A barrel roll can be whatever you want it to be. No such thing as one "right" way to do them. A barrel roll is simply a roll where the CG of the airplane describes some degree of corkscrewing flight path through the air. A plain old positive G aileron roll is technically a barrel roll...just a very tight one, with limited pitch and yaw excursions. But barrelling is still present during a 1G aileron roll. Or you could barrel it such that the airplane is 90 degrees off heading at the top with large altitude deviations...and anywhere in between. It's all barrel roll.
A full barrel roll is not a competition figure, but you can still do them with competition precision. A quarter clover is a competition figure, and is basically half a barrel roll, either up or down. Blend two clovers together perfectly, and you could actually have a standard for precision when doing barrel rolls.
For example, a quarter clover up consists of pitching the airplane up from level flight while perfectly integrating roll such that the airplane flies a round profile upwards while finishing a half roll simultaneous with reaching both the inverted level attitude AND a perfect 90 degree heading displacement. From there, it's just a half loop down, ending 90 degrees from your original heading. The goal is to evenly integrate the pitch and roll such that there is no pitching or rolling without both occuring at an even rate. Roll rate should be constant, and the roll should stop concurrent with reaching the inverted attitude, and 90 degrees off heading. Fairly challenging to do perfectly.
A quarter clover down is the same concept, reversed. Fly a round half loop up, and immediately upon reaching the inverted level attitude, start a roll that perfectly integrates with the second half of the loop such that you simultaneously reach level flight, wings level, and 90 degrees from your entry heading. Finish the roll before you have pitched to level flight, or reach level pitch attitude before finishing the roll, and you've done something wrong. Again, put two clovers together, and you've got a precision barrel roll. Anyway, just gives you something challenging to work on rather than just boring holes in the sky, if you're into that sort of thing.
