There isn't a "Time Used In Arena" per se, but since your ammount of points won't increase if you don't play others will soon get more points than you and thus your rank in this catagory will increase (getting worse). Since your fighter rank is found by adding each individual fighter-skill rank (K/D, hit% etc.) and seeing who has the lowest number, you will slowly increase.
PS: It seems a lot of players try to see how good a K/D they can get the first few days of a tour before they start fly less catious. This makes a K/D of 3+ a regular sight at the beginning, than later. That means that your 3.75 might give you a better and better rank in the K/D stat as time goes, somewhat cancelling the effect of your low points value.
PPS: I think I am one of the few that says they DO care about score. I am not fanatic about having a good one, but feel I have more fun when I play to achive something.
It's not like I am doing milkruns endlessly to training facilities just to rack up bomb hit% of 500+ for instance.