A team has finished a game with 14-13 singles and extra-base hits 1 time since 1897, most recently San Francisco Giants on 1 September 2020. That is about one every 443,004 team-games.
Box score for the most recent one ↗
14-7 14-8 14-9 14-10 14-11 14-12 14-13 14-14 15-0 15-1 15-2 15-3 15-4
The whole distribution — Singles and Extra-Base Hits · All 18 shapes