Thank you! The "split hit" is a misnomer imo. I've probably called well over a thousand close hits in my time, many of them extremely close. But you can ALWAYS tell by the action of the balls what took place. You need to observe the paths that the object balls (and the cue ball) take after contact. Rarely is there a situation where it cannot be determined which ball was contacted first. In that rare instance where I just cannot tell, then I will rule in favor of the shooter.
99% of the time you "know" when a foul has been committed just by observing closely what takes place. Unfortunately many officials/referees don't know where to stand to have the best view of the shot. I like to stand where I can see the cue ball making contact with the object balls at the point of contact. Standing behind the shooter and watching the cue ball travel in the direction of the balls is not the best place to be to see the hit properly. The closer you can stand to that point of contact (ideally where you can see it going in from the back and not the front) affords you the best opportunity to make the correct call.
Unlike the players who do well to play at a 90% success rate, a good tournament official should perform at or near 100% for the entire event. No one is perfect but for me I consider that I've only had a good tournament if I didn't miss one call. If I missed just one then it's only a fair to average tournament from my point of view. In a major event, I will make between fifty (that's low) to one hundred (that's on the high side) calls in total during the course of the event.