diff --git a/bigframes/series.py b/bigframes/series.py
index 87f1f1d141..37a3723a0a 100644
--- a/bigframes/series.py
+++ b/bigframes/series.py
@@ -1712,9 +1712,18 @@ def apply(
             # as a whole.
             if by_row:
                 raise ValueError(
-                    "A vectorized non-BigFrames BigQuery function can be "
-                    "provided only with by_row=False. For element-wise operation "
-                    "it must be a BigFrames BigQuery function."
+                    "You have passed a function as-is. If your intention is to "
+                    "apply this function in a vectorized way (i.e. to the "
+                    "entire Series as a whole, and you are sure that it "
+                    "performs only the operations that are implemented for a "
+                    "Series (e.g. a chain of arithmetic/logical operations, "
+                    "such as `def foo(s): return s % 2 == 1`), please also "
+                    "specify `by_row=False`. If your function contains "
+                    "arbitrary code, it can only be applied to every element "
+                    "in the Series individually, in which case you must "
+                    "convert it to a BigFrames BigQuery function using "
+                    "`bigframes.pandas.udf`, "
+                    "or `bigframes.pandas.remote_function` before passing."
                 )
 
             try: