ELO

ELO is a small TypeScript library for calculating Elo ratings — the system used in chess and many other competitive games to measure relative skill.

It follows FIDE rules out of the box: K-factors by age, games played, and rating tier; a 400-point rating difference cap; and performance rating calculation. Zero runtime dependencies.

Why this library?

Most Elo libraries on npm give you the basic formula and nothing else. If you're building a chess platform or any app that follows FIDE rules, you'd have to implement the rest yourself. This library ships it all out of the box:

• FIDE K-factor rules — K=40 for new players (≤ 30 games) and juniors (age < 18, rating < 2300), K=10 for players who have ever reached 2400, K=20 for everyone else. Includes the §8.3.3 per-period cap: if K × n > 700, K is reduced so the total change stays within bounds.
• Game type awareness — blitz and rapid games always use K=20, regardless of rating or experience, matching FIDE §B02.
• Official FIDE scoring table — win probabilities come from the discrete §8.1.2 lookup table, not an approximation formula. Rating differences above 400 are clamped as required by §8.3.1; players rated 2650 or above are exempt from this cap (effective 1 October 2025). Most libraries skip both rules.
• Performance rating — calculates a player's FIDE performance rating (§8.2.3) over a series of games. No other Elo library on npm implements this.
• Initial rating calculation — computes a new player's first published rating (§8.2) using the FIDE hypothetical-opponent adjustment and 2200 cap. No other Elo library on npm implements this.

If you don't need FIDE compliance, any Elo library will do. If you do, this is the one.

Installation

npm install @echecs/elo

Quick Start

import { update } from '@echecs/elo';

// Two players both rated 1400. Player A wins.
const [playerA, playerB] = update(1400, 1400, 1);

console.log(playerA); // 1410
console.log(playerB); // 1390

Usage

Basic — when you just need new ratings after a game:

import { update } from '@echecs/elo';

const [newRatingA, newRatingB] = update(1400, 1400, 1); // → [1410, 1390]

Player options — pass a player object when you need to apply FIDE K-factor rules for age or experience:

import { update } from '@echecs/elo';

// Young player (age < 18, rating < 2300) gets K=40
const [newRatingA, newRatingB] = update({ age: 15, rating: 1400 }, 1400, 1); // → [1420, 1390]

// New player (≤ 30 games played) also gets K=40
const [newRatingC, newRatingD] = update(
  { gamesPlayed: 10, rating: 1400 },
  1400,
  1,
); // → [1420, 1390]

Game options — pass a game object as the third argument when the game type affects the K-factor:

import { update } from '@echecs/elo';

// Blitz and rapid games always use K=20
const [newRatingA, newRatingB] = update(2400, 2400, {
  gameType: 'blitz',
  result: 1,
}); // → [2410, 2390]

K-factor cap — pass gamesInPeriod when a player has played many games in the current rating period and the §8.3.3 cap applies:

import { update } from '@echecs/elo';

// New player (K=40) with 18 games played in the period — K is capped to 38
const [newRatingA, newRatingB] = update(
  { gamesInPeriod: 18, gamesPlayed: 0, rating: 1400 },
  1400,
  1,
); // → [1419, 1390]

Performance rating — use performance() to calculate a player's FIDE performance rating over a tournament:

import { performance } from '@echecs/elo';

const rating = performance([
  { opponentRating: 1600, result: 1 },
  { opponentRating: 1600, result: 0.5 },
  { opponentRating: 1600, result: 0 },
]); // 1600

Initial rating — use initial() to calculate a new (unrated) player's first FIDE rating. If the player scored zero points across their entire first event, omit all games from that event before calling (§8.2.1):

import { initial } from '@echecs/elo';

const rating = initial([
  { opponentRating: 1600, result: 1 },
  { opponentRating: 1500, result: 0.5 },
  { opponentRating: 1700, result: 0 },
  { opponentRating: 1600, result: 1 },
  { opponentRating: 1550, result: 1 },
]); // → 1752

API

Full API reference is available at https://mormubis.github.io/elo/

Functions

update(a, b, resultOrOptions)

Updates the Elo ratings of two players after a game. Returns a tuple [ratingA, ratingB] with the new ratings rounded per FIDE §8.3.4.

function update(
  a: number | PlayerOptions,
  b: number | PlayerOptions,
  resultOrOptions: Result | GameOptions,
): [ratingA: number, ratingB: number];

kFactor(options)

Returns the FIDE K-factor for a player given their profile. Decision order:

1. gameType === 'blitz' | 'rapid' → 20
2. gamesPlayed <= 30 or (age < 18 && rating < 2300) → 40
3. rating >= 2400 || everHigher2400 → 10
4. otherwise → 20

If gamesInPeriod is set and K × gamesInPeriod > 700, K is reduced to Math.floor(700 / gamesInPeriod) per §8.3.3.

function kFactor(options: KFactorOptions): number;

expected(a, b)

Returns the expected win probability for player A against player B, using the FIDE §8.1.2 discrete lookup table. Rating differences are clamped to ±400 unless either player is rated ≥ 2650 (§8.3.1).

function expected(a: number, b: number): number;

delta(actual, expected, k)

Returns the raw rating change: k * (actual - expected). Use this when you need the unrounded delta before applying it to a rating.

function delta(actual: number, expected: number, k: number): number;

performance(games)

Calculates a player's FIDE performance rating (§8.2.3) over a series of games. Throws RangeError if games is empty or contains invalid result values.

function performance(games: ResultAndOpponent[]): number;

initial(games)

Calculates an unrated player's first FIDE published rating (§8.2). Injects two hypothetical 1800-rated draws, caps the result at 2200. Throws RangeError if games is empty.

function initial(games: ResultAndOpponent[]): number;

Types

Result

type Result = 0 | 0.5 | 1;

Game outcome from the perspective of player A: 1 = win, 0.5 = draw, 0 = loss.

GameType

type GameType = 'blitz' | 'rapid' | 'standard';

GameOptions

Options for a single game passed as the third argument to update().

interface GameOptions {
  gameType?: GameType;
  result: Result;
}

PlayerOptions

Per-player options for update(). All fields except rating are optional.

interface PlayerOptions {
  age?: number; // player's age — affects K-factor for juniors (< 18)
  everHigher2400?: boolean; // whether the player has ever been rated ≥ 2400
  gamesInPeriod?: number; // games played this rating period — used for §8.3.3 cap
  gamesPlayed?: number; // total career games — new players (≤ 30) get K=40
  k?: number; // override computed K-factor entirely
  rating: number; // current rating
}

The k field bypasses all FIDE K-factor logic and uses the supplied value directly.

KFactorOptions

Options for kFactor(). Mirrors PlayerOptions minus the k override.

interface KFactorOptions {
  age?: number;
  everHigher2400?: boolean;
  gameType?: GameType;
  gamesInPeriod?: number;
  gamesPlayed?: number;
  rating: number;
}

ResultAndOpponent

A single game result used by performance() and initial().

interface ResultAndOpponent {
  opponentRating: number;
  result: Result;
}