When your phone starts ringing at an inappropriate time, the scramble to shut it off is embarrassing. Give yourself a buffer by adding a few seconds of silence to the beginning of your ringtones so you only feel the vibrations at first.
Many phones can be set to both vibrate and play a sound when you're receiving a call. If you're in a meeting or a movie, though, the sound can disrupt those around you. By adding a few seconds of silence to the beginning of your ringtone, you can feel that your phone is buzzing before the ringtone actually starts making noise. Those few seconds will (hopefully) be enough time to silence your phone before the disruption gets worse.