The bonus roll system is a personal loot feature introduced in Mists of Pandaria
which gives you extra chances at loot on the raid bosses of your choice. Most people have a love/hate relationship with it, myself included. We don't know the exact numbers, but it appears the chance of loot is roughly 15% in current content (usually made higher in previous tiers). There are other variables behind the scenes which affect this drop chance, such as the bad luck streak protection, but we do not know the exact math behind it. When asked on Twitter, Watcher replied that they're happy with the bonus roll system and it will most likely be making a return in Warlords of Draenor
I'm happy it's sticking around. Bonus rolls have gotten me out of some pretty bad loot dry spells. If I could change one thing about them going forward, it would be the lesser charm conversion system. Either have them acquired in a different manner, or make the charms useful for something else. Of course, this is coming from someone sitting on a three year supply of lesser charms. I've seen other player suggestions such as having the option to use multiple rolls on a single kill, or a smarter system which doesn't give you loot you already own. Are you happy with the bonus roll system or would you like to see some changes?