A team has finished a game with 15-13 singles and extra-base hits 1 time since 1897, most recently New York Giants on 15 June 1929. That is about one every 443,004 team-games.
Box score for the most recent one ↗
15-7 15-8 15-9 15-10 15-11 15-12 15-13 16-0 16-1 16-2 16-3 16-4 16-5
The whole distribution — Singles and Extra-Base Hits · All 18 shapes