A team has finished a game with 4-4-4 runs-hits-errors line 20 times since 1897, most recently Kansas City Royals on 23 April 1983. That is about one every 22,150 team-games.
Box score for the most recent one ↗
4-4-3 4-4-0 4-4-2 4-4-1 4-4-8 4-4-7 4-4-4 4-4-6 4-4-5 4-5-3 4-5-2 4-5-1 4-5-6
The whole distribution — Runs-Hits-Errors Lines · All 18 shapes