{ "openapi": "3.1.1", "info": { "title": "Elo/Glicko Rating Lab API", "version": "1.0.0", "summary": "Rate players from game results with Elo, Glicko-1 and Glicko-2; history chart and win odds.", "description": "Every endpoint performs the same calculation as the human page and returns inputs, result, units, assumptions, sources, warnings and computedAt. MCP endpoint: /mcp." }, "servers": [ { "url": "https://eloglickoratinglab.usefulweb.site" } ], "paths": { "/api/v1/calculate": { "post": { "operationId": "calculate", "summary": "Rate players from game results with Elo, Glicko-1 and Glicko-2; history chart and win odds.", "description": "Enter game results (win, draw, loss) grouped into rating periods and see the ratings under Elo (fixed K or FIDE-style K), Glicko-1 and Glicko-2, implemented exactly as in Mark Glickman's papers, with the rating deviation and volatility, a rating history chart and the win probability between any two players.\n\nMethodology:\n- Elo: expected score E = 1 / (1 + 10^((R_opp − R)/400)); after every game R ← R + K(S − E) for both players, in input order. The FIDE-style option uses K = 40 for a player's first 30 games, then 20, and 10 once the player has reached 2400 (the age rule is not modelled).\n- Glicko-1 (Glickman 1999): all games of a period are rated together with each player's pre-period values; RD shrinks with games and grows by c per idle period: RD = min(√(RD² + c²·t), 350).\n- Glicko-2 (Glickman, \"Example of the Glicko-2 system\"): steps 1–8 on the μ/φ scale (÷ 173.7178) with the Illinois algorithm (ε = 0.000001) for the new volatility; players without games only have φ increased to √(φ² + σ²).\n- Win probability: Elo uses E above; Glicko uses E = 1 / (1 + 10^(−g(√(RD_A² + RD_B²))·(R_A − R_B)/400)) with g(RD) = 1 / √(1 + 3q²RD²/π²), q = ln 10 / 400. Draws count as half a win.", "tags": [ "fun" ], "x-mcp-tool": "elo_glicko_rating_lab", "requestBody": { "required": true, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/EloGlickoRatingLabInput" }, "examples": { "example1": { "summary": "Glickman's worked example (1500 vs 1400, 1550, 1700)", "value": { "games": [ { "period": 1, "player": "Player", "opponent": "A", "score": "1" }, { "period": 1, "player": "Player", "opponent": "B", "score": "0" }, { "period": 1, "player": "Player", "opponent": "C", "score": "0" } ], "players": [ { "name": "Player", "rating": 1500, "rd": 200, "volatility": 0.06 }, { "name": "A", "rating": 1400, "rd": 30 }, { "name": "B", "rating": 1550, "rd": 100 }, { "name": "C", "rating": 1700, "rd": 300 } ], "tau": 0.5 } }, "example2": { "summary": "Small club league over three periods", "value": { "games": [ { "period": 1, "player": "Ana", "opponent": "Ben", "score": "1" }, { "period": 1, "player": "Cleo", "opponent": "Dev", "score": "0.5" }, { "period": 2, "player": "Ana", "opponent": "Cleo", "score": "0" }, { "period": 2, "player": "Ben", "opponent": "Dev", "score": "1" }, { "period": 3, "player": "Ana", "opponent": "Dev", "score": "1" }, { "period": 3, "player": "Cleo", "opponent": "Ben", "score": "1" } ], "eloK": "fide" } } } } } }, "responses": { "200": { "description": "Calculation result envelope.", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/EloGlickoRatingLabResult" } } } }, "400": { "description": "Malformed JSON body.", "content": { "application/problem+json": { "schema": { "$ref": "#/components/schemas/Problem" } } } }, "422": { "description": "Invalid input (see errors[]).", "content": { "application/problem+json": { "schema": { "$ref": "#/components/schemas/Problem" } } } }, "429": { "description": "Rate limit exceeded (see Retry-After).", "content": { "application/problem+json": { "schema": { "$ref": "#/components/schemas/Problem" } } } } } } }, "/api/v1/tool": { "get": { "operationId": "getToolDefinition", "summary": "Inputs, output schema and examples for this tool", "responses": { "200": { "description": "Tool definition.", "content": { "application/json": { "schema": { "type": "object" } } } } } } } }, "components": { "schemas": { "Problem": { "type": "object", "description": "RFC 9457 problem details. 422 responses include per-field `errors`.", "required": [ "type", "title", "status", "detail" ], "properties": { "type": { "type": "string" }, "title": { "type": "string" }, "status": { "type": "integer" }, "detail": { "type": "string" }, "code": { "type": "string" }, "errors": { "type": "array", "items": { "type": "object", "required": [ "field", "message" ], "properties": { "field": { "type": "string" }, "message": { "type": "string" } } } } } }, "EloGlickoRatingLabInput": { "type": "object", "additionalProperties": false, "properties": { "games": { "title": "Games", "description": "One row per game. The score is from the first player's point of view. Games with the same period number form one Glicko rating period.", "type": "array", "minItems": 1, "maxItems": 200, "items": { "type": "object", "additionalProperties": false, "properties": { "period": { "title": "Period", "type": "integer", "minimum": 1, "maximum": 10000, "default": 1 }, "player": { "title": "Player", "type": "string", "maxLength": 40 }, "opponent": { "title": "Opponent", "type": "string", "maxLength": 40 }, "score": { "title": "Result for player", "type": "string", "enum": [ "1", "0.5", "0" ], "default": "1" } }, "required": [ "player", "opponent", "score" ] } }, "players": { "title": "Starting ratings (optional)", "description": "Players not listed start at 1500, RD 350, volatility 0.06 (Glickman's defaults for unrated players).", "type": "array", "maxItems": 100, "items": { "type": "object", "additionalProperties": false, "properties": { "name": { "title": "Name", "type": "string", "maxLength": 40 }, "rating": { "title": "Rating", "type": "number", "minimum": 0, "maximum": 4000 }, "rd": { "title": "RD", "type": "number", "minimum": 1, "maximum": 350 }, "volatility": { "title": "Volatility σ", "type": "number", "minimum": 0.0001, "maximum": 1 } }, "required": [ "name" ] } }, "eloK": { "title": "Elo K-factor", "type": "string", "enum": [ "10", "16", "20", "24", "32", "40", "fide" ], "default": "32" }, "tau": { "title": "Glicko-2 τ (volatility constraint)", "description": "Glickman suggests 0.3–1.2; smaller values change the volatility more slowly.", "type": "number", "minimum": 0.2, "maximum": 1.2, "default": 0.5 }, "glickoC": { "title": "Glicko-1 c (RD growth per idle period)", "description": "34.6 lets an RD of 50 grow back to 350 in 100 periods.", "type": "number", "minimum": 0, "maximum": 200, "default": 34.6 }, "playerA": { "title": "Win probability: player A", "description": "Default: the two highest-rated players.", "type": "string", "maxLength": 40 }, "playerB": { "title": "Win probability: player B", "type": "string", "maxLength": 40 }, "chartSystem": { "title": "Chart", "type": "string", "enum": [ "glicko2", "glicko1", "elo" ], "default": "glicko2" } }, "required": [ "games" ] }, "EloGlickoRatingLabResult": { "type": "object", "additionalProperties": false, "required": [ "schemaVersion", "tool", "computedAt", "inputs", "summary", "result", "units", "assumptions", "sources", "warnings", "presentation", "links" ], "properties": { "schemaVersion": { "type": "string", "const": "1.0" }, "tool": { "type": "object", "additionalProperties": false, "required": [ "id", "name", "version" ], "properties": { "id": { "type": "string" }, "name": { "type": "string" }, "version": { "type": "string" } } }, "computedAt": { "type": "string", "format": "date-time" }, "inputs": { "type": "object", "description": "Normalised inputs actually used, including applied defaults." }, "summary": { "type": "string" }, "result": { "type": "object", "required": [ "players", "periods", "winProbability" ], "properties": { "periods": { "type": "array", "items": { "type": "integer" } }, "players": { "type": "array", "items": { "type": "object", "required": [ "name", "games", "score", "elo", "glicko1", "glicko2" ], "properties": { "name": { "type": "string" }, "games": { "type": "integer" }, "score": { "type": "number" }, "elo": { "type": "number" }, "glicko1": { "type": "object", "required": [ "rating", "rd" ], "properties": { "rating": { "type": "number" }, "rd": { "type": "number" } } }, "glicko2": { "type": "object", "required": [ "rating", "rd", "volatility" ], "properties": { "rating": { "type": "number" }, "rd": { "type": "number" }, "volatility": { "type": "number" } } } } } }, "history": { "type": "array", "items": { "type": "object", "required": [ "period", "player", "elo", "glicko1", "glicko2", "rd2" ], "properties": { "period": { "type": "integer" }, "player": { "type": "string" }, "elo": { "type": "number" }, "glicko1": { "type": "number" }, "glicko2": { "type": "number" }, "rd2": { "type": "number" } } } }, "winProbability": { "type": [ "object", "null" ], "properties": { "a": { "type": "string" }, "b": { "type": "string" }, "elo": { "type": "number" }, "glicko1": { "type": "number" }, "glicko2": { "type": "number" } } } } }, "units": { "type": "object", "additionalProperties": { "type": "string" } }, "assumptions": { "type": "array", "items": { "type": "string" } }, "sources": { "type": "array", "items": { "type": "object", "additionalProperties": false, "required": [ "title" ], "properties": { "title": { "type": "string" }, "url": { "type": "string" }, "publisher": { "type": "string" }, "retrievedAt": { "type": "string" }, "note": { "type": "string" } } } }, "warnings": { "type": "array", "items": { "type": "string" } }, "presentation": { "type": "array", "items": { "type": "object" }, "description": "Display blocks used by the human page (same data)." }, "links": { "type": "object", "additionalProperties": false, "required": [ "human", "api", "openapi", "methodology" ], "properties": { "human": { "type": "string", "format": "uri" }, "api": { "type": "string", "format": "uri" }, "openapi": { "type": "string", "format": "uri" }, "methodology": { "type": "string", "format": "uri" } } } } } } } }