Thanks for your question. By the things that you are telling me, the difference is in the "run stage".
Most definately this a problem that most of the time is started by the rider. Whether we know it or
not or want to recognize it, the way we ride is repetitive. By doing several things to a horse over a long time period, sends a horse a signal which they diagnose and analyze in reference to the training that you,
the rider have given them in the past.
When you run a horse, I'm sure you already recognize the fact that you may work with one pocket, while at a run...a horse goes another spot that is closer---correct?? Now take that philosophy and put it to use. When you are running across the pen in the past, you might be sending a signal which to you means "i have to get a better grip on the rein, or I need to get me/the rider ready for the turn"...but as the horse, by the doing these things in advance you have put him in a situation where he has been tuned on in the practice pen at a slower pace and feels you do these things which tells him "turn here"....does that make sense to you? Now use the philosophy about the pocket and put it into place. If you have tuned a horse two feet back away from a barrel before the turn--he will anticipate having to get his body into place the way YOU as the rider have to get your body into place before the turn, and shorten his length to the barrel to prepare himself. For a horse wanting to do his job so badly and wanting to work, that ends up in disaster usually---either a horse that hits a barrel on the front side (which is probably what you were doing before he started this ducking) or a horse that simply ducks.
The cure?? Remember when you tune...the point of which a horse needs to set his hocks down is called the "point of the turn"...that is usually about where your knee or his flank hits the front side of the barrel going in...when you tune you must tune to the point of the turn...find it and do it the same each and every time. Also, reinforce what LIFT means to your horse...does lift mean turn here, or does lift mean get off my hand and move over?? Take all that into consideration. Your horse simply is repetitive to what you have already taught him. If Lift means turn here to him---you either need to go back and regroup your training to teach him that lift means move over and get off my hand or learn to ride a harder outside rein (which is NOT the cure, but a quick fix if you can't teach it) going into your turn and not drop the outside until you are already in the turn. I prefer to fix the problem rather than "band aid" it so to speak so I will go back and teach them to move over.
In closing I have to say this as well. In my opinion, there are 2 kinds of horses that duck...and you can diagnose what you have by this simple formula. A horse that ducks is either malicious with it, or is a horse that truly loves their job. The horse that is malicious will find a place to go after they duck...want to run back to the alley, run past the timer, ect. The horse that truly is getting the mixed signals, and wants to work and most likely has been exposed to rider error is the one who simply ducks and might even turn before the barrel and pretend it is a barrel and want to go to the next one. Those horses are easy to retrain and are very salvagable without much worry. The malicious ones are the ones I check for physical problems and hurt somewhere. No horse intends to be that bad---if you knew something wasn't going to go well before you did it, you'd find a way out too.
If you need anything else...let me know...horses that run off, and duck off are my specialty. They've been "my claim to fame" for quite some time so to speak...so if you have a question...just let me know and we can go thru it step by step.
Thanks and I wish you luck and have a great holiday season!