Your problem isn't the competitive aspect. Its that your Arena is bare bones and stale as all hell.

Zero infrastructure. Your answer isn't in yet ANOTHER friggen tournament... God, someone please stop that trend. Its like beating a dead horse around here. Tournaments and Safe Spaces don't build community. Neither does this absurd notion of taking a dive on purpose for the "sake of story" which only cheapens the experience. This is RP Fighting, that's the format. The Arena has been a thing ever since 1997 for Christ sake.

Its super simple, guys.

[b]1:[/b] Your ranks mean jack shit. There's no value to those records. Step One is doing a hard reset on all player scores. You want change? It starts there. Next, ACTUALLY HAVE LEGIT RANKS... What you have is just a stupid Leaderboard. What you want to do is have actual established "Ranks" that have requirements for each the higher you go that progressively get more difficult. Back in the community where I started, we had a pretty clear cut system in place. 
[b]-E Rank;[/b] Entry Level, everyone starts at the bottom.
[b]-D Rank;[/b] Acquire 5 Wins using a Martial Archetype Character. (What you would know around here as RM, I believe?)
[b]-C Rank;[/b] Acquire 10 Wins using a Tech Archetype Character. (Whether real world technology or sci-fi technology)
[b]-B Rank;[/b] Acquire 10 Wins using a Magic Archetype Character. (Anything Fantasy based)
[b]-A Rank;[/b] Acquire 20 Wins using a Hybrid Archetype Character (Mix at least 2 of the 3 Basic Archetypes in one character) in ADDITION to completing a Level Up Exam administered by an Arena Mod. (The Level Up Exam is meant to test your Problem Solving Skills, Combat Tactics and how Creative you are)
[b]-S Rank;[/b] Granted the Title of "ACER" for completing this challenge, the only requirement necessary is for you to actually defeat a Team of A Ranked Fighters. (3 Person Squad)

There will be a list of pre-made Battlegrounds for each Rank. Players can ONLY participate in the Battlegrounds listed for their Rank or below. A Rank Battlegrounds will include special conditions, environmental hazards, Hostile NPCs that can randomly be controlled by an Arena Mod at any time during the fight along with other potential gimmicks to further encourage creative approach to challenging situations.

IN ADDITION, if you LOSE a fight, your score suffers. Yes, there is a damn good reason for that. It discourages you from simply quitting a fight and provides legitimate risk involved for losing. Once you manage to hit a milestone and Rank up, though, you can't be DROPPED a Rank. Your score also doesn't go into the negatives, it just stays at 0.

[b]2:[/b] Create a legitimate RULEBOOK for the Arena that includes all the Rules and explanations for how to actually play the game within an RPF Format. Using said Rulebook will be mandatory for all Ranked Matches and Guild Events.

[b]3:[/b] Encourage the formation of "TEAMS" by having a Team Registration thread and hosting Team Events. Give Teams ranks also. This builds community as even weaker players can overcome the odds with proper teamwork. In fact, do MORE Team related stuff. Make it a central focus of the Arena.

[b]4:[/b] Introduce Gauntlet Challenges. Another old school concept, basically a mix of PvE and PvP. The Arena Mods will take control of dangers present within a set location for either Solo Players or Teams can enter to test their mettle against whatever crazy challenges the Mods throw at them. Like a legitimate ARMY that said Mods have total control over. (And because its a Gauntlet Challenge, NPCs in this setting are treated as Player Characters, effectively giving the Mods plenty of options to let loose) You can even include a "Raid Boss" at the end with some spiffy reward(s) for the player's character if they manage to complete the challenge.

[b]5:[/b] Create a Hall of Fame. Players who hit serious achievements should be honored and shown the proper respect for overcoming legitimate challenges.

RPing and the Arena has always been a time honored tradition for any RP Community. You need to understand what the Arena actually MEANS and the actual flame of passion that continues to burn bright. Its all about our EMOTION, an expression of who YOU are and the true values it symbolizes.
Ahem;
[youtube]https://youtu.be/RAk0sw_H50M[/youtube]
That's what I'm talking about.