diff --git a/qdrant_client/hybrid/fusion.py b/qdrant_client/hybrid/fusion.py
index 015f4a73..1c8f280a 100644
--- a/qdrant_client/hybrid/fusion.py
+++ b/qdrant_client/hybrid/fusion.py
@@ -33,14 +33,20 @@ def distribution_based_score_fusion(
     responses: list[list[models.ScoredPoint]], limit: int
 ) -> list[models.ScoredPoint]:
     def normalize(response: list[models.ScoredPoint]) -> list[models.ScoredPoint]:
-        if len(response) <= 1:
+        if len(response) == 1:
+            response[0].score = 0.5
             return response
 
         total = sum([point.score for point in response])
         mean = total / len(response)
         variance = sum([(point.score - mean) ** 2 for point in response]) / (len(response) - 1)
-        std_dev = variance**0.5
 
+        if variance == 0:
+            for point in response:
+                point.score = 0.5
+            return response
+
+        std_dev = variance**0.5
         low = mean - 3 * std_dev
         high = mean + 3 * std_dev
 
diff --git a/qdrant_client/hybrid/test_reranking.py b/qdrant_client/hybrid/test_reranking.py
index fa9aa05c..bced877f 100644
--- a/qdrant_client/hybrid/test_reranking.py
+++ b/qdrant_client/hybrid/test_reranking.py
@@ -50,9 +50,6 @@ def test_distribution_based_score_fusion() -> None:
     assert fused[1].id == 0
     assert fused[2].id == 4
 
-    fused = distribution_based_score_fusion([[responses[0][0]]], limit=3)
-    assert fused[0].id == 1
-
 
 def test_reciprocal_rank_fusion_empty_responses() -> None:
     responses: list[list[models.ScoredPoint]] = [[]]
@@ -97,3 +94,24 @@ def test_distribution_based_score_fusion_empty_response() -> None:
     assert fused[0].id == 1
     assert fused[1].id == 0
     assert fused[2].id == 5
+
+
+def test_distribution_based_score_fusion_zero_variance() -> None:
+    score = 85.0
+    responses = [
+        [
+            models.ScoredPoint(id=1, version=0, score=score),
+            models.ScoredPoint(id=0, version=0, score=score),
+            models.ScoredPoint(id=5, version=0, score=score),
+        ],
+        [],
+    ]
+    fused = distribution_based_score_fusion(
+        [[models.ScoredPoint(id=1, version=0, score=score)]], limit=3
+    )
+    assert fused[0].id == 1
+    assert fused[0].score == 0.5
+
+    fused = distribution_based_score_fusion(responses, limit=3)
+    assert len(fused) == 3
+    assert all([p.score == 0.5 for p in fused])