A team has finished a game with 0-3-7 runs-hits-errors line 4 times since 1897, most recently St. Louis Browns on 31 August 1915. That is about one every 110,751 team-games.
Box score for the most recent one ↗
0-3-0 0-3-4 0-3-3 0-3-2 0-3-6 0-3-5 0-3-7 0-3-8 0-4-1 0-4-3 0-4-2 0-4-0 0-4-5
The whole distribution — Runs-Hits-Errors Lines · All 18 shapes