Generally, an animal is assessed on its "degree of difficulty". An animal with very athletic action and variations in pattern and style, coupled with weight speed and power, will test the best of any contestant.
While saddle and bareback broncs may have similar bucking characteristics, riding styles and equipment determine very different scoring elements between both of these events, whilst bull riding again has very separate elements. In all riding events, the contestant is scored on control, timing, balance, and the technical requirements of each event.
If the Judges consider the animal didn't perform well enough, not giving the rider a fair crack at the competition, they then have the discretion to award the contestant a ‘re-ride' which means he gets another ride on a different animal.