.

The rating of the puzzles is calculated using a mix of dynamic rating calculations and a static value that is assigned by the puzzle author.

The 'Blind routeplanner' game comes with it's own rating list that follows exactly the same rules as the standard rating.

That's about it. Do let us know if you have more questions about our rating system, or ideas to improve it. We are happy to answer your questions! 

Have a nice day, 



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Labelle 02:24 - 25 Sep 2014
And how is rated a puzzle?
arunjchess 06:49 - 25 Sep 2014
You mean how the rating of a puzzle is determined?

-- Two methods:
1. Steps method
2. Automatically adjusted based on how the users solve them. The puzzles are automatically graded based on the strength of the users solving them and their success rate. Sometimes a new puzzle is automatically at 1400 -- But after 10 tries by users, the puzzle jumps to its actual level. During these 10 tries, the users will not have much rating change to be fair.
arunjchess 07:29 - 28 Sep 2014
@Dayalsoap says:
"Sorry, I think there is a BUG in the rating calculation.

If you do NOT fail out, or solve ALL puzzles, you do not get any rating increase. For example, if you get 3 puzzles correctly, but then time out on the 4th, you will get no rating points for the first 3. Likewise, if your opponent wins the game, you do not get any rating boost.

Surely for solving two puzzles 300+ rating points higher than me, and the one puzzle 50 points lower than me (getting none wrong), I should gain SOME rating points."
kingc6 21:45 - 29 Sep 2014
Hi, where can I find those solo exercises Mobile and Chessboard?
arunjchess 07:41 - 1 Oct 2014
Here's how:
http://www.chessity.com/train.php >> training tab
kingc6 09:41 - 1 Oct 2014
thanks arunjchess, but that is obvious. I mean where on the training tab, ;-)
kingc6 09:49 - 1 Oct 2014
sorry, very, very stupid of me. I found them!
Labelle 15:14 - 5 Oct 2014
Hi Arjuna,

Thank you very much for your answer Arjuna. Sometimes I am very surprised by how relatively easy puzzles solved by a great proportion of users are highly rated and, conversely, how puzzles solved by a low proportion of users are lowly rated but, as you mention, it also depends of the ratings of the users who solve or do not solve the puzzles, which is a statistics which does not appear in training - that may explain that mystery.

Other questions, follow-ups of your answer on the same subject. What is the "step method" for determining the rating of a puzzle, and when and why is a method used rather than another one for making such determination?
Labelle 20:35 - 5 Oct 2014
Sorry Arun, Arjuna is someone else.
AoxomoxoA 00:52 - 22 Nov 2014
Do the problems have a fixed rating? Usually they get rated like the users too.

One problem of this ratingsystem here is, that duplicates get rated. Sometimes i dee the same puzzle twice in one single session. Of cause i can solve it the second time but and so my rating should not improve.

A second problem is the rating without time. As longer someone thinks as better the move. Somehow the rating just tells how long the tactician did spend with the puzzle.

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