Back to your original question...
I trust what i see during the match, if i am happy with the player (positioning, runs, mistakes, etc.) i 'll keep him otherwise i 'll sub him.
I don't even know how the avg. rating is calculated or what exactly is showing during a match (i see a 'jump' in the end of halftime and fulltime, making me wondering ... why)
And avg. rating is very important since it's affecting player value, development, morale...