Do humans mentally discretize numbers? It seems reasonable to me that humans discretize numbers: this number is bigger than than number, or when faced with a series of numbers that range from 0 - 100, 50 is "middling", 10 is "low" and 90 is "high". It doesn't seem to me that the brain would place much value in the difference between 76 or 77.

I ask this in the context of scoring in games: many games present scores to players as numbers, but it seems to me the numbers themselves are meaningless, and actually translate to mental buckets where you can say "this is a good score" or "this is a bad score". Players don't actually perceive the numbers. This would indicate that games that use grading systems like A-F would be better communicators of player performance.

Is there any research to back up this theory? I'm coming up short, but I can't believe no-one has tried to answer this question.
One common way of framing numerical cognition is in terms of a "mental number line". This mental number line is thought to have a logarithmic scale, so perceived differences are inversely proportional to their magnitude. For example, the difference between 6 and 7 is perceived as bigger than the difference between 76 and 77. This is just a variant of the Weber-Fechner Law, which applies in many perceptual domains (sound loudness, object weight, light brightness, etc.). So people don't exactly put numbers into discrete bins, but small differences begin to blur together for larger numbers. 

In typical, educated adults there is also thought to be an explicit symbolic or linguistic representation of numbers that captures their exact value and allows us to do exact calculations.

For theories of numerical cognition, one good place to start is:

Feigenson, L., Dehaene, S., &amp; Spelke, E. (2004). Core systems of number. Trends in cognitive sciences, 8(7), 307-314.