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/

Contributing

Contributions are welcome. Please read CONTRIBUTING.md for guidelines on how to submit issues and pull requests.