feat: initial project setup

backend/app/elo.py

@@ -0,0 +1,26 @@
+"""ELO rating calculation."""
+
+
+def calculate_elo(
+    winner_rating: float,
+    loser_rating: float,
+    k_factor: float = 32.0,
+) -> tuple[float, float]:
+    """Calculate new ELO ratings after a match.
+
+    Uses the standard ELO formula:
+        E = 1 / (1 + 10^((R_opponent - R_self) / 400))
+        R_new = R_old + K * (S - E)
+
+    where S = 1 for a win, S = 0 for a loss.
+
+    Returns:
+        (new_winner_rating, new_loser_rating)
+    """
+    expected_winner = 1.0 / (1.0 + 10.0 ** ((loser_rating - winner_rating) / 400.0))
+    expected_loser = 1.0 - expected_winner
+
+    new_winner = winner_rating + k_factor * (1.0 - expected_winner)
+    new_loser = loser_rating + k_factor * (0.0 - expected_loser)
+
+    return round(new_winner, 2), round(new_loser, 2)