# Wonder how Chessity's rating system worked?

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

etc...

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,

Arun