Fortunately, the odds of getting into a fight with Frank Mir are very slim.
Not likely you'll run into Mike Tyson either.
What you really need for self-defense is a method to quickly put the hurt on the attacker, giving you time to get away.
Just about all self-defense systems are designed for this, not for fighting someone in the octagon.
For example, the well-known karate punch is targeted for the solar plexus. One solid blow to the solar plexus will incapacitate the opponent, giving enough time to get away. No need to roll around for several minutes on the floor.
A wise person will avoid places where violence tends to happen, like in bars with drunk people.
Don't get drunk yourself and become an asshole.
Both of the above I have done of course.