Home • Learn to Play Chess • Improve Your Game • Chess History • Chess for Fun • Chess Blog

Calculate Your Chess Rating

A chess rating is based on your opponents' ratings and your results against those opponents.

Overview - Step By Step A: Note the ratings of your opponents B: Compute the rating differences C: Look up your winning expectancies D: Compare your expected score to your actual score E: Determine your k-factor F: Compute your new rating G: Determine your performance per game H: Calculate your performance rating for the event A: Note the ratings of your opponents A chess rating is based on your opponents' ratings and your results against those opponents. It is usually calculated after an event (a tournament or a match) has completed and is based on all the games played against rated opponents in that event. To find out more about ratings see Suggested Reading in the link box at the bottom. If you don't like math or are looking for a quick way to calculate ratings, see the rating calculator tool, also in the link box. The first step in calculating a rating is to note the ratings of your opponents and your result against each. Let's say that your rating is 1500 and that you have just played a 5-round event. (If you don't have a rating, you can still calculate a tentative rating. See performance rating below.) You won against a player rated 1400, lost to a 1650, won against a 1575, drew with a 1625, and lost to a 1700. We'll summarize your results as +1400 -1650 +1575 =1625 -1700. The following steps will use these as an example. Do you already have a rating? Follow steps B through F to calculate your new rating. You don't have a rating? Follow steps G and H to calculate your performance rating. Knowing your performance rating for an event can be useful even if you already have a rating. B: Compute the rating differences From step (A) : Your current rating is 1500 and the results in your last event were +1400 -1650 +1575 =1625 -1700. Now calculate the difference between your rating and each of your opponents' ratings. The sign ('+' or '-') is important. If you were rated higher than an opponent, the sign is positive ('+'). If you were rated lower, the sign is negative ('-'). In your first game, your opponent was rated 1400. You were rated 1500, so the rating difference was (1500 - 1400) which is +100. In your second game, your opponent was rated 1650, so the difference was (1500 - 1650) which is -150. Continuing for all 5 games, you calculate that the rating differences were +100 -150 -75 -125 -200. C: Look up your winning expectancies From step (B) : The rating differences for your last event were +100 -150 -75 -125 -200. Now you need to compute your winning expectancy for each game. The math for this is complicated, so we are going to rely on a table lookup. Note that the table, which is shown below, has two real columns. The first column is a number from 677 to -677. The second column is a number from .99 to .01. The first column corresponds to rating differences and the second corresponds to winning expectancies. The first entry in the table (677 .99) means that when the stronger player is rated more than 677 points higher than an opponent, the stronger player has a 99% chance of winning the game. The last entry (-677 .01) means that a player rated more than 677 points lower has a 1% chance of winning. The middle entry (0 .50) means that when there is no rating difference, both players have a 50% chance of winning. This is the same as saying that two players with the same rating are evenly matched. For each of your games, use the table to look up the winning expectancy that corresponds to the rating difference that you calculated. The rating difference of +100 in your first game corresponds to a winning expectancy of .64. The difference of -150 in the second game corresponds to an expectancy of .29. Continuing for all 5 games, we calculate that the winning expectancies were .64 .29 .39 .33 .24. Rating differences vs. winning expectancies D: Compare your expected score to your actual score From step (C) : The winning expectancies for your last event were .64 .29 .39 .33 .24. Your new rating will be determined by the difference between your winning expectancies and the score you achieved. First, add up your winning expectancies:- .64 + .29 + .39 + .33 + .24 = 1.89 This was your expected score for the event. Second, calculate your total score using the three possible results for any chess game. Count 1 point for a win; ½ point for a draw, and 0 points for a loss. In our example event you won two games, lost two games, and had one draw. Your total score was (2 x 1.0) + (2 x 0.0) + (1 x 0.5) = 2.5 Since your total score (2.5) was higher than your expected result (1.89), your rating will increase. If your total score had been lower than your expected result, your rating would decrease. If your total score had been exactly the same as your expected result (which doesn't happen often), your rating would not change. E: Determine your k-factor This is the trickiest step, because there is no agreed formula to determine the k-factor. You just have to know what your chess federation (or other rating agency) uses. The k-factor determines how fast your rating changes. It is a number which usually lies between 10 and 40. The higher the k-factor, the faster a rating changes; the lower the k-factor, the slower a rating changes. Some considerations for setting a k-factor are:- the age of a player, the number of rated games already used to determine a player's current rating, and/or the player's current rating. FIDE, the international chess federation, uses the following k-factors:- 25 until a player has completed enough events to have played at least 30 games; 15 for a player rated less than 2400; and 10 once a player has reached 2400 and played 30 games. Thereafter it remains permanently at 10. Four the next step, we'll assume a k-factor of 25. F: Compute your new rating From steps (A), (D), and (E):- Your current rating is 1500 (Ro). Your total winning expectancy for your last event was 1.89 (We). The score you achieved for that event was 2.5 (W). Your k-factor is 25 (K). Your new rating will be determined by the k-factor (K) multiplied by the difference between your real score (W) and your expected score (We). Expressed as a formula this gives K * (W - We), which we'll call D. Plugging in the numbers gives 25 * (2.5 - 1.89) = 15 (D, rounded to the nearest whole number). Your new rating is your old rating (Ro) plus the result of that last calculation (D). Expressed as a formula this gives Ro + D. Plugging in the numbers gives 1500 + 15 = 1515. Congratulations! Your rating has increased by 15 points and you are now rated 1515. As an exercise, go back to step (A) and assume that you won your last game against the player rated 1700. What would your new rating be? Your current rating (Ro) hasn't changed; it's still 1500. Your total winning expectancy (We) also hasn't changed; it's 1.89. Your k-factor rarely changes. The only thing that changes is your score (W). It's 3.5 instead of 2.5. Ro + (K * (W - We)) = 1500 + 25 * (3.5 - 1.89) = 1540. Wins against higher rated players mean big rating gains! G: Determine your performance per game It's also possible to calculate a rating if you have no current rating. Let's go back to our initial example. From step (A) : The results in your last event were +1400 -1650 +1575 =1625 -1700. The performance rating for a single game is based on your opponent's rating adjusted as follows:- Opponent's rating plus 400 points if you win. Opponent's rating if you draw. Opponent's rating minus 400 points if you lose. In your first game, you achieved a performance of 1400 + 400 for a rating of 1800. In your second game, you achieved 1650 - 400 for a rating of 1250. Continuing for all 5 games, we calculate that the performances were 1800 1250 1975 1625 1300. H: Calculate your performance rating for the event From step (G) : Your game performances were 1800 1250 1975 1625 1300. Your performance rating (Rp) for the event is the average of your game performances. Our example uses five games, so you calculate. 1800 + 1250 + 1975 + 1625 + 1300 = 7950, and 7950 / 5 = 1590. Your performance rating for the event is 1590. If you're mathematically inclined, you might confirm that the performance rating is the average of your opponents' ratings (Ra) plus 400 times the difference between your wins and losses divided by the number of games (Gms). Expressed as a formula this gives Rp = Ra + 400 * (Wins - Losses) / Gms. This means that if you score 50% in an event, your performance rating is simply the average of your opponents' ratings. If you have a perfect score, your performance rating is the average of your opponents' ratings plus 400. How do you know you've had a great tournament? When your performance rating is much higher than your official rating!

Related Resources • Chess Ratings • Rating Calculator • Tools to Calculate Your Rating