diff --git a/openskill/rate.py b/openskill/rate.py
index 11a0b98..c5d1cde 100644
--- a/openskill/rate.py
+++ b/openskill/rate.py
@@ -200,9 +200,10 @@ def predict_win(teams: List[List[Rating]], **options) -> List[Union[int, float]]
         raise ValueError(f"Expected at least two teams.")
 
     n = len(teams)
+    denom = (n * (n - 1)) / 2
 
     pairwise_probabilities = []
-    for pairwise_subset in itertools.permutations(teams, len(teams)):
+    for pairwise_subset in itertools.permutations(teams, 2):
         current_team_a_rating = team_rating([pairwise_subset[0]])
         current_team_b_rating = team_rating([pairwise_subset[1]])
         mu_a = current_team_a_rating[0][0]
@@ -216,22 +217,12 @@ def predict_win(teams: List[List[Rating]], **options) -> List[Union[int, float]]
             )
         )
 
-    if n > 2:
-        cache = deque(pairwise_probabilities)
-        probabilities = []
-        partial = len(pairwise_probabilities) / n
-        while len(cache) > 0:
-            aggregate = []
-            for length in range(int(partial)):
-                aggregate.append(cache.popleft())
-            aggregate_sum = sum(aggregate)
-            aggregate_multiple = n
-            for length in range(1, n - 2):
-                aggregate_multiple *= n - length
-            probabilities.append(aggregate_sum / aggregate_multiple)
-        return probabilities
-    else:
-        return pairwise_probabilities
+    return [
+        (sum(team_prob) / denom)
+        for team_prob in itertools.zip_longest(
+            *[iter(pairwise_probabilities)] * (n - 1)
+        )
+    ]
 
 
 def predict_draw(teams: List[List[Rating]], **options) -> Union[int, float]:
@@ -255,7 +246,7 @@ def predict_draw(teams: List[List[Rating]], **options) -> Union[int, float]:
     )
 
     pairwise_probabilities = []
-    for pairwise_subset in itertools.permutations(teams, len(teams)):
+    for pairwise_subset in itertools.permutations(teams, 2):
         current_team_a_rating = team_rating([pairwise_subset[0]])
         current_team_b_rating = team_rating([pairwise_subset[1]])
         mu_a = current_team_a_rating[0][0]
@@ -273,10 +264,8 @@ def predict_draw(teams: List[List[Rating]], **options) -> Union[int, float]:
             )
         )
 
+    denom = 1
     if n > 2:
-        aggregate_multiple = n
-        for length in range(1, n):
-            aggregate_multiple *= n - length
-        return abs(sum(pairwise_probabilities)) / aggregate_multiple
-    else:
-        return abs(sum(pairwise_probabilities))
+        denom = n * (n - 1)
+
+    return abs(sum(pairwise_probabilities)) / denom
diff --git a/poetry.lock b/poetry.lock
index 1ac14e4..85408c8 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -170,7 +170,7 @@ python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
 
 [[package]]
 name = "coverage"
-version = "6.3.1"
+version = "6.3.2"
 description = "Code coverage measurement for Python"
 category = "dev"
 optional = false
@@ -240,7 +240,7 @@ python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
 
 [[package]]
 name = "importlib-metadata"
-version = "4.11.1"
+version = "4.11.2"
 description = "Read metadata from Python packages"
 category = "dev"
 optional = false
@@ -250,7 +250,7 @@ python-versions = ">=3.7"
 zipp = ">=0.5"
 
 [package.extras]
-docs = ["sphinx", "jaraco.packaging (>=8.2)", "rst.linker (>=1.9)"]
+docs = ["sphinx", "jaraco.packaging (>=9)", "rst.linker (>=1.9)"]
 perf = ["ipython"]
 testing = ["pytest (>=6)", "pytest-checkdocs (>=2.4)", "pytest-flake8", "pytest-cov", "pytest-enabler (>=1.0.1)", "packaging", "pyfakefs", "flufl.flake8", "pytest-perf (>=0.9.2)", "pytest-black (>=0.3.7)", "pytest-mypy (>=0.9.1)", "importlib-resources (>=1.3)"]
 
@@ -368,7 +368,7 @@ python-versions = "*"
 
 [[package]]
 name = "numpy"
-version = "1.22.2"
+version = "1.22.3"
 description = "NumPy is the fundamental package for array computing with Python."
 category = "main"
 optional = false
@@ -555,7 +555,7 @@ python-versions = "*"
 
 [[package]]
 name = "readme-renderer"
-version = "32.0"
+version = "33.0"
 description = "readme_renderer is a library for rendering \"readme\" descriptions for Warehouse"
 category = "dev"
 optional = false
@@ -567,7 +567,7 @@ docutils = ">=0.13.1"
 Pygments = ">=2.5.1"
 
 [package.extras]
-md = ["cmarkgfm (>=0.5.0,<0.7.0)"]
+md = ["cmarkgfm (>=0.8.0)"]
 
 [[package]]
 name = "requests"
@@ -814,7 +814,7 @@ dev = ["packaging"]
 
 [[package]]
 name = "tqdm"
-version = "4.62.3"
+version = "4.63.0"
 description = "Fast, Extensible Progress Meter"
 category = "dev"
 optional = false
@@ -859,6 +859,14 @@ rfc3986 = ">=1.4.0"
 tqdm = ">=4.14"
 urllib3 = ">=1.26.0"
 
+[[package]]
+name = "typing-extensions"
+version = "4.1.1"
+description = "Backported and Experimental Type Hints for Python 3.6+"
+category = "dev"
+optional = false
+python-versions = ">=3.6"
+
 [[package]]
 name = "urllib3"
 version = "1.26.8"
@@ -906,7 +914,7 @@ docs = []
 [metadata]
 lock-version = "1.1"
 python-versions = ">=3.10, < 3.11"
-content-hash = "984602f39e558123e0413c49a236d5c6d3a08ea047e4b06725d704576762777f"
+content-hash = "68be0b15539da8f04869652695733ea6ec36c475f0a13a747fb7f2a8692d3cc4"
 
 [metadata.files]
 alabaster = [
@@ -1039,47 +1047,47 @@ colorama = [
     {file = "colorama-0.4.4.tar.gz", hash = "sha256:5941b2b48a20143d2267e95b1c2a7603ce057ee39fd88e7329b0c292aa16869b"},
 ]
 coverage = [
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@@ -1202,25 +1210,25 @@ mypy-extensions = [
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+    {file = "numpy-1.22.3-cp39-cp39-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:5bfb1bb598e8229c2d5d48db1860bcf4311337864ea3efdbe1171fb0c5da515d"},
+    {file = "numpy-1.22.3-cp39-cp39-manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:97098b95aa4e418529099c26558eeb8486e66bd1e53a6b606d684d0c3616b168"},
+    {file = "numpy-1.22.3-cp39-cp39-win32.whl", hash = "sha256:fdf3c08bce27132395d3c3ba1503cac12e17282358cb4bddc25cc46b0aca07aa"},
+    {file = "numpy-1.22.3-cp39-cp39-win_amd64.whl", hash = "sha256:639b54cdf6aa4f82fe37ebf70401bbb74b8508fddcf4797f9fe59615b8c5813a"},
+    {file = "numpy-1.22.3-pp38-pypy38_pp73-manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:c34ea7e9d13a70bf2ab64a2532fe149a9aced424cd05a2c4ba662fd989e3e45f"},
+    {file = "numpy-1.22.3.zip", hash = "sha256:dbc7601a3b7472d559dc7b933b18b4b66f9aa7452c120e87dfb33d02008c8a18"},
 ]
 packaging = [
     {file = "packaging-21.3-py3-none-any.whl", hash = "sha256:ef103e05f519cdc783ae24ea4e2e0f508a9c99b2d4969652eed6a2e1ea5bd522"},
@@ -1306,8 +1314,8 @@ pywin32-ctypes = [
     {file = "pywin32_ctypes-0.2.0-py2.py3-none-any.whl", hash = "sha256:9dc2d991b3479cc2df15930958b674a48a227d5361d413827a4cfd0b5876fc98"},
 ]
 readme-renderer = [
-    {file = "readme_renderer-32.0-py3-none-any.whl", hash = "sha256:a50a0f2123a4c1145ac6f420e1a348aafefcc9211c846e3d51df05fe3d865b7d"},
-    {file = "readme_renderer-32.0.tar.gz", hash = "sha256:b512beafa6798260c7d5af3e1b1f097e58bfcd9a575da7c4ddd5e037490a5b85"},
+    {file = "readme_renderer-33.0-py3-none-any.whl", hash = "sha256:f02cee0c4de9636b5a62b6be50c9742427ba1b956aad1d938bfb087d0d72ccdf"},
+    {file = "readme_renderer-33.0.tar.gz", hash = "sha256:e3b53bc84bd6af054e4cc1fe3567dc1ae19f554134221043a3f8c674e22209db"},
 ]
 requests = [
     {file = "requests-2.27.1-py2.py3-none-any.whl", hash = "sha256:f22fa1e554c9ddfd16e6e41ac79759e17be9e492b3587efa038054674760e72d"},
@@ -1437,8 +1445,8 @@ towncrier = [
     {file = "towncrier-21.9.0.tar.gz", hash = "sha256:9cb6f45c16e1a1eec9d0e7651165e7be60cd0ab81d13a5c96ca97a498ae87f48"},
 ]
 tqdm = [
-    {file = "tqdm-4.62.3-py2.py3-none-any.whl", hash = "sha256:8dd278a422499cd6b727e6ae4061c40b48fce8b76d1ccbf5d34fca9b7f925b0c"},
-    {file = "tqdm-4.62.3.tar.gz", hash = "sha256:d359de7217506c9851b7869f3708d8ee53ed70a1b8edbba4dbcb47442592920d"},
+    {file = "tqdm-4.63.0-py2.py3-none-any.whl", hash = "sha256:e643e071046f17139dea55b880dc9b33822ce21613b4a4f5ea57f202833dbc29"},
+    {file = "tqdm-4.63.0.tar.gz", hash = "sha256:1d9835ede8e394bb8c9dcbffbca02d717217113adc679236873eeaac5bc0b3cd"},
 ]
 trueskill = [
     {file = "trueskill-0.4.5.tar.gz", hash = "sha256:9d62b48d2428369d712bd9becff9f9a2caa325e1a2ab5f9392d34bff757867bb"},
@@ -1447,6 +1455,10 @@ twine = [
     {file = "twine-3.8.0-py3-none-any.whl", hash = "sha256:d0550fca9dc19f3d5e8eadfce0c227294df0a2a951251a4385797c8a6198b7c8"},
     {file = "twine-3.8.0.tar.gz", hash = "sha256:8efa52658e0ae770686a13b675569328f1fba9837e5de1867bfe5f46a9aefe19"},
 ]
+typing-extensions = [
+    {file = "typing_extensions-4.1.1-py3-none-any.whl", hash = "sha256:21c85e0fe4b9a155d0799430b0ad741cdce7e359660ccbd8b530613e8df88ce2"},
+    {file = "typing_extensions-4.1.1.tar.gz", hash = "sha256:1a9462dcc3347a79b1f1c0271fbe79e844580bb598bafa1ed208b94da3cdcd42"},
+]
 urllib3 = [
     {file = "urllib3-1.26.8-py2.py3-none-any.whl", hash = "sha256:000ca7f471a233c2251c6c7023ee85305721bfdf18621ebff4fd17a8653427ed"},
     {file = "urllib3-1.26.8.tar.gz", hash = "sha256:0e7c33d9a63e7ddfcb86780aac87befc2fbddf46c58dbb487e0855f7ceec283c"},
diff --git a/pyproject.toml b/pyproject.toml
index 47cfa2d..37d58fb 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -58,6 +58,7 @@ prompt-toolkit = "^3.0.28"
 trueskill = "^0.4.5"
 towncrier = "^21.9.0"
 scikit-learn = "^1.0.2"
+typing-extensions = "^4.1.1"
 pandas = "^1.4.1"
 
 [tool.poetry.extras]
diff --git a/tests/predictions/test_predict_win.py b/tests/predictions/test_predict_win.py
index af82622..63869b9 100644
--- a/tests/predictions/test_predict_win.py
+++ b/tests/predictions/test_predict_win.py
@@ -21,3 +21,80 @@ def test_predict_win():
 
     with pytest.raises(ValueError):
         predict_win(teams=[team_1])
+
+
+def test_predict_win_1v1():
+    a1 = Rating()
+    a2 = Rating(mu=32.444, sigma=5.123)
+    b1 = Rating(mu=73.381, sigma=1.421)
+    b2 = Rating(mu=25.188, sigma=6.211)
+    team1 = [a1, a2]
+    team2 = [b1, b2]
+
+    prob1, prob2 = predict_win(teams=[team1, team2])
+    assert prob1 == pytest.approx(0.34641823958165474)
+    assert prob2 == pytest.approx(0.6535817604183453)
+
+
+def test_predict_win_asymmetric():
+    a1 = Rating()
+    a2 = Rating(mu=32.444, sigma=5.123)
+    b1 = Rating(mu=73.381, sigma=1.421)
+    b2 = Rating(mu=25.188, sigma=6.211)
+    team1 = [a1, a2]
+    team2 = [b1, b2]
+    prob1, prob2, prob3, prob4 = predict_win(teams=[team1, team2, [a2], [b2]])
+    assert prob1 == pytest.approx(0.2613515941642222)
+    assert prob2 == pytest.approx(0.41117430943389155)
+    assert prob3 == pytest.approx(0.1750905983112395)
+    assert prob4 == pytest.approx(0.15238349809064686)
+
+
+def test_predict_win_3p_ffa():
+    a1 = Rating()
+    prob1, prob2, prob3 = predict_win(teams=[[a1], [a1], [a1]])
+    assert prob1 == pytest.approx(0.333333333333)
+    assert prob2 == pytest.approx(0.333333333333)
+    assert prob3 == pytest.approx(0.333333333333)
+
+
+def test_predict_win_4p_ffa():
+    a1 = Rating()
+    p1, p2, p3, p4 = predict_win(teams=[[a1], [a1], [a1], [a1]])
+    assert p1 == pytest.approx(0.25)
+    assert p2 == pytest.approx(0.25)
+    assert p3 == pytest.approx(0.25)
+    assert p4 == pytest.approx(0.25)
+
+
+def test_predict_win_4p_varying_skill():
+    r1 = Rating(mu=1, sigma=0.1)
+    r2 = Rating(mu=2, sigma=0.1)
+    r3 = Rating(mu=3, sigma=0.1)
+    r4 = Rating(mu=4, sigma=0.1)
+    p1, p2, p3, p4 = predict_win(teams=[[r1], [r2], [r3], [r4]])
+    assert p1 == pytest.approx(0.2028051110543726)
+    assert p2 == pytest.approx(0.23419421333676907)
+    assert p3 == pytest.approx(0.2658057866632309)
+    assert p4 == pytest.approx(0.29719488894562746)
+
+
+def test_predict_win_5p_ffa():
+    a1 = Rating()
+    p1, p2, p3, p4, p5 = predict_win(teams=[[a1], [a1], [a1], [a1], [a1]])
+    assert p1 == pytest.approx(0.2)
+    assert p2 == pytest.approx(0.2)
+    assert p3 == pytest.approx(0.2)
+    assert p4 == pytest.approx(0.2)
+    assert p5 == pytest.approx(0.2)
+
+
+def test_predict_5p_impostor():
+    a1 = Rating()
+    a2 = Rating(mu=32.444, sigma=5.123)
+    p1, p2, p3, p4, p5 = predict_win(teams=[[a1], [a1], [a1], [a2], [a1]])
+    assert p1 == pytest.approx(0.196037416522638)
+    assert p2 == pytest.approx(0.196037416522638)
+    assert p3 == pytest.approx(0.196037416522638)
+    assert p4 == pytest.approx(0.21585034503812)
+    assert p5 == pytest.approx(0.196037416522638)