feat(ratings): Add Python implementation for Elo Expected Score formula

maths/elo_expected_score.py

@@ -0,0 +1,34 @@
+import math
+
+def calculate_elo_expected_score(rating_a: int, rating_b: int) -> float:
+    """
+    Calculate the expected score (probability of winning) for Player A
+    against Player B using Elo ratings.
+
+    The formula is: E_A = 1 / (1 + 10^((R_B - R_A) / 400)).
+
+    Args:
+        rating_a (int): Elo rating of Player A.
+        rating_b (int): Elo rating of Player B.
+
+    Returns:
+        float: Expected score for Player A (between 0.0 and 1.0).
+    """
+    exponent = (rating_b - rating_a) / 400
+    return 1.0 / (1.0 + math.pow(10, exponent))
+
+def test_calculate_elo_expected_score():
+    # Player A higher rating
+    assert 0.5 < calculate_elo_expected_score(1600, 1400) < 1.0
+    # Player B higher rating
+    assert 0.0 < calculate_elo_expected_score(1400, 1600) < 0.5
+    # Equal ratings
+    assert calculate_elo_expected_score(1500, 1500) == 0.5
+
+if __name__ == "__main__":
+    ra, rb = 1600, 1400
+    expected_a = calculate_elo_expected_score(ra, rb)
+    print(f"Player A Rating: {ra}")
+    print(f"Player B Rating: {rb}")
+    print(f"Expected Score for Player A: {expected_a:.4f}")
+    print(f"Expected Score for Player B: {1.0 - expected_a:.4f}")