Add chess-style Elo ratings for players

Each player's rating starts at 1500 and updates transactionally with
every finished match: a team's rating is the mean of its two members
and the standard K=32 formula decides the zero-sum delta applied to
both members of a team. Ratings are per game type in a new
player_rating table; match_player records each match's elo_delta.

- GET /api/leaderboard exposes elo and sorts by it
- GET /api/me/matches includes per-player elo deltas
- new GET /api/me/ratings returns the caller's rating per game type
- frontend: Elo column on the leaderboard, per-match delta in the
  history page, current rating in the lobby
- python -m tavolo.backfill_elo recomputes all ratings from the
  recorded match history (one-off backfill for existing matches)

server/README.md

@@ -133,12 +133,31 @@ loggers:
   scoped per game), both teams' final scores, winner, target score, hands
   played, start/finish timestamps.
 - `match_player` — one row per participant: the OIDC `sub`, display name,
-  seat, team and whether they won. Unique per `(match, user_sub)`.
+  seat, team, whether they won and the Elo change the match produced
+  (`elo_delta`). Unique per `(match, user_sub)`.
+- `player_rating` — current Elo rating per `(user_sub, game_type)`, with
+  the number of rated matches played.
 
 When a match ends, the result is written transactionally to Postgres
 (once, guarded by a flag on the Redis state); the finished state stays in
 Redis until its TTL expires so clients can still fetch the final board.
 
+### Elo ratings
+
+Players carry a chess-style Elo rating per game type (`tavolo.elo`):
+everyone starts at 1500, a team's rating is the mean of its two members,
+and the standard formula `E = 1 / (1 + 10 ** ((R_opp - R_team) / 400))`
+with `K = 32` decides how many points the match result moves — the same
+delta for both members of a team, zero-sum between teams. Ratings update
+in the same transaction as the match result. To recompute every rating
+from the recorded match history (e.g. to backfill matches recorded before
+ratings existed):
+
+```sh
+DATABASE_URL=postgres://tavolo:tavolo@localhost:5432/tavolo \
+  .venv/bin/python -m tavolo.backfill_elo
+```
+
 ## REST API
 
 All endpoints except `/api/health`, `/api/docs`, `/api/openapi.json`,
@@ -150,8 +169,9 @@ All endpoints except `/api/health`, `/api/docs`, `/api/openapi.json`,
 | `POST` | `/api/games` | Create a lobby game. Optional body `{"game_type": "scopone_scientifico", "target_score": 11, "napola": true}`. Returns `{id, join_code}` |
 | `POST` | `/api/games/join` | Join with `{"code": "ABC123"}`. The fourth player triggers the deal |
 | `GET` | `/api/games/{id}` | Personalized snapshot (only your own hand is visible) |
-| `GET` | `/api/me/matches` | Cursor-paginated match history with final scores (`?limit=&cursor=&game_type=`) |
+| `GET` | `/api/me/matches` | Cursor-paginated match history with final scores and per-player Elo deltas (`?limit=&cursor=&game_type=`) |
-| `GET` | `/api/leaderboard` | Aggregated wins / matches / team points per player (`?game_type=`) |
+| `GET` | `/api/me/ratings` | The caller's Elo rating per game type |
+| `GET` | `/api/leaderboard` | Elo rating, aggregated wins / matches / team points per player, sorted by Elo (`?game_type=`) |
 
 ## WebSocket protocol
 
@@ -271,8 +291,10 @@ src/tavolo/
 ├── openapi.py          # shared OpenAPI parameter fragments
 ├── tortoise_mixin.py   # TortoiseORM lifecycle (HTTP + WebSocket)
 ├── aerich_config.py    # aerich CLI configuration
-├── models.py           # Match, MatchPlayer (Postgres)
+├── models.py           # Match, MatchPlayer, PlayerRating (Postgres)
-├── stats.py            # finished match -> Postgres persistence
+├── elo.py              # chess-style Elo math (1500 start, K=32)
+├── stats.py            # finished match -> Postgres persistence + Elo update
+├── backfill_elo.py     # recompute all ratings from the match history
 ├── store.py            # Redis / in-memory live-game store (+ deadline queue)
 ├── deadlines.py        # connection-independent timeout scheduler
 ├── ws.py               # WebSocket live-play endpoint
@@ -283,5 +305,5 @@ src/tavolo/
 └── routes/
     ├── health.py       # GET /api/health
     ├── games.py        # lobby: create / join / snapshot
-    └── stats.py        # match history + leaderboard
+    └── stats.py        # match history + leaderboard + Elo ratings
 ```

server/migrations/models/2_20260918120620_elo.py

@@ -0,0 +1,55 @@
+from tortoise import BaseDBAsyncClient
+
+RUN_IN_TRANSACTION = True
+
+
+async def upgrade(db: BaseDBAsyncClient) -> str:
+    return """
+        CREATE TABLE IF NOT EXISTS "player_rating" (
+    "id" UUID NOT NULL PRIMARY KEY,
+    "user_sub" VARCHAR(255) NOT NULL,
+    "game_type" VARCHAR(32) NOT NULL,
+    "rating" INT NOT NULL,
+    "matches_played" INT NOT NULL,
+    "updated_at" TIMESTAMPTZ NOT NULL,
+    CONSTRAINT "uid_player_rati_user_su_655b53" UNIQUE ("user_sub", "game_type")
+);
+CREATE INDEX IF NOT EXISTS "idx_player_rati_game_ty_3326d1" ON "player_rating" ("game_type", "rating");
+COMMENT ON TABLE "player_rating" IS 'Current Elo rating of one player for one game type.';
+        ALTER TABLE "match_player" ADD "elo_delta" SMALLINT;"""
+
+
+async def downgrade(db: BaseDBAsyncClient) -> str:
+    return """
+        ALTER TABLE "match_player" DROP COLUMN "elo_delta";
+        DROP TABLE IF EXISTS "player_rating";"""
+
+
+MODELS_STATE = (
+    "eJztmltv4jgUgP9KlKeuNFsBvY1Wq5WAUg07pVSF7q6mqiyTGLAa7IztbAd1+9/Xdm7EuR"
+    "RoYUrFyww59nHsz87xufTJnlEXefywB4UztX+znmwCZ0j+yDZ8smzo+6lYCQQceWHPpMuI"
+    "CwYdIYVj6HEkRS7iDsO+wJSork3LoTPfQwK5llaz6NiiBKn/xBRZDE0wF4jJ5omchyXmPu"
+    "KHamyXOnJwTCavGyYg+HuAgKATJDsyOdjdvRRj4qIfiMeP/gMYY+S5GSDYVQNoOVADKtnt"
+    "bff8QvdUUxwBh3rBjKS9/bmYUpJ0DwLsHiod1TZBBDEol7CAiwSeF2GNReGMpUCwACVTdV"
+    "OBi8Yw8BR0+/dxQBzF2tJvUv8c/xFNbaEbAFf9IRh0hgDYuT1SUzB4RyKHErW/mAgF6uk5"
+    "HDcFoqW2ekH7S/Pm4Oj0F42AcjFhulHjsp+1IhQwVNXQU8pqv0JeOdjtKWTFsDNKBnM55X"
+    "Vox4Iq3Nyhvjx1gDsYEYHH2KGbgi0/sh/AQ2Qi1Fd61KiA/1fzJuTf0Pyp/CLD7/Qqamno"
+    "JrUNKXaB4AxAuRLKCsgPZtDzukQU0zd1jQ2QS3ibDUhtSgw3xrcJ4BM1iV+PGmenn2Wrnq"
+    "N6OKsgP+g1Ly+7V8MitqNXsB3t2ZaxfcRELh0oTKsYDENtUyZju1QzJqK+hIWolxqIes4+"
+    "QCZvzDXPsKG7P8NZtlNIXA58D85RgYtRzdbU3bPNsuXy8Ml1AyjyZM8lEYFnqJhsVtPg6k"
+    "aqh/GPHaRcAXPY7XUGw2bvWg0/4/y7p3k1hx3V0tDSuSE9ODWsSTKI9Xd3+MVSj9a3/lXH"
+    "dAqTfsNvtpoTDAQFhD4C6C4yicWxKLPNY0wwn661z4bqfqPf3UariGz8sBAtKMEIOg+PkL"
+    "kg05KeCG0SGc+fhlakePH1BnlQs8xv+2Lwe61H2t19T6V2GMRooLRBy4jmm2aNmSmBBE70"
+    "ktS71ZsKkJWlE1KiLyQVwouNLZdbuJb2GjvY13saJwQCjpiFif6th8wnE1bQK8ge3KXpD6"
+    "UDeDCy7/cphfeUUkj2ZYUAYVFnawmFrQUHjZOTJcID2as0QNBtWVfLxVx9rkA/r4Da1PuA"
+    "wVijVluGd61Wzlu1Ga4tKnJ2qsOFWGcfJuRTNKuc2X3ioOSc5hIHj6F/ZfhglHoIkpLcTK"
+    "FHNpIqO8i2Amar37/MuN2t7tDAettrdWLashMWWpw/vsijcuqegKvag4ziWkYhusTeC+83"
+    "tAmhB7qai7ao85aO2vs9xS/4ZbnYzeCbh3tBGcIT8hXNNeKunAgkTpFnYFYodxNqLjyTYg"
+    "Yfk2ghc6bk6uWaUWgH2s1Bu3nesZ/L4+FNRnphFHcjwya9yFyol2n/VBXrhVEeYGnXF4O9"
+    "dsAYIsLqeNQK9eLILRzMGlOmH5P6bz7wW3OMwiBwMV5Iq5FmIHiXrVRGC77fx4f7+PBnW6"
+    "MtBIjvt7T/E0m/fSk/NaNZxqVOYKqwvbCwflKrbdYFbNSPz44/H50eJ35gIqlyBkv8QFRe"
+    "oCvlmlfcHt9dgRv4qrCyTt0mq/kByzY2Q9DtE28e3bu7W8ZJig5LVnE26bU2EcPFf+kYtV"
+    "R6qjDt85KLWr7Pb/w3iKX2p9AfLLA5kVP3Okdw8zH9K21Ouf/3L2IcF6Wpyr2SBZUP6JNs"
+    "xPtTH9UKhKPuH5BufaliQL2iGFDPFwPkGwUiBZfon4P+VTHhBRXz9sSOsP6zPMx3sSxQAV"
+    "fByFyRMdODXvMfE3f7st8y7z41QKsorbXNy+z5fy/uTSo="
+)

server/src/tavolo/backfill_elo.py

@@ -0,0 +1,66 @@
+"""Recompute every Elo rating from the recorded match history.
+
+Ratings are deterministic given the finished matches, so this replays all
+matches in chronological order and rewrites the ``player_rating`` table
+and each ``match_player.elo_delta`` from scratch. Run once after
+deploying the ratings feature to backfill pre-existing matches, or any
+time ratings need to be rebuilt::
+
+    python -m tavolo.backfill_elo
+"""
+from __future__ import annotations
+
+import asyncio
+from collections import defaultdict
+from logging import getLogger
+from typing import Dict, List
+
+from tortoise.transactions import in_transaction
+
+from .config import settings
+from .stats import apply_elo
+from .tortoise_mixin import TortoiseMixin
+
+log = getLogger(__name__)
+
+
+async def backfill_elo() -> int:
+    """Rebuild all ratings; returns the number of matches replayed."""
+    from .models import Match, MatchPlayer, PlayerRating
+
+    replayed = 0
+    async with in_transaction():
+        await PlayerRating.all().delete()
+        matches = await Match.all().order_by("finished_at", "id")
+        for match in matches:
+            players = await MatchPlayer.filter(match_id=match.id)
+            team_members: Dict[str, List[str]] = defaultdict(list)
+            for player in players:
+                team_members[player.team].append(player.user_sub)
+            deltas = await apply_elo(
+                match.game_type, match.winner_team, team_members
+            )
+            for player in players:
+                player.elo_delta = deltas[player.user_sub]
+                await player.save()
+            replayed += 1
+    return replayed
+
+
+async def _main() -> None:
+    mixin = TortoiseMixin(
+        database_url=settings.database_url,
+        models_modules=["tavolo.models"],
+    )
+    await mixin._bind()
+    try:
+        replayed = await backfill_elo()
+        log.info("elo backfill complete: %d matches replayed", replayed)
+        print(f"Recomputed ratings from {replayed} matches.")
+    finally:
+        if mixin._ctx is not None:
+            await mixin._ctx.close_connections()
+
+
+if __name__ == "__main__":
+    asyncio.run(_main())

server/src/tavolo/elo.py

@@ -0,0 +1,49 @@
+"""Chess-style Elo ratings, generalized to two-team matches.
+
+Every player starts at :data:`INITIAL_RATING`. A team's rating is the mean
+of its members' current ratings, so the usual chess formula applies
+unchanged between the two teams:
+
+* expected score ``E = 1 / (1 + 10 ** ((R_opponent - R_team) / 400))``
+* actual score ``S`` is 1 for a win and 0 for a loss (matches never draw)
+* every member of a team gains/loses the same ``round(K * (S - E))``
+
+Deltas are rounded to integers and ratings are stored as integers, so the
+system is exactly zero-sum: what the winners gain the losers lose.
+"""
+from __future__ import annotations
+
+from typing import Sequence
+
+INITIAL_RATING = 1500
+K_FACTOR = 32
+
+
+def expected_score(rating: float, opponent_rating: float) -> float:
+    """Expected score (0..1) of a side rated ``rating`` against
+    ``opponent_rating``."""
+    return 1.0 / (1.0 + 10.0 ** ((opponent_rating - rating) / 400.0))
+
+
+def team_rating(ratings: Sequence[float]) -> float:
+    """A team's rating is the mean of its members' ratings."""
+    if not ratings:
+        raise ValueError("a team needs at least one rating")
+    return sum(ratings) / len(ratings)
+
+
+def match_delta(
+    team_a_ratings: Sequence[float],
+    team_b_ratings: Sequence[float],
+    winner_team: int,
+) -> int:
+    """Rating change applied to each member of team A.
+
+    ``winner_team`` is 0 when team A won, 1 when team B won. Team B
+    members change by the negation of the returned value (zero-sum).
+    """
+    rating_a = team_rating(team_a_ratings)
+    rating_b = team_rating(team_b_ratings)
+    expected = expected_score(rating_a, rating_b)
+    score = 1.0 if winner_team == 0 else 0.0
+    return round(K_FACTOR * (score - expected))

server/src/tavolo/models.py

@@ -7,12 +7,17 @@ a player took part in, with the final score":
 * :class:`Match` — one row per finished match with both teams' scores.
 * :class:`MatchPlayer` — one row per participant, linking an OIDC
   ``sub`` to a seat/team and whether they won.
+* :class:`PlayerRating` — current chess-style Elo rating of a player for
+  one game type, updated transactionally with every finished match (see
+  :mod:`tavolo.elo`).
 """
 from __future__ import annotations
 
 from tortoise import fields
 from tortoise.models import Model
 
+from .elo import INITIAL_RATING
+
 
 class Match(Model):
     """A completed match of one of the registered game types."""
@@ -50,7 +55,28 @@ class MatchPlayer(Model):
     seat = fields.SmallIntField()
     team = fields.CharField(max_length=1)
     won = fields.BooleanField()
+    # Elo change this match produced for the player (see tavolo.elo);
+    # null for matches recorded before ratings existed.
+    elo_delta = fields.SmallIntField(null=True)
 
     class Meta:
         table = "match_player"
         unique_together = (("match", "user_sub"),)
+
+
+class PlayerRating(Model):
+    """Current Elo rating of one player for one game type."""
+
+    id = fields.UUIDField(pk=True)
+    # OIDC subject of the player; no local users table.
+    user_sub = fields.CharField(max_length=255)
+    # Which card game the rating applies to (tavolo.games.GAME_TYPES).
+    game_type = fields.CharField(max_length=32)
+    rating = fields.IntField(default=INITIAL_RATING)
+    matches_played = fields.IntField(default=0)
+    updated_at = fields.DatetimeField(auto_now=True)
+
+    class Meta:
+        table = "player_rating"
+        unique_together = (("user_sub", "game_type"),)
+        indexes = (("game_type", "rating"),)

server/src/tavolo/routes/stats.py

@@ -13,9 +13,10 @@ from kaya.openapi import operation
 
 from ..app import app, oidc_mixin
 from ..auth import require_auth
-from ..games import get_game_type
+from ..elo import INITIAL_RATING
+from ..games import DEFAULT_GAME_TYPE, get_game_type
 from ..http import extract_query_params, send_error, send_json
-from ..models import Match, MatchPlayer
+from ..models import Match, MatchPlayer, PlayerRating
 from ..openapi import PAGINATION_PARAMETERS
 from ..pagination import CursorDecodeError, paginate, parse_cursor_params
 
@@ -55,6 +56,9 @@ async def _serialize_match(match: Match, viewer: str) -> Dict[str, Any]:
         "started_at": match.started_at.isoformat(),
         "finished_at": match.finished_at.isoformat(),
         "you_won": any(p.user_sub == viewer and p.won for p in participants),
+        "your_elo_delta": next(
+            (p.elo_delta for p in participants if p.user_sub == viewer), None
+        ),
         "players": [
             {
                 "user_sub": p.user_sub,
@@ -62,6 +66,7 @@ async def _serialize_match(match: Match, viewer: str) -> Dict[str, Any]:
                 "seat": p.seat,
                 "team": p.team,
                 "won": p.won,
+                "elo_delta": p.elo_delta,
             }
             for p in participants
         ],
@@ -104,8 +109,11 @@ async def my_matches(ctx: HttpContext) -> None:
 
 @app.GET("/api/leaderboard")
 @operation(summary="Global leaderboard",
-           description="Aggregated wins, matches played and team points for every "
+           description="Elo rating, aggregated wins, matches played and team "
-                       "player with at least one finished match. Sorted by wins.",
+                       "points for every player with at least one finished "
+                       "match. Sorted by Elo rating (the rating for the "
+                       "requested game_type, or the default game when the "
+                       "filter is absent).",
            tags=["stats"],
            parameters=[GAME_TYPE_PARAMETER],
            responses={
@@ -121,6 +129,9 @@ async def leaderboard(ctx: HttpContext) -> None:
     if game_type is not None:
         queryset = queryset.filter(match__game_type=game_type)
     rows = await queryset.prefetch_related("match")
+    # Ratings are per game type; without a filter show the default game's.
+    rating_rows = await PlayerRating.filter(game_type=game_type or DEFAULT_GAME_TYPE)
+    ratings = {row.user_sub: row.rating for row in rating_rows}
     aggregate: Dict[str, Dict[str, Any]] = {}
     for row in rows:
         entry = aggregate.setdefault(
@@ -131,6 +142,7 @@ async def leaderboard(ctx: HttpContext) -> None:
                 "matches": 0,
                 "wins": 0,
                 "points": 0,
+                "elo": ratings.get(row.user_sub, INITIAL_RATING),
             },
         )
         entry["matches"] += 1
@@ -145,7 +157,33 @@ async def leaderboard(ctx: HttpContext) -> None:
 
     ranking: List[Dict[str, Any]] = sorted(
         aggregate.values(),
-        key=lambda e: (e["wins"], e["points"], -e["matches"]),
+        key=lambda e: (e["elo"], e["wins"], e["points"], -e["matches"]),
         reverse=True,
     )
     await send_json(ctx, 200, {"results": ranking})
+
+
+@app.GET("/api/me/ratings")
+@operation(summary="My Elo ratings",
+           description="The caller's current Elo rating for every game type "
+                       "they have played.",
+           tags=["stats"],
+           responses={
+               200: {"description": "The caller's ratings"},
+               401: {"description": "Authentication required"},
+           })
+@require_auth
+async def my_ratings(ctx: HttpContext) -> None:
+    user = oidc_mixin.get_user(ctx)
+    assert user is not None
+    rows = await PlayerRating.filter(user_sub=user.sub).order_by("game_type")
+    await send_json(ctx, 200, {
+        "results": [
+            {
+                "game_type": row.game_type,
+                "rating": row.rating,
+                "matches_played": row.matches_played,
+            }
+            for row in rows
+        ]
+    })

server/src/tavolo/stats.py

@@ -2,17 +2,19 @@
 
 Called once when a game reaches the finished phase (guarded by the
 ``stats_saved`` flag on the state). The write is transactional so a match
-never appears with only some of its players.
+never appears with only some of its players. The same transaction also
+updates the participants' Elo ratings (see :mod:`tavolo.elo`).
 """
 from __future__ import annotations
 
 import uuid
 from datetime import datetime, timezone
 from logging import getLogger
-from typing import Optional
+from typing import Dict, List, Optional
 
 from tortoise.transactions import in_transaction
 
+from .elo import match_delta
 from .game.state import PHASE_FINISHED, TEAM_NAMES, GameState
 
 log = getLogger(__name__)
@@ -27,6 +29,46 @@ def _parse_timestamp(value: Optional[str]) -> datetime:
     return datetime.now(timezone.utc)
 
 
+async def apply_elo(
+    game_type: str, winner_team: str, team_members: Dict[str, List[str]]
+) -> Dict[str, int]:
+    """Update the Elo ratings of ``team_members`` for ``game_type``.
+
+    ``team_members`` maps a team name ("A"/"B") to its players' subs.
+    Ratings are read from (and written back to) the ``player_rating``
+    table; unrated players start at the initial rating. Returns the
+    per-player delta. Must be called inside a transaction.
+    """
+    from .models import PlayerRating
+
+    ratings: Dict[str, PlayerRating] = {}
+    for subs in team_members.values():
+        for sub in subs:
+            rating = await PlayerRating.get_or_none(
+                user_sub=sub, game_type=game_type
+            )
+            if rating is None:
+                rating = await PlayerRating.create(
+                    id=uuid.uuid4(), user_sub=sub, game_type=game_type
+                )
+            ratings[sub] = rating
+    delta_a = match_delta(
+        [ratings[sub].rating for sub in team_members["A"]],
+        [ratings[sub].rating for sub in team_members["B"]],
+        0 if winner_team == "A" else 1,
+    )
+    deltas: Dict[str, int] = {
+        **{sub: delta_a for sub in team_members["A"]},
+        **{sub: -delta_a for sub in team_members["B"]},
+    }
+    for sub, delta in deltas.items():
+        rating = ratings[sub]
+        rating.rating += delta
+        rating.matches_played += 1
+        await rating.save()
+    return deltas
+
+
 async def save_match_result(state: GameState) -> None:
     """Persist ``state`` to Postgres if it is finished and not yet saved."""
     if state.stats_saved or state.phase != PHASE_FINISHED or state.winner is None:
@@ -36,18 +78,23 @@ async def save_match_result(state: GameState) -> None:
 
     started_at = _parse_timestamp(state.created_at)
     finished_at = _parse_timestamp(state.finished_at)
+    winner_team = TEAM_NAMES[state.winner]
+    team_members: Dict[str, List[str]] = {"A": [], "B": []}
+    for player in state.players:
+        team_members[TEAM_NAMES[player.team]].append(player.sub)
     async with in_transaction():
         match = await Match.create(
             id=uuid.uuid4(),
             game_type=state.game_type,
             team_a_score=state.scores[0],
             team_b_score=state.scores[1],
-            winner_team=TEAM_NAMES[state.winner],
+            winner_team=winner_team,
             target_score=state.target_score,
             hands_played=state.hand_number,
             started_at=started_at,
             finished_at=finished_at,
         )
+        deltas = await apply_elo(state.game_type, winner_team, team_members)
         for player in state.players:
             await MatchPlayer.create(
                 id=uuid.uuid4(),
@@ -57,6 +104,7 @@ async def save_match_result(state: GameState) -> None:
                 seat=player.seat,
                 team=TEAM_NAMES[player.team],
                 won=player.team == state.winner,
+                elo_delta=deltas[player.sub],
             )
     state.stats_saved = True
     log.info(

server/tests/test_elo.py

@@ -0,0 +1,73 @@
+"""Unit tests for the chess-style Elo math in :mod:`tavolo.elo`."""
+from __future__ import annotations
+
+import unittest
+
+from tavolo.elo import (
+    INITIAL_RATING,
+    K_FACTOR,
+    expected_score,
+    match_delta,
+    team_rating,
+)
+
+
+class ExpectedScoreTest(unittest.TestCase):
+    def test_equal_ratings_give_even_odds(self) -> None:
+        self.assertAlmostEqual(0.5, expected_score(1500, 1500))
+
+    def test_higher_rating_is_favoured(self) -> None:
+        self.assertGreater(expected_score(1700, 1500), 0.5)
+        self.assertLess(expected_score(1500, 1700), 0.5)
+
+    def test_scores_sum_to_one(self) -> None:
+        self.assertAlmostEqual(
+            1.0, expected_score(1600, 1400) + expected_score(1400, 1600)
+        )
+
+    def test_four_hundred_points_is_ten_to_one(self) -> None:
+        self.assertAlmostEqual(10 / 11, expected_score(1900, 1500))
+
+
+class TeamRatingTest(unittest.TestCase):
+    def test_mean_of_members(self) -> None:
+        self.assertEqual(1600, team_rating([1500, 1700]))
+
+    def test_empty_team_rejected(self) -> None:
+        with self.assertRaises(ValueError):
+            team_rating([])
+
+
+class MatchDeltaTest(unittest.TestCase):
+    def test_equal_teams_exchange_half_k(self) -> None:
+        delta = match_delta([1500, 1500], [1500, 1500], winner_team=0)
+        self.assertEqual(K_FACTOR // 2, delta)
+
+    def test_favourite_gains_less_than_underdog(self) -> None:
+        favourite = match_delta([1700, 1700], [1500, 1500], winner_team=0)
+        underdog = match_delta([1500, 1500], [1700, 1700], winner_team=0)
+        self.assertGreater(underdog, favourite)
+        self.assertGreater(favourite, 0)
+
+    def test_losing_side_loses_the_winners_gain(self) -> None:
+        # Zero-sum: the losers' delta is the negation of the winners'.
+        win = match_delta([1600, 1500], [1400, 1500], winner_team=0)
+        loss = match_delta([1600, 1500], [1400, 1500], winner_team=1)
+        self.assertEqual(-win, -abs(win))  # winner gains
+        # Losing the same pairing costs K * E, winning gains K * (1 - E);
+        # both are computed from the same expectation, so loss = win - K.
+        self.assertEqual(win - K_FACTOR, loss)
+
+    def test_team_average_decides_not_individual_ratings(self) -> None:
+        # [1700, 1300] averages 1500, same as [1500, 1500].
+        mixed = match_delta([1700, 1300], [1500, 1500], winner_team=0)
+        even = match_delta([1500, 1500], [1500, 1500], winner_team=0)
+        self.assertEqual(even, mixed)
+
+    def test_initial_rating_constant(self) -> None:
+        self.assertEqual(1500, INITIAL_RATING)
+        self.assertEqual(32, K_FACTOR)
+
+
+if __name__ == "__main__":
+    unittest.main()

server/tests/test_stats.py

@@ -9,9 +9,10 @@ from httpx import ASGITransport, AsyncClient
 from pwo import async_test
 
 from tavolo.app import app, tortoise_mixin
+from tavolo.elo import INITIAL_RATING
 from tavolo.game import engine
 from tavolo.game.state import GameState
-from tavolo.models import Match, MatchPlayer
+from tavolo.models import Match, MatchPlayer, PlayerRating
 from tavolo.stats import save_match_result
 from tests.helpers import oidc_user
 
@@ -48,6 +49,28 @@ def _finished_state() -> GameState:
     return state
 
 
+def _finished_state_reversed() -> GameState:
+    """Same one-capture ending as ``_finished_state``, but team B scores it."""
+    state = GameState(
+        id="stats-game-2",
+        join_code="STATS2",
+        creator_sub="alice",
+        target_score=2,
+        phase=engine.PHASE_PLAYING,
+        turn=1,
+        table=[engine.parse_card("02C")],
+    )
+    from tavolo.game.state import PlayerState, Card
+
+    state.players = [
+        PlayerState(sub="alice", name="alice", seat=0),
+        PlayerState(sub="bob", name="bob", seat=1, hand=[Card.parse("02D")]),
+        PlayerState(sub="carol", name="carol", seat=2),
+        PlayerState(sub="dave", name="dave", seat=3),
+    ]
+    return state
+
+
 class SaveMatchResultTest(unittest.TestCase):
     @async_test
     async def test_finished_match_is_persisted_once(self) -> None:
@@ -71,6 +94,58 @@ class SaveMatchResultTest(unittest.TestCase):
             winners = await MatchPlayer.filter(won=True)
             self.assertEqual({"alice", "carol"}, {p.user_sub for p in winners})
 
+    @async_test
+    async def test_finished_match_updates_elo_ratings(self) -> None:
+        ctx = await _use_app_db()
+        state = _finished_state()
+        engine.play(state, "alice", "02D", ["02C"])
+
+        with ctx:
+            await save_match_result(state)
+
+            ratings = {
+                row.user_sub: row for row in await PlayerRating.all()
+            }
+            self.assertEqual(4, len(ratings))
+            # Four players at 1500: winners gain K/2, losers lose it.
+            for winner in ("alice", "carol"):
+                self.assertEqual(INITIAL_RATING + 16, ratings[winner].rating)
+                self.assertEqual(1, ratings[winner].matches_played)
+            for loser in ("bob", "dave"):
+                self.assertEqual(INITIAL_RATING - 16, ratings[loser].rating)
+                self.assertEqual(1, ratings[loser].matches_played)
+
+            # The per-match delta is recorded on each participation row.
+            deltas = {
+                p.user_sub: p.elo_delta for p in await MatchPlayer.all()
+            }
+            self.assertEqual(
+                {"alice": 16, "carol": 16, "bob": -16, "dave": -16}, deltas
+            )
+
+    @async_test
+    async def test_elo_ratings_accumulate_across_matches(self) -> None:
+        ctx = await _use_app_db()
+        state = _finished_state()
+        engine.play(state, "alice", "02D", ["02C"])
+        reversed_state = _finished_state_reversed()
+        engine.play(reversed_state, "bob", "02D", ["02C"])
+
+        with ctx:
+            await save_match_result(state)
+            # A second match between the same players, won by team B.
+            await save_match_result(reversed_state)
+
+            ratings = {
+                row.user_sub: row.rating for row in await PlayerRating.all()
+            }
+            # Match 1: even teams, team A wins (+16/-16). Match 2: team A
+            # is now the favourite (1516 vs 1484), so losing costs 17.
+            self.assertEqual(INITIAL_RATING - 1, ratings["alice"])
+            self.assertEqual(INITIAL_RATING + 1, ratings["bob"])
+            bob = await PlayerRating.get(user_sub="bob")
+            self.assertEqual(2, bob.matches_played)
+
 
 async def _seed_two_matches(game_types: tuple = ("scopone_scientifico", "scopone_scientifico")) -> None:
     ctx = await _use_app_db()
@@ -167,6 +242,116 @@ class StatsRouteTest(unittest.TestCase):
         # Alice leads on points after tying Bob on wins.
         self.assertEqual("alice", response.json()["results"][0]["user_sub"])
 
+    @async_test
+    async def test_leaderboard_includes_elo_and_sorts_by_it(self) -> None:
+        await _seed_two_matches()
+        ctx = await _use_app_db()
+        with ctx:
+            # Bob outranks everyone despite Alice leading on points.
+            await PlayerRating.create(
+                id=uuid.uuid4(),
+                user_sub="bob",
+                game_type="scopone_scientifico",
+                rating=1600,
+                matches_played=2,
+            )
+        transport = ASGITransport(app=app)
+        async with AsyncClient(transport=transport, base_url="http://127.0.0.1") as client:
+            response = await client.get("/api/leaderboard")
+        self.assertEqual(200, response.status_code)
+        results = response.json()["results"]
+        by_sub = {row["user_sub"]: row for row in results}
+        self.assertEqual(1600, by_sub["bob"]["elo"])
+        # Players without a rating row report the initial rating.
+        self.assertEqual(INITIAL_RATING, by_sub["alice"]["elo"])
+        # Elo outranks wins/points.
+        self.assertEqual("bob", results[0]["user_sub"])
+
+    @async_test
+    async def test_leaderboard_elo_scoped_by_game_type(self) -> None:
+        await _seed_two_matches()
+        ctx = await _use_app_db()
+        with ctx:
+            await PlayerRating.create(
+                id=uuid.uuid4(),
+                user_sub="alice",
+                game_type="scopone_scientifico",
+                rating=1516,
+                matches_played=1,
+            )
+            # Alice's rating in another game must not leak into the
+            # scopone leaderboard.
+            await PlayerRating.create(
+                id=uuid.uuid4(),
+                user_sub="alice",
+                game_type="other_game",
+                rating=1800,
+                matches_played=1,
+            )
+        transport = ASGITransport(app=app)
+        async with AsyncClient(transport=transport, base_url="http://127.0.0.1") as client:
+            response = await client.get("/api/leaderboard?game_type=scopone_scientifico")
+        self.assertEqual(200, response.status_code)
+        results = response.json()["results"]
+        by_sub = {row["user_sub"]: row for row in results}
+        self.assertEqual(1516, by_sub["alice"]["elo"])
+        self.assertEqual(INITIAL_RATING, by_sub["bob"]["elo"])
+
+    @async_test
+    async def test_my_matches_include_elo_delta(self) -> None:
+        ctx = await _use_app_db()
+        state = _finished_state()
+        engine.play(state, "alice", "02D", ["02C"])
+        with ctx:
+            await save_match_result(state)
+        transport = ASGITransport(app=app)
+        async with AsyncClient(transport=transport, base_url="http://127.0.0.1") as client:
+            with oidc_user("alice"):
+                response = await client.get("/api/me/matches")
+        self.assertEqual(200, response.status_code)
+        players = {
+            p["user_sub"]: p
+            for p in response.json()["results"][0]["players"]
+        }
+        self.assertEqual(16, players["alice"]["elo_delta"])
+        self.assertEqual(-16, players["bob"]["elo_delta"])
+        self.assertEqual(16, response.json()["results"][0]["your_elo_delta"])
+
+    @async_test
+    async def test_my_ratings_requires_auth(self) -> None:
+        transport = ASGITransport(app=app)
+        async with AsyncClient(transport=transport, base_url="http://127.0.0.1") as client:
+            response = await client.get("/api/me/ratings")
+        self.assertEqual(401, response.status_code)
+
+    @async_test
+    async def test_my_ratings_returns_only_own_rows(self) -> None:
+        ctx = await _use_app_db()
+        with ctx:
+            await PlayerRating.create(
+                id=uuid.uuid4(),
+                user_sub="alice",
+                game_type="scopone_scientifico",
+                rating=1516,
+                matches_played=1,
+            )
+            await PlayerRating.create(
+                id=uuid.uuid4(),
+                user_sub="bob",
+                game_type="scopone_scientifico",
+                rating=1484,
+                matches_played=1,
+            )
+        transport = ASGITransport(app=app)
+        async with AsyncClient(transport=transport, base_url="http://127.0.0.1") as client:
+            with oidc_user("alice"):
+                response = await client.get("/api/me/ratings")
+        self.assertEqual(200, response.status_code)
+        self.assertEqual(
+            [{"game_type": "scopone_scientifico", "rating": 1516, "matches_played": 1}],
+            response.json()["results"],
+        )
+
 
 class GameTypeFilterTest(unittest.TestCase):
     """Stats endpoints scope results by the match's game type."""

web/src/api.rs

@@ -91,6 +91,18 @@ pub async fn my_matches(cursor: Option<&str>) -> Result<MatchesPage, String> {
     resp.json().await.map_err(|e| e.to_string())
 }
 
+/// Fetch the caller's Elo ratings (one row per game type played).
+pub async fn my_ratings() -> Result<RatingsPage, String> {
+    let resp = Request::get("/api/me/ratings")
+        .send()
+        .await
+        .map_err(|e| e.to_string())?;
+    if !resp.ok() {
+        return Err(server_error(resp.status()));
+    }
+    resp.json().await.map_err(|e| e.to_string())
+}
+
 pub async fn leaderboard() -> Result<LeaderboardPage, String> {
     let resp = Request::get("/api/leaderboard")
         .send()

web/src/model.rs

@@ -184,6 +184,10 @@ pub struct MatchPlayer {
     pub seat: usize,
     pub team: String,
     pub won: bool,
+    /// Elo change this match produced for the player; absent for matches
+    /// recorded before ratings existed.
+    #[serde(default)]
+    pub elo_delta: Option<i32>,
 }
 
 #[derive(Debug, Clone, Deserialize)]
@@ -201,6 +205,9 @@ pub struct MatchSummary {
     pub finished_at: String,
     #[serde(default)]
     pub you_won: bool,
+    /// The viewer's Elo change in this match; absent when unrated.
+    #[serde(default)]
+    pub your_elo_delta: Option<i32>,
     #[serde(default)]
     pub players: Vec<MatchPlayer>,
 }
@@ -213,16 +220,38 @@ pub struct MatchesPage {
     pub next_cursor: Option<String>,
 }
 
+fn default_elo() -> i32 {
+    1500
+}
+
 #[derive(Debug, Clone, Deserialize)]
 #[allow(dead_code)]
 pub struct LeaderboardEntry {
     pub user_sub: String,
     pub display_name: String,
+    /// Chess-style Elo rating for the requested game type.
+    #[serde(default = "default_elo")]
+    pub elo: i32,
     pub matches: i32,
     pub wins: i32,
     pub points: i32,
 }
 
+/// The caller's Elo rating for one game type (GET /api/me/ratings).
+#[derive(Debug, Clone, Deserialize)]
+#[allow(dead_code)]
+pub struct PlayerRating {
+    pub game_type: String,
+    pub rating: i32,
+    pub matches_played: i32,
+}
+
+#[derive(Debug, Clone, Deserialize)]
+pub struct RatingsPage {
+    #[serde(default)]
+    pub results: Vec<PlayerRating>,
+}
+
 #[derive(Debug, Clone, Deserialize)]
 pub struct LeaderboardPage {
     #[serde(default)]

web/src/pages/history.rs

@@ -72,6 +72,10 @@ pub fn HistoryPage() -> View {
                                 .collect::<Vec<_>>()
                                 .join(" & ");
                             let outcome = if m.you_won { "Won" } else { "Lost" };
+                            let elo_delta = m
+                                .your_elo_delta
+                                .map(|d| if d >= 0 { format!("+{d}") } else { d.to_string() })
+                                .unwrap_or_else(|| "—".to_string());
                             view! {
                                 tr {
                                     td { (m.finished_at.replace('T', " ").chars().take(16).collect::<String>()) }
@@ -80,6 +84,9 @@ pub fn HistoryPage() -> View {
                                     td { (m.team_a_score) " – " (m.team_b_score) }
                                     td { "Team " (m.winner_team) }
                                     td(class=if m.you_won { "won" } else { "lost" }) { (outcome) }
+                                    td(class=if m.you_won { "won" } else { "lost" }) {
+                                        (elo_delta)
+                                    }
                                 }
                             }
                         })
@@ -94,6 +101,7 @@ pub fn HistoryPage() -> View {
                                     th { "Score" }
                                     th { "Winner" }
                                     th { "You" }
+                                    th { "Elo" }
                                 }
                             }
                             tbody { (table_rows) }

web/src/pages/leaderboard.rs

@@ -39,6 +39,7 @@ pub fn LeaderboardPage() -> View {
                                 tr {
                                     td { (i + 1) }
                                     td { (e.display_name.clone()) }
+                                    td { (e.elo) }
                                     td { (e.wins) }
                                     td { (e.matches) }
                                     td { (e.points) }
@@ -52,6 +53,7 @@ pub fn LeaderboardPage() -> View {
                                 tr {
                                     th { "#" }
                                     th { "Player" }
+                                    th { "Elo" }
                                     th { "Wins" }
                                     th { "Matches" }
                                     th { "Points" }

web/src/pages/lobby.rs

@@ -20,6 +20,8 @@ fn fallback_game_types() -> Vec<GameTypeInfo> {
 pub fn LobbyPage() -> View {
     // Outer None = still loading; Some(None) = logged out.
     let user = create_signal(Option::<Option<User>>::None);
+    // The player's Elo rating for the first rated game; None while loading.
+    let rating = create_signal(Option::<i32>::None);
     let error = create_signal(Option::<String>::None);
     let code = create_signal(String::new());
     let game_types = create_signal(fallback_game_types());
@@ -28,7 +30,17 @@ pub fn LobbyPage() -> View {
 
     spawn_local(async move {
         match api::me().await {
-            Ok(me) => user.set(Some(me)),
+            Ok(me) => {
+                if me.is_some() {
+                    spawn_local(async move {
+                        if let Ok(p) = api::my_ratings().await {
+                            // Unrated players sit at the initial 1500.
+                            rating.set(Some(p.results.first().map(|r| r.rating).unwrap_or(1500)));
+                        }
+                    });
+                }
+                user.set(Some(me));
+            }
             Err(e) => {
                 error.set(Some(e));
                 user.set(Some(None));
@@ -88,7 +100,12 @@ pub fn LobbyPage() -> View {
                 Some(Some(me)) => view! {
                     div(class="lobby-grid") {
                         nav(class="top-nav") {
-                            span(class="whoami") { "Signed in as " strong { (me.name.clone()) } }
+                            span(class="whoami") {
+                                "Signed in as " strong { (me.name.clone()) }
+                                (rating.get_clone().map(|r| view! {
+                                    span(class="rating") { " · Elo " (r) }
+                                }))
+                            }
                             a(href="/history") { "My matches" }
                             a(href="/leaderboard") { "Leaderboard" }
                             a(href="/auth/logout", rel="external") { "Log out" }

web/style.css

@@ -49,6 +49,10 @@ body {
     margin-right: auto;
 }
 
+.whoami .rating {
+    color: var(--muted, #888);
+}
+
 .panel {
     background: var(--panel);
     border-radius: 12px;