diff --git a/datafusion/expr/src/udf.rs b/datafusion/expr/src/udf.rs
index d623d3541fc7..8ec5c50766c4 100644
--- a/datafusion/expr/src/udf.rs
+++ b/datafusion/expr/src/udf.rs
@@ -205,10 +205,6 @@ impl ScalarUDF {
     pub fn short_circuits(&self) -> bool {
         self.inner.short_circuits()
     }
-
-    pub fn support_randomness(&self) -> bool {
-        self.inner.support_randomness()
-    }
 }
 
 impl<F> From<F> for ScalarUDF
@@ -348,7 +344,15 @@ pub trait ScalarUDFImpl: Debug + Send + Sync {
         )
     }
 
-    /// Invoke the function without `args` but number of rows, returning the appropriate result
+    /// Invoke the function without `args` but number of rows, returning the
+    /// appropriate result
+    ///
+    /// Note this is different than [`Self::invoke`] in that it is called with
+    /// the number of rows in the batch.
+    ///
+    /// For functions that return a constant such as `pi()` the number of rows
+    /// does not matter. However for functions such as `random()` that return a
+    /// batch with different values for each row, the number of rows is needed.
     fn invoke_no_args(&self, _number_rows: usize) -> Result<ColumnarValue> {
         not_impl_err!(
             "Function {} does not implement invoke_no_args but called",
@@ -407,12 +411,6 @@ pub trait ScalarUDFImpl: Debug + Send + Sync {
     fn short_circuits(&self) -> bool {
         false
     }
-
-    /// Returns true if the function supports randomness, This is useful for functions that need to generate
-    /// random values for each row. `invoke_no_args` can be called in this case.
-    fn support_randomness(&self) -> bool {
-        false
-    }
 }
 
 /// ScalarUDF that adds an alias to the underlying function. It is better to
diff --git a/datafusion/functions-array/src/make_array.rs b/datafusion/functions-array/src/make_array.rs
index 0439a736ee42..c8e30c9df574 100644
--- a/datafusion/functions-array/src/make_array.rs
+++ b/datafusion/functions-array/src/make_array.rs
@@ -104,6 +104,10 @@ impl ScalarUDFImpl for MakeArray {
         make_scalar_function(make_array_inner)(args)
     }
 
+    fn invoke_no_args(&self, _num_rows: usize) -> Result<ColumnarValue> {
+        self.invoke(&[])
+    }
+
     fn aliases(&self) -> &[String] {
         &self.aliases
     }
diff --git a/datafusion/functions/src/math/pi.rs b/datafusion/functions/src/math/pi.rs
index c135a13f1256..108efdf92975 100644
--- a/datafusion/functions/src/math/pi.rs
+++ b/datafusion/functions/src/math/pi.rs
@@ -66,6 +66,10 @@ impl ScalarUDFImpl for PiFunc {
         ))))
     }
 
+    fn invoke_no_args(&self, _number_rows: usize) -> Result<ColumnarValue> {
+        self.invoke(&[])
+    }
+
     fn monotonicity(&self) -> Result<Option<FuncMonotonicity>> {
         Ok(Some(vec![Some(true)]))
     }
diff --git a/datafusion/functions/src/math/random.rs b/datafusion/functions/src/math/random.rs
index 8a993541eee3..4f6650fb9539 100644
--- a/datafusion/functions/src/math/random.rs
+++ b/datafusion/functions/src/math/random.rs
@@ -63,11 +63,8 @@ impl ScalarUDFImpl for RandomFunc {
         Ok(Float64)
     }
 
-    fn support_randomness(&self) -> bool {
-        true
-    }
-
     fn invoke_no_args(&self, num_rows: usize) -> Result<ColumnarValue> {
+        // Since random is volatile, return a different value each row
         let mut rng = thread_rng();
         let values = std::iter::repeat_with(|| rng.gen_range(0.0..1.0)).take(num_rows);
         let array = Float64Array::from_iter_values(values);
diff --git a/datafusion/functions/src/string/uuid.rs b/datafusion/functions/src/string/uuid.rs
index 707ac8130fff..869e1629ad94 100644
--- a/datafusion/functions/src/string/uuid.rs
+++ b/datafusion/functions/src/string/uuid.rs
@@ -57,10 +57,6 @@ impl ScalarUDFImpl for UuidFunc {
         Ok(Utf8)
     }
 
-    fn support_randomness(&self) -> bool {
-        true
-    }
-
     /// Prints random (v4) uuid values per row
     /// uuid() = 'a0eebc99-9c0b-4ef8-bb6d-6bb9bd380a11'
     fn invoke_no_args(&self, num_rows: usize) -> Result<ColumnarValue> {
diff --git a/datafusion/physical-expr/src/scalar_function.rs b/datafusion/physical-expr/src/scalar_function.rs
index a16a00103f9d..f592fdc44996 100644
--- a/datafusion/physical-expr/src/scalar_function.rs
+++ b/datafusion/physical-expr/src/scalar_function.rs
@@ -146,7 +146,7 @@ impl PhysicalExpr for ScalarFunctionExpr {
         // evaluate the function
         match self.fun {
             ScalarFunctionDefinition::UDF(ref fun) => {
-                if fun.support_randomness() {
+                if inputs.is_empty() {
                     fun.invoke_no_args(batch.num_rows())
                 } else {
                     fun.invoke(&inputs)