My opinion, I think the arena should have a ranking based on the total players in the game and your arena points.
So, let’s say, there is 850.000 total players, the tiers should be something like this (just an example):
Platinum:
top 1% of total players = 8500 players.
Gold V:
next top 4% of total players = 34000 players.
Gold IV:
next top 3% of total players = 25500 players.
Gold III:
next top 3% of total players = 25500 players.
Gold II:
next top 2% of total players = 17000 players.
Gold I:
next top 2% of total players = 17000 players.
Silver IV:
next top 3% of total players = 25500 players.
Silver III:
next top 3% of total players = 25500 players.
Silver II:
next top 2% of total players = 17000 players.
Silver I:
next top 2% of total players = 17000 players.
Bronze IV:
next top 15% of total players = 127500 players.
Bronze III:
next top 20% of total players = 170000 players.
Bronze II:
next top 20% of total players = 170000 players.
Bronze I:
last 20% of total players = 170000 players.
So, the player with the highest total points will be the first place (highest position in Platinum), while the player with the lowest points will be at bottom in Bronze I.
Then, if the game gets more players, that % will be the same, just that if the total players grew to 920.000, the total players that can be Platinum will be 9200 and so on so forth, so the numbers will be dynamic instead of static.