Your hand position is incredibly important regarding your push ups. All of the tension in your upper body has to flow into your hands which mean if your hand position is off, your whole push up is off.
The thing is, just changing your hand position isn’t enough. You also have to take your elbows, shoulders and even your shoulder blades into account. Once you do, you’ll improve not only your hand position but your entire push up technique as a whole.
Check out how to do this in this video: