Elo Calculator

Note. This is the final Part 2 of a simple explanation of the Elo rating system in chess (how it works in FIDE, Kfactor, winning probability, etc.). You can start reading from the very beginning  from Part 1, or continue with this Part 2:
The Expected Result for chess tournament is calculated individually as the sum of all expected results with each opponent. The FIDE rule of 400 points has impact on the Expected Result. Before, FIDE calculated the Expected Result in another way. The following 3 examples explain how the Expected Result is calculated.
Example 1: (the FIDE rule of 400 points not applied): Player A rated 2000, played 2 games against Player B rated 2100 and Player C rated 1750. The Expected Result for player A is therefore calculated as this: Expected Result 1 (rating difference 100, Player A weaker) = 0.36 Expected Result 2 (rating difference 250, Player A stronger) = 0.81 Expected Result for Player A (for 2 games) = 0.36 + 0.81 = 1.17
Example 2: (the FIDE rule of 400 points applied): Player A rated 2000, played 2 games against Player B rated 2450 and Player C rated 1750. The Expected Result for player A is therefore calculated as this: Expected Result 1 (rating difference more than 400, the rule applied (for weaker 0.08), Player A weaker) = 0.08 Expected Result 2 (rating difference 250, Player A stronger) = 0.81 Expected Result for Player A (for 2 games) = 0.08 + 0.81 = 0.89
Example 3: (the FIDE rule of 400 points applied): Player A rated 2000, played 2 games against Player B rated 2100 and Player C rated 1500. The Expected Result for player A is therefore calculated as this: Expected Result 1 (rating difference 100, Player A weaker) = 0.36 Expected Result 2 (rating difference more than 400, the rule applied (for stronger 0.92), Player A stronger) = 0.92 Expected Result for Player A (for 2 games) = 0.36 + 0.92 = 1.28
Calculating New Rating and Kfactor
New Rating = Old Rating + Rating Change ... or ... New Rating = Old Rating + Kfactor * (Result  Expected Result) The Kfactor is assigned, and in FIDE it may be one of the following 3: 10, 20, or 40. Effective from 1 July 2014, FIDE uses the following rules for the assigned values of the Kfactor:
• The Kfactor is 40 for a player new to the rating list until he has completed events with at least 30 games; • The Kfactor is 20 as long as a player's rating remains under 2400; • The Kfactor is 10 once a player's published rating has reached 2400 and remains at that level subsequently, even if the rating drops below 2400. • The Kfactor is 40 for all players until their 18th birthday, as long as their rating remains under 2300 (then 20).
Note 1. According to the FIDE rules, the Kfactor 10, 20, or 40 is used for rating calculations in all standard chess tournaments. In rapid and blitz chess tournaments, the only Kfactor 20 is used for all chess players.
Note 2. As stated above, today FIDE uses the Kfactors 10, 20, 40. From 1 November 2011 until 1 July 2014, FIDE used the Kfactors 10, 15, 30. And before 1 November 2011, FIDE used the Kfactors 10, 15, 25.
Calculating Rating Increase/Decrease
Rating Increase/Decrease is very important for your Rating Change. If your Rating Increase is 0.15 and your Kfactor 20, then your Rating Change will be 3. If your Rating Decrease is  0.20 and your Kfactor 10, then your Rating Change will be  2.
Rating Increase/Decrease is actually not called like this. Officially, it is called in the FIDE Players' Database as "change". But let's name it Rating Increase/Decrease for better understanding. It is an absolute value which can be plus, minus, or zero and is calculated as this:
Rating Increase/Decrease = Result  Expected Result
Example 1: Player A in a 9game chess tournament scored 5.5 and his Expected Result was 4.0. The Rating Increase/Decrease for player A is therefore calculated as this: Rating Increase = 5.5  4.0 = 1.5
Example 2: Player A in a 5game chess event scored 1.5 and his Expected Result was 3.5. The Rating Increase/Decrease for player A is therefore calculated as this: Rating Decrease = 1.5  3.5 =  2.0
Example 3: Player A in a 9game chess tournament scored 4.5 and his Expected Result was 4.5. The Rating Increase/Decrease for player A is therefore calculated as this: Rating Increase/Decrease = 4.5  4.5 = 0
Calculating Performance Rating
Performance Rating = Opponents' Average + Performance Change
Performance Change is based on the Performance Ratio. If a player scored 9 in 9 games, his or her Performance Ratio is 1.00 and Performance Change +800. If he scores 4.5 in 9 games, it is correspondingly 0.50 and Performance Change will be 0. The needed value is taken from the Table of Performance Change.
Please notice that your Performance Rating does not depend on your own rating but does depend on your Opponents' Average and "how you performed" (Performance Change). Performance Rating is very important for getting the Grandmaster and International Master norms.
In some Chess Organizations (but not in FIDE), the Performance Rating is calculated with "the algorithm of 400": If you win, add 400 to the opponent's rating; if lose, subtract 400, if you make a draw, no change. Then find the average.
Calculating Grandmaster and International Master norms
The Grandmaster (Woman Grandmaster) or International Master (Woman International Master) norm is the minimum score at which the player may get the norm. The Grandmaster or International Master norm is possible under the following 2 conditions:
1. The player must meet the FIDE norm requirements. 2. The player's score must provide, at least, the minimum Performance Rating needed for the norm but only under the minimum Opponents' Average, both defined by FIDE.
The following is some of the FIDE norm requirements: • At minimum, 9 games played. • At least 50% of the opponents must be titled. • For a GM norm, at least 1/3 with a minimum 3 must be GMs. • For a IM norm, at least 1/3 with a minimum 3 must be IMs.
The following minimum Performance Rating is needed: • 2600 for the Grandmaster Norm (under Opponents' Average at least 2380). • 2450 for the International Master Norm (under Opponents' Average at least 2230).
• 2400 for the Woman Grandmaster Norm (under Opponents' Average at least 2180). • 2250 for the Woman International Master Norm (under Opponents' Average at least 2030).
You can get the International Master Title if you have 3 (three) 9gametournament's International Master Norms, and if FIDE recalculated your current rating at 2400 even once. You can get the Grandmaster Title if you have 3 (three) 9gametournament's Grandmaster Norms, and if FIDE recalculated your current rating at 2500 even once.
There is no need to have any Norms for getting the third Title in FIDE  the FIDE Master Title. You just need to "hit" the specific current rating as defined by FIDE. For more details on awarding the Titles of Grandmaster, Woman Grandmaster, International Master, Woman International Master, and FIDE Master, please see the FIDE Titles.
Calculating Opponents' Average
There is no need to explain Opponents' Average; it is quite understandable. The only thing you must remember is that the FIDE rule of 400 points in rating difference has impact on Opponents' Average too as shown below.
If you are rated 2400, and 2 your opponents 1000 each, the FIDE average of your opponents will be 2000 (2400400), but not 1000 as expected. If you are rated 1800, and 2 your opponents 2400 each, the FIDE average of your opponents will be 2200 (1800+400), but not 2400 as expected.
Conclusion
Elegant and beautiful, this is the Elo rating system which was named after its creator Arpad Emrick Elo who had improved the original Harkness' system. Nowadays the Chess Organizations usually use their own interpretation of the Elo system...
Elo rating is often used to mean a player’s chess rating as calculated by FIDE. However, other Chess Organizations, National Federations, Internet Servers, and so one have adopted Elo’s and Harkness’ general ideas, but added their own rules to them.
For example, the same chess player at the same time can be rated 2500 by FIDE, 2600 by USCF (The United States Chess Federation), and 3000 by ICC (The Internet Chess Club) because of a different approach in Elo calculation.
Some Chess Federations have Rating Scale Categories for the chess players. It is a division of the chess players by their ratings but not by their real titles. Please click on the following links for reference on the FIDE Rating Scale Categories or USCF Rating Scale Categories.
At the end of each tournament, the organizers calculate Elo results for each participant and prepare socalled Final Standings Table. It is line by line Table which includes the chess players' names, their current ratings at the start day, and Elo results for the tournament.
The Final Standings Tables are submitted to FIDE. The latter recalculates Elo results for each chess player, makes corrections if any mistake, and prepare the FIDE Players' Database which is updated monthly and is available online.
Each month FIDE publishes 3 FIDE Players Rating Lists (for standard games, for rapid games, and for blitz). Each list is an official FIDE document to confirm the current rating of a chess player. The lists are used by the tournament organizer to look up for the current rating of the FIDE chess player.
If you are an unrated chess player, the following link will briefly explain you how to get initial rating in FIDE. Once you have an initial rating, you may officially move on in the ancient, noble, and beautiful game of chess that makes people think...
The FIDE rating system is changeable, and from time to time FIDE can change the rules. For example, the FIDE rating system was slightly changed effective form 1 July 2014. To understand the changes, you can click the following link Updated 1 July 2014 FIDE Rating System.
On the next pages, you will see Chess Players Top List, valuable links on Chess Elo in FIDE (FIDE Players' Database, original information on the FIDE rating system, FIDE norm requirements), chess puzzles, and more...
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