Genetics definately play an important role in colour breeding. While we never bred paints, I am guessing that it follows the basic genetic rule that the two "colour" breeds shouldn't be bred together (breed a spotted horse to a solid horse) and, when this is done, the foal takes a gene from each parent, making it a 50/50 chance of getting colour. Of course, you can increase your chances by ensuring that the solid horse has at least one colour gene themselves and by breeding with horses (even solids) who have a history of producing (or siring) colour.