Has an MLB game ever ended 16-13?
Yes. MLB has seen a final score of 16-13 19 times. It first happened on June 14, 1884, when Indianapolis Hoosiers beat Philadelphia Athletics, and most recently on July 18, 2023, when Arizona Diamondbacks beat Atlanta Braves.
That makes 16-13 the 176th most common final score out of 330 that have ever occurred in MLB. One point away, 17-13 has happened 15 times and 16-14 has happened 8 times. At one point the score disappeared for 35 years, between 1934 and 1969.