ENH: Infer best datetime format from a sample

doc/source/user_guide/io.rst

@@ -977,11 +977,10 @@ Note that format inference is sensitive to ``dayfirst``.  With
 ``dayfirst=True``, it will guess "01/12/2011" to be December 1st. With
 ``dayfirst=False`` (default) it will guess "01/12/2011" to be January 12th.
 
-If you try to parse a column of date strings, pandas will attempt to guess the format
-from the first non-NaN element, and will then parse the rest of the column with that
-format. If pandas fails to guess the format (for example if your first string is
-``'01 December US/Pacific 2000'``), then a warning will be raised and each
-row will be parsed individually by ``dateutil.parser.parse``. The safest
+If you try to parse a column of date strings, pandas will attempt to find the format
+which work best from a sample of non-NaN elements, and will then parse the rest of the
+column with that format. If pandas fails to guess the format, then a warning will be
+raised and each row will be parsed individually by ``dateutil.parser.parse``. The safest
 way to parse dates is to explicitly set ``format=``.
 
 .. ipython:: python
@@ -994,7 +993,9 @@ way to parse dates is to explicitly set ``format=``.
    df
 
 In the case that you have mixed datetime formats within the same column, you can
-pass  ``format='mixed'``
+pass  ``format='mixed'``. Pandas will convert rows to the best format found (the one
+which matches the most rows), and then iteratively convert the remaining rows with the
+remaining formats.
 
 .. ipython:: python
 

doc/source/whatsnew/v0.19.0.rst

@@ -765,6 +765,7 @@ Previously if ``.to_datetime()`` encountered mixed integers/floats and strings,
 This will now convert integers/floats with the default unit of ``ns``.
 
 .. ipython:: python
+   :okwarning:
 
    pd.to_datetime([1, "foo"], errors="coerce")
 

doc/source/whatsnew/v2.1.0.rst

@@ -16,8 +16,53 @@ Enhancements
 
 .. _whatsnew_210.enhancements.enhancement1:
 
-enhancement1
-^^^^^^^^^^^^
+``pd.to_datetime`` now tries to infer the datetime format of each string by considering
+a random sample (instead of the first non-null sample),
+and tries to find the format which work for most strings. If several
+formats work as well, the one which matches the ``dayfirst`` parameter is returned. If
+``format="mixed"``, pandas does the same thing, then tries the second best format on the
+strings which failed to parse with the first best format, and so on (:issue:`52508`).
+
+*Previous behavior*:
+
+.. code-block:: ipython
+
+    In [1]: pd.to_datetime(["01-02-2012", "01-03-2012", "30-01-2012"])
+    Out[1]:
+    ValueError: time data "30-01-2012" doesn't match format "%m-%d-%Y", at position 2. You might want to try:
+    - passing `format` if your strings have a consistent format;
+    - passing `format='ISO8601'` if your strings are all ISO8601 but not necessarily in exactly the same format;
+    - passing `format='mixed'`, and the format will be inferred for each element individually. You might want to use `dayfirst` alongside this.
+
+    In [2]: pd.to_datetime(["01-02-2012", "01-03-2012", "30-01-2012"], errors="coerce")
+    Out[2]:
+    DatetimeIndex(['2012-01-02', '2012-01-03', 'NaT'], dtype='datetime64[ns]', freq=None)
+
+    In [3]: pd.to_datetime(["01-02-2012", "01-03-2012", "30-01-2012"], format="mixed")
+    Out[3]:
+    DatetimeIndex(['2012-01-02', '2012-01-03', '2012-01-30'], dtype='datetime64[ns]', freq=None)
+
+
+*New behavior*:
+
+.. code-block:: ipython
+
+    In [1]: pd.to_datetime(["01-02-2012", "01-03-2012", "30-01-2012"])
+    Out[1]:
+    UserWarning: Parsing dates in %d-%m-%Y format when dayfirst=False was specified.
+    Pass `dayfirst=True` or specify a format to silence this warning.
+    DatetimeIndex(['2012-02-01', '2012-03-01', '2012-01-30'], dtype='datetime64[ns]',
+    freq=None)
+
+    In [2]: pd.to_datetime(["01-02-2012", "01-03-2012", "30-01-2012"], errors="coerce")
+    Out[2]:
+    UserWarning: Parsing dates in %d-%m-%Y format when dayfirst=False was specified. Pass `dayfirst=True` or specify a format to silence this warning.
+    DatetimeIndex(['2012-02-01', '2012-03-01', '2012-01-30'], dtype='datetime64[ns]', freq=None)
+
+    In [3]: pd.to_datetime(["01-02-2012", "01-03-2012", "30-01-2012"], format="mixed")
+    Out[3]:
+    DatetimeIndex(['2012-02-01', '2012-03-01', '2012-01-30'], dtype='datetime64[ns]', freq=None)
+
 
 .. _whatsnew_210.enhancements.enhancement2: