{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"elo-rating"},"result":{"entity_type":"calculator","id":"elo-rating","calculator_id":"elo-rating","canonical_url":"https://tttkmbb.com/gaming/elo-rating","name":"Elo Rating Calculator","title":"Elo Rating Calculator – Expected Score and New Ratings after a Game with a Chosen K-factor","category":"gaming","category_name":"Games & Betting Math","tool_name":"calculate_elo_rating","featured_mcp_tool":false,"description":"Computes the expected score of two players from their Elo ratings with the logistic formula E = 1/(1 + 10^((R_b − R_a)/400)) and the rating change of each after a win, draw or loss for a given K-factor.","use_when":"You want the win expectancy between two rated players or the new ratings after a result, for chess or any Elo-based ranking (games, sports, matchmaking).","do_not_use_when":"The rating system uses a different scale or rating deviations (Glicko, TrueSkill), or you need ratings after a whole tournament with FIDE's rounding and 400-point rule. Mathematics only; not gambling advice.","inputs":[{"name":"rating_a","label":"Rating of player A","type":"number","required":true,"min":0,"max":4000,"description":"Current Elo rating of player A.","example":1500},{"name":"rating_b","label":"Rating of player B","type":"number","required":true,"min":0,"max":4000,"description":"Current Elo rating of player B (the opponent).","example":1600},{"name":"result","label":"Result","type":"enum","required":true,"values":[{"value":"a_wins","label":"A wins (1–0)","aliases":["a","win","1-0","1"]},{"value":"draw","label":"Draw (½–½)","aliases":["d","tie","0.5","1/2-1/2"]},{"value":"b_wins","label":"B wins (0–1)","aliases":["b","loss","0-1","0"]}],"description":"Outcome of the game from player A's point of view.","example":"a_wins"},{"name":"k_factor","label":"K-factor","type":"number","required":false,"default":32,"min":1,"max":200,"description":"Maximum rating change per game. FIDE uses 40 (new players and juniors), 20 (established) and 10 (rated 2400+); 32 is common in club and online systems.","example":32}],"outputs":[{"name":"expected_score_a","label":"Expected score of A","type":"number","decimals":4,"description":"E_a = 1/(1 + 10^((rating_b − rating_a)/400))."},{"name":"expected_score_b","label":"Expected score of B","type":"number","decimals":4,"description":"E_b = 1 − E_a."},{"name":"new_rating_a","label":"New rating of A","type":"number","decimals":2,"description":"rating_a + k_factor × (S_a − E_a) with S_a = 1, 0.5 or 0."},{"name":"new_rating_b","label":"New rating of B","type":"number","decimals":2,"description":"rating_b + k_factor × (S_b − E_b)."},{"name":"change_a","label":"Rating change of A","type":"number","decimals":2,"description":"k_factor × (S_a − E_a)."},{"name":"change_b","label":"Rating change of B","type":"number","decimals":2,"description":"k_factor × (S_b − E_b) = −change_a."},{"name":"win_probability_a_percent","label":"Win expectancy of A","type":"number","unit":"%","decimals":2,"description":"E_a × 100: A's expected score as a percentage (the win probability when draws are impossible)."}],"input_schema":{"type":"object","properties":{"rating_a":{"description":"Current Elo rating of player A.","type":"number","minimum":0,"maximum":4000,"examples":[1500]},"rating_b":{"description":"Current Elo rating of player B (the opponent).","type":"number","minimum":0,"maximum":4000,"examples":[1600]},"result":{"description":"Outcome of the game from player A's point of view.","type":"string","enum":["a_wins","draw","b_wins"],"examples":["a_wins"]},"k_factor":{"description":"Maximum rating change per game. FIDE uses 40 (new players and juniors), 20 (established) and 10 (rated 2400+); 32 is common in club and online systems.","type":"number","minimum":1,"maximum":200,"default":32,"examples":[32]}},"additionalProperties":false,"required":["rating_a","rating_b","result"]},"output_schema":{"type":"object","properties":{"expected_score_a":{"description":"E_a = 1/(1 + 10^((rating_b − rating_a)/400)).","type":"number"},"expected_score_b":{"description":"E_b = 1 − E_a.","type":"number"},"new_rating_a":{"description":"rating_a + k_factor × (S_a − E_a) with S_a = 1, 0.5 or 0.","type":"number"},"new_rating_b":{"description":"rating_b + k_factor × (S_b − E_b).","type":"number"},"change_a":{"description":"k_factor × (S_a − E_a).","type":"number"},"change_b":{"description":"k_factor × (S_b − E_b) = −change_a.","type":"number"},"win_probability_a_percent":{"description":"E_a × 100: A's expected score as a percentage (the win probability when draws are impossible). Unit: %.","type":"number","x-unit":"%"}}},"formula":"E_a = 1 / (1 + 10^((rating_b − rating_a) / 400)); E_b = 1 − E_a; new_rating_a = rating_a + k_factor × (S_a − E_a); new_rating_b = rating_b + k_factor × (S_b − E_b); S = 1 for a win, 0.5 for a draw, 0 for a loss","method":"Standard logistic Elo formula (Elo 1978) in which a 400-point difference gives the stronger player an expected score of about 0.91. FIDE reads E from a table and counts differences above 400 points as 400; both differ from this formula by at most a few hundredths of a rating point per game. Probability mathematics only; not gambling advice.","sources":[{"name":"Elo rating system (Wikipedia)","url":"https://en.wikipedia.org/wiki/Elo_rating_system","type":"reference","retrieved_at":"2026-09-24"},{"name":"FIDE Handbook – B.02 FIDE Rating Regulations (fide.com)","url":"https://handbook.fide.com/","type":"standard","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"1500 beats 1600, K = 32","inputs":{"rating_a":1500,"rating_b":1600,"result":"a_wins","k_factor":32},"expected":{"expected_score_a":0.3599,"expected_score_b":0.6401,"new_rating_a":1520.48,"new_rating_b":1579.52,"change_a":20.48,"change_b":-20.48,"win_probability_a_percent":35.99},"url":"https://tttkmbb.com/api/v1/calculate/elo-rating?rating_a=1500&rating_b=1600&result=a_wins&k_factor=32"},{"name":"2000 draws with 1800, K = 20","inputs":{"rating_a":2000,"rating_b":1800,"result":"draw","k_factor":20},"expected":{"expected_score_a":0.7597,"change_a":-5.19,"new_rating_a":1994.81,"new_rating_b":1805.19},"url":"https://tttkmbb.com/api/v1/calculate/elo-rating?rating_a=2000&rating_b=1800&result=draw&k_factor=20"}],"faq":[{"q":"Which K-factor should I use?","a":"The one your rating system prescribes: FIDE 40/20/10 by experience and rating, USCF a rating-dependent formula, many online chess and game servers 16–32. A larger K makes ratings move faster."},{"q":"Does the expected score equal the win probability?","a":"Only when draws cannot happen. In chess E_a = P(win) + ½·P(draw), so a 0.36 expected score can be, for example, 25 % wins and 22 % draws."},{"q":"Why is FIDE's published change slightly different?","a":"FIDE reads the expected score from a table rounded to two decimals, caps rating differences at 400 points and rounds the sum of a tournament's changes, so individual games can differ by a fraction of a point."}],"tags":["elo rating","elo calculator","chess rating","expected score","k factor","rating change"],"related":[{"calculator_id":"bet-expected-value","reason":"Use the win expectancy as the probability estimate for a price on the game."},{"calculator_id":"probability-of-events","reason":"Combine win probabilities of several games."},{"calculator_id":"percentage","reason":"Percent arithmetic on scores and expectancies."}],"links":{"html":"https://tttkmbb.com/gaming/elo-rating","markdown":"https://tttkmbb.com/gaming/elo-rating.md","json":"https://tttkmbb.com/gaming/elo-rating.json","api":"https://tttkmbb.com/api/v1/calculate/elo-rating","schema":"https://tttkmbb.com/api/v1/calculators/elo-rating","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T03:45:41Z","next_actions":[{"tool":"run_calculator","calculator_id":"elo-rating","reason":"Run Elo Rating Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/gaming/elo-rating.md"}}