diff --git a/osu.Game.Tests/Visual/Online/TestScenePlayHistorySubsection.cs b/osu.Game.Tests/Visual/Online/TestScenePlayHistorySubsection.cs
index c9dbc9dc24..cf5ecf5bf2 100644
--- a/osu.Game.Tests/Visual/Online/TestScenePlayHistorySubsection.cs
+++ b/osu.Game.Tests/Visual/Online/TestScenePlayHistorySubsection.cs
@@ -69,6 +69,20 @@ namespace osu.Game.Tests.Visual.Online
             AddAssert("Section is visible", () => section.Alpha == 1);
         }
 
+        [Test]
+        public void TestConstantValues()
+        {
+            AddStep("Load user", () => user.Value = user_with_constant_values);
+            AddAssert("Section is visible", () => section.Alpha == 1);
+        }
+
+        [Test]
+        public void TestConstantZeroValues()
+        {
+            AddStep("Load user", () => user.Value = user_with_zero_values);
+            AddAssert("Section is visible", () => section.Alpha == 1);
+        }
+
         [Test]
         public void TestFilledValues()
         {
@@ -117,10 +131,32 @@ namespace osu.Game.Tests.Visual.Online
             }
         };
 
-        private static readonly User user_with_filled_values = new User
+        private static readonly User user_with_constant_values = new User
         {
             Id = 5,
             MonthlyPlaycounts = new[]
+            {
+                new UserHistoryCount { Date = new DateTime(2010, 5, 1), Count = 5 },
+                new UserHistoryCount { Date = new DateTime(2010, 6, 1), Count = 5 },
+                new UserHistoryCount { Date = new DateTime(2010, 7, 1), Count = 5 }
+            }
+        };
+
+        private static readonly User user_with_zero_values = new User
+        {
+            Id = 6,
+            MonthlyPlaycounts = new[]
+            {
+                new UserHistoryCount { Date = new DateTime(2010, 5, 1), Count = 0 },
+                new UserHistoryCount { Date = new DateTime(2010, 6, 1), Count = 0 },
+                new UserHistoryCount { Date = new DateTime(2010, 7, 1), Count = 0 }
+            }
+        };
+
+        private static readonly User user_with_filled_values = new User
+        {
+            Id = 7,
+            MonthlyPlaycounts = new[]
             {
                 new UserHistoryCount { Date = new DateTime(2010, 5, 1), Count = 1000 },
                 new UserHistoryCount { Date = new DateTime(2010, 6, 1), Count = 20 },
@@ -134,7 +170,7 @@ namespace osu.Game.Tests.Visual.Online
 
         private static readonly User user_with_missing_values = new User
         {
-            Id = 6,
+            Id = 8,
             MonthlyPlaycounts = new[]
             {
                 new UserHistoryCount { Date = new DateTime(2020, 1, 1), Count = 100 },
diff --git a/osu.Game/Graphics/UserInterface/LineGraph.cs b/osu.Game/Graphics/UserInterface/LineGraph.cs
index 42b523fc5c..70db26c817 100644
--- a/osu.Game/Graphics/UserInterface/LineGraph.cs
+++ b/osu.Game/Graphics/UserInterface/LineGraph.cs
@@ -119,7 +119,11 @@ namespace osu.Game.Graphics.UserInterface
 
         protected float GetYPosition(float value)
         {
-            if (ActualMaxValue == ActualMinValue) return 0;
+            if (ActualMaxValue == ActualMinValue)
+                // show line at top if the only value on the graph is positive,
+                // and at bottom if the only value on the graph is zero or negative.
+                // just kind of makes most sense intuitively.
+                return value > 1 ? 0 : 1;
 
             return (ActualMaxValue - value) / (ActualMaxValue - ActualMinValue);
         }
diff --git a/osu.Game/Overlays/Profile/Sections/Historical/ProfileLineChart.cs b/osu.Game/Overlays/Profile/Sections/Historical/ProfileLineChart.cs
index c1eb0811fb..989871745d 100644
--- a/osu.Game/Overlays/Profile/Sections/Historical/ProfileLineChart.cs
+++ b/osu.Game/Overlays/Profile/Sections/Historical/ProfileLineChart.cs
@@ -124,8 +124,16 @@ namespace osu.Game.Overlays.Profile.Sections.Historical
                 if (currentTick < min)
                     continue;
 
-                float y = -Interpolation.ValueAt(currentTick, 0, 1f, min, max);
-                addRowTick(y, currentTick);
+                float y;
+                // special-case the min == max case to match LineGraph.
+                // lerp isn't really well-defined over a zero interval anyway.
+                if (min == max)
+                    y = currentTick > 1 ? 1 : 0;
+                else
+                    y = Interpolation.ValueAt(currentTick, 0, 1f, min, max);
+
+                // y axis is inverted in graph-like coordinates.
+                addRowTick(-y, currentTick);
             }
         }