A team has finished a game with 3-1-0 runs-hits-errors line 19 times since 1897, most recently San Diego Padres on 4 June 2014. That is about one every 23,316 team-games.
Box score for the most recent one ↗
2-17-3 2-17-2 2-17-1 2-18-2 2-19-1 3-1-2 3-1-0 3-1-4 3-1-3 3-1-1 3-2-1 3-2-2 3-2-3
The whole distribution — Runs-Hits-Errors Lines · All 18 shapes