Something that's arbitrary seems like it's chosen at random instead of following a consistent rule. Team members would dislike their coach using a totally arbitrary method to pick starting players.
Even though arbitrary comes from a word meaning "judge" (arbiter), that doesn't mean judges are always fair. Calling a decision-maker arbitrary is usually a negative thing, suggesting the person is making rules based on whim rather than justice. A coach who selects starting players arbitrarily isn't strictly applying a rule; he could just be picking names out of a hat.
adj based on or subject to individual discretion or preference or sometimes impulse or caprice
not limited by law
capricious, impulsive, whimsical
determined by chance or impulse or whim rather than by necessity or reason
having or using the ability to act or decide according to your own discretion or judgment