You could go with a basic grade system for moving up through the ranks.
Fresh Meat starts off at Rank 10, or you may want to start at Rank 25 as you prefer. The ranks run from 1 - 100.
Edit: Forgot some conditions
WINNINGIf the Winner was Higher rank than the Loser: No change in Rank. You can not beat up kids for their lunch money and claim the title of Master.

If the Winner and Loser were evenly ranked: Winner gains 1 Rank
If Winner was lower ranked than Loser: Increases your rank by half the difference between you rounding down, minimum rank adjustment of 1.
LOSINGIf Loser was higher ranked than Winner: Loser drop in rank by half the difference rounding
up, because losing sucks, minimum rank adjustment of 1.
If Loser and Winner are evenly ranked: Loser drops 1 Rank
If Loser was lower ranked than Winner: No change in rank. You tried but were out of your league.

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If you have a rule about no more than 10 ranks difference between contestants the max you can move in any one fight is 5, so you have quite a few fights to work your way up.
So two new guys meet in the ring with a starting rank of 10.
A wins and gets bumped to 11.
B loses and drops to 9.
A&B have a rematch later that week and B wins.
A drops to 10 (losing half the difference rounding up which is still a 1 ) and B goes up to 10 (half the difference rounding down for 1), next week will see who comes out on top.
B feeling a need to test himself challenges C who is ranked 15 and wins.
B goes up from 10 to 12 (half the difference of 5, rounding down) while C drops from 15 down to 12 (half the difference rounding UP).
But what if B had really been feeling their oats so instead of going after C they had gone up to the local boss D who is rank 19 and, against the odds laid out by the bookie, wins.
B goes up from 10 to 14 (half of 9, rounding down) while D drops from 19 to 14 ( half of 9 rounding up). Way to go champ.
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This allows for advancement while also slowing down flukes from catapulting someone to too high a spot just for being lucky once in a fight.
Plus you don't have to come up with tons of tables and calculations to figure out what a players 'rank' is based on their augmentations/stats/skills.
Advancement is based on wins or losses and the differences between differently skilled/augmented characters will sort itself out over time.
I would suggest adding a rule that Rank 90+ can only challenge 1 rank higher so no skipping in the home stretch.
This draws out the suspense of making it to the top as these will probably be the most spectacular fights.
In the absence of a middling rank one can challenge the next step up as if they were the missing rank.
So for example say you are the only rank 98 (so you don't have another 98 to fight and get bumped to 99, slapping around the 97's won't help) and for some reason there is no rank 99 available to fight (dead, missing, etc..) then the 98 could challenge the 100 as if he were the missing 99 and if he wins would take the 100 spot while the former 100 drops to 99. If he loses, he remains at 98.