First implementation of ELO logic

app/elo/README.md

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+Implementation of an ELO-like algorithm.
+
+(Yes, [this](https://github.com/sublee/elo/) exists, and a [more mathematical treatment](https://cs.stanford.edu/people/paulliu/files/www-2021-elor.pdf), but eh, a bit of self implementation doesn't hurt in a personal project)
+
+Ref. [here](http://web.archive.org/web/20130308190719/http://elo.divergentinformatics.com/) for testing, and [here](http://sradack.blogspot.com/2008/06/elo-rating-system-multiple-players.html) for implementation.

app/elo/__init__.py

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+from .elo import rerank  # noqa

app/elo/elo.py

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+from typing import Iterable
+
+K_FACTOR = 10
+BETA = 200
+
+
+def rerank(ratings: Iterable[int], winning_player_idx: int) -> Iterable[int]:
+    expectations = _expectations(ratings)
+    return [
+        rating
+        + (K_FACTOR * ((1 if winning_player_idx == idx else 0) - expectations[idx]))
+        for idx, rating in enumerate(ratings)
+    ]
+
+
+def _expectations(ratings: Iterable[int]) -> Iterable[int]:
+    return [
+        _calculate_expectation(rating, ratings[:idx] + ratings[idx + 1 :])
+        for idx, rating in enumerate(ratings)
+    ]
+
+
+def _calculate_expectation(rating: int, other_ratings: Iterable[int]) -> int:
+    return sum(
+        [_pairwise_expectation(rating, other_rating) for other_rating in other_ratings]
+    ) / (float(len(other_ratings) + 1) * len(other_ratings) / 2)
+
+
+def _pairwise_expectation(rating: int, other_rating: int) -> Iterable[int]:
+    """
+    Gives the expected score of `rating` against `other_rating`
+    """
+    diff = float(other_rating) - float(rating)
+    f_factor = 2 * BETA  # rating disparity
+    return 1.0 / (1 + 10 ** (diff / f_factor))

tests/elo/test_elo.py

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+from typing import Iterable
+
+from app.elo import rerank
+
+
+def test():
+    # From https://github.com/sublee/elo/blob/master/elotests.py
+    assert _almost_equal(rerank([1200, 800], 1), [1190.909, 809.091])
+    # Couldn't find any test-cases for multiplayer games.
+
+
+def _almost_equal(actual: Iterable, expected: Iterable) -> bool:
+    assert len(actual) == len(expected)
+    for f, s in zip(actual, expected):
+        if (s - f) > (0.00001 * f):
+            return False
+    else:
+        return True