A team has finished a game with 13-14 singles and extra-base hits 1 time since 1897, most recently Philadelphia Phillies on 11 June 1985. That is about one every 443,004 team-games.
Box score for the most recent one ↗
13-8 13-9 13-10 13-11 13-12 13-13 13-14 13-15 14-0 14-1 14-2 14-3 14-4
The whole distribution — Singles and Extra-Base Hits · All 18 shapes