A team has finished a game with 14-14 singles and extra-base hits 1 time since 1897, most recently Montreal Expos on 30 July 1978. That is about one every 443,004 team-games.
Box score for the most recent one ↗
14-8 14-9 14-10 14-11 14-12 14-13 14-14 15-0 15-1 15-2 15-3 15-4 15-5
The whole distribution — Singles and Extra-Base Hits · All 18 shapes