near miss

noun3

1. •
   A miss which was nearly a hit or collision.

   • The first wave, 24 dive bombers, fell on her through broken clouds; she took two hits and an uncomfortably close near miss. — 2000
2. •
   A scenario which ends safely but might well have ended in disaster.

   • In recent years there have been two fatalities and one near miss due to the inappropriate use of boom trucks. — 2009
3. •
   An attempt which fails narrowly; a performance which falls just short of a certain benchmark.

   • Dean Chance […] wasn't crying over his near miss of a no-hitter Monday night. — 1962