Apparently, Reagan confused Alexander with Grover Cleveland who the pitcher was named after.
The Speaker pointed out that a desk the new President was using belonged to Grover Cleveland. O’Neill wrote that Reagan was thrilled and stated, “Hey, Grover Cleveland! I played him in the movies!”. Reagan was referring to Grover Cleveland Alexander in 1952’s The Winning Team. O’ Neill stated, “No, no, Mr. President. You played Grover Cleveland Alexander, the baseball player”.