Odds of Getting In
Everyone wants the final word in an argument, but most don't want the years upon years of study and practice required to legally earn it. Basically, there aren't many people with the credentials to knock at the door of arbitration who don't end up getting in. There are about as many arbitrators as people who want to be arbitrators, and that's just fine with everyone involved.
Part of the reason for that is that arbitration is just one of the many, many things you can do with the expertise required to be an arbitrator. Things aren't looking up? Oh well, guess you'll just have to settle for being a lawyer making over $120,000 a year. So if you want the job and you have the skills, chances are you're made in the shade.