How do transitions improve jumping performance in hunter jumper horses?

Transitions — both between gaits and within gaits — improve jumping performance by developing the specific hindquarter engagement, balance, and responsiveness that quality jumping requires, and their effect on jumping is so direct and well-documented that quality transitions are considered the single most important flatwork exercise by many experienced hunter jumper trainers. The downward transition specifically is the most valuable: when a horse transitions from canter to trot or trot to walk in response to the rider's half-halt or seat aid, it must shift its weight backward onto its hindquarters to decelerate, which both develops the carrying capacity of the hindquarters and teaches the horse to respond to the rider's balancing aids. This is precisely the response that the approach to a fence requires — the half-halt before a fence that reorganizes the horse's balance and prepares it for the takeoff is a micro-version of the downward transition, and a horse trained through many quality downward transitions will respond to the approach half-halt more readily and more completely than one trained without systematic transition work. The upward transition is equally valuable from a different direction: a transition from walk to trot or trot to canter develops the horse's forward responsiveness to the driving aids, which is the response needed when the horse needs to be encouraged forward to a long distance or maintained in front of the rider's leg through a difficult combination. Transitions within the canter — collected to working to medium canter and back — develop the specific adjustability that allows the horse to lengthen to a long distance and compress to a short one, which is the practical application of canter adjustability in course riding. The quality of the transitions — whether they are prompt, balanced, and maintain the rhythm — is as important as the quantity, and ten excellent transitions are more valuable than thirty mediocre ones.