There is also a function called “VSYNC” that synchronizes the game FPS with the refresh rate per second. Vsync prevents tearing when the game FPS is not aligned with the refresh rate, causing stuttering in the process (unless the game is fps is above refresh rate in that case it’s ok). So, if you play with Vsync on:

• If you have a game that can run at 60 fps almost all the time, I recommend you to run the game at default settings.
• If you have a game that can run at 50-59 fps almost all the time, but struggles keeping 60 fps. Then I recommend you lowering the refresh rate to 50Hz. You will have a 50 FPS experience but you will avoid frequent stuttering caused by vsync.
• if you want to play at 30 FPS to save battery life and the game can easily run 30 FPS at all times, especially on a game that barely keeps 60 fps, you don’t need to reduce refresh rate to 30Hz, you can keep refresh rate at 60Hz and cap the FPS to 30. (So the game never reaches 60 fps, causing stuttering).

Vsync, more or less gives you a half-refresh-rate experience when your game fps sits below your refresh rate and above the half of it. (So if you cap a game at 59 fps with 60Hz, you will experience the game “like” running at very smooth 30 fps). If you cap the game at 29 fps with refresh rate at 60Hz it gives you “like” a smooth 15fps experience, but looks horrible.

All this stuff I mentioned, doesn’t apply to displays that can handle VRR (variable refresh rate) technologies like FreeSync/G-Sync_compatible or G-Sync.