diff --git a/orion/evaluation/point.py b/orion/evaluation/point.py
index 4a0bde8f..f9989def 100644
--- a/orion/evaluation/point.py
+++ b/orion/evaluation/point.py
@@ -5,13 +5,13 @@ def _point_partition(expected, observed, start=None, end=None):
     expected = set(expected)
     observed = set(observed)
 
-    edge_start = min(expected.union(observed))
-    if start is not None:
-        edge_start = start
+    edge_start = start
+    if edge_start is None:
+        edge_start = min(expected.union(observed))
 
-    edge_end = max(expected.union(observed))
-    if end is not None:
-        edge_end = end
+    edge_end = end
+    if edge_end is None:
+        edge_end = max(expected.union(observed))
 
     length = int(edge_end) - int(edge_start) + 1
 
@@ -62,6 +62,13 @@ def _ws(x, y, z, w):
     if not isinstance(observed, list):
         observed = list(observed['timestamp'])
 
+    if not expected and not observed and (start is None or end is None):
+        # Without any anomalies there is no range to partition, and none was
+        # supplied through ``data``/``start``/``end``. There are no true or
+        # false positives and no false negatives, but the number of true
+        # negatives is unknown.
+        return None, 0, 0, 0
+
     return _ws(expected, observed, start, end)
 
 
diff --git a/tests/unit/evaluation/test_point.py b/tests/unit/evaluation/test_point.py
index 31d9faec..ed1ea1df 100644
--- a/tests/unit/evaluation/test_point.py
+++ b/tests/unit/evaluation/test_point.py
@@ -67,3 +67,36 @@ def test_point_f1_score_nan():
     observed = pd.DataFrame({"timestamp": [4, 5]})
     returned = point_f1_score(expected, observed)
     assert np.isnan(returned)
+
+
+def test_point_confusion_matrix_empty():
+    empty = pd.DataFrame({"timestamp": []})
+
+    returned = point_confusion_matrix(empty, empty)
+
+    # There is no range to partition, so the number of true negatives is
+    # unknown, but there are no positives and no false negatives.
+    assert returned == (None, 0, 0, 0)
+
+
+def test_point_confusion_matrix_empty_with_range():
+    empty = pd.DataFrame({"timestamp": []})
+
+    returned = point_confusion_matrix(empty, empty, start=0, end=9)
+
+    # Every point in the range is correctly considered normal.
+    np.testing.assert_array_equal(np.array(returned), np.array((10, 0, 0, 0)))
+
+
+def test_point_scores_empty():
+    empty = pd.DataFrame({"timestamp": []})
+
+    assert np.isnan(point_precision(empty, empty))
+    assert np.isnan(point_recall(empty, empty))
+    assert np.isnan(point_f1_score(empty, empty))
+
+    # Accuracy needs the true negatives, which are unknown without a range.
+    with pytest.raises(ValueError):
+        point_accuracy(empty, empty)
+
+    assert point_accuracy(empty, empty, start=0, end=9) == 1.0