Horse Show Math

BY Daphne Thornton of Two Bit Training

We call it Horse Show Math but, really, it is just Horse Riding Math. In many ways, you can think of a hunter or jumper course as a simple math problem that you and your horse solve together. Surprisingly, horses are pretty good at figuring out the “math” of a jump, or a line, or a course. Once they have practiced it a few times and found a pace and step that works, they tend to stay there. It’s up to us to help them find that perfect step and pace with our riding MATH. 


We begin our riding math with simple arithmetic. Almost everything we do on course is based on the  idea of a 12’ canter stride, so we learn to think in “units” of 12 feet. When we are looking for that “ideal” hunter, we are looking for a horse with close to a 12’ stride, or one who can easily be adjusted to a 12’  stride. Since judges like hunters to look “slow”, our ideal hunter will have a stride that can be adjusted DOWN to a 12’ stride, rather than having to adjust UP. In a jumper, a long stride is also better, but a really ADJUSTABLE stride is most important. 

If we are thinking in terms of a single jump, then our 12’ unit, in relation to the jump, is the 6’ in front of  the jump, and the 6’ in back of the jump. In a perfect world (and depending on the height of the jump) our horse takes off 6’ in front of the jump and lands 6’ behind it. 

If we put two jumps together in a line, then the 6’ behind the first jump and the 6’ in front of the second  jump are used for landing and take-off. So, 12’ of our line is unusable for our horse’s canter strides between the jumps. It’s already occupied as the take-off and landing zone. If we were to count the number of strides (units) in a 60’ line, we would have to count the first 12’ as ZERO. Then the second 12’ would be ONE stride, the next 12’ TWO strides, and so on. So, while there are 5 UNITS in a 60’ line, there are only four STRIDES. 

In the jumpers, distances are not as precisely aligned with a 12’ unit, so how well you and your horse can lengthen and shorten your strides is critical. In addition, the “math” of your take-off and landing zones is more important. Too long at take-off will result in a flat jump and a rail down. Too close and your horse may not get his front end out of the way quick enough and, again, may pull a rail. 

So, our goal would be to have our horse cantering on or close to a 12’ stride throughout our course, while we used the bridle to make minor adjustments to find the perfect take-off spot. The exercises you do in your lessons with GROUND LINES and IN-AND-OUT gymnastics are to help reinforce the perfect take-off and landing spots and to help you and your horse learn that desirable 12’ stride. If you ride a pony, the stride lengths (units) are adjusted based on the size of your pony (small, medium, large).


Once we get to Algebra, we learn to solve equations. What is an equation? In an equation, the quantities on both sides of the equal sign are the same. So, if a + b = 10, a and b have to be two numbers that add up to 10. Both sides of the equation have to be the SAME THING, or equal. 

On a hunter course, for our purposes the jump is the = sign. As we are cantering a jump, or a line, or a course, we want what happens on the back side of the jump to mirror what happens on the front side, and vice versa. We want our approach and our ride away to be equal. 

In our flatwork, we are always striving for an EVEN pace. The USEF rulebook even mentions even hunting pace as one of the criteria on which rounds are judged. Our Equine Algebra is a way of thinking about keeping the pace on both sides of the jump equal. 

When we have you count strides out loud, we are having you use your voice as another way to monitor and reinforce the evenness of your strides. If you hear your count speeding up or slowing down (in addition to feeling it, which is harder) you can work on making adjustments and getting back to an even hunting pace. 

Therefore, a QUALITY CANTER is the most important asset to help you get around a course and be the winner. You may think we are teaching you to jump, but what we are really teaching you is how to achieve a quality canter, maintain a quality canter, and find the jumps. And, that quality canter includes having accessible adjustability immediately in your bridle – without sacrificing your IMPULSION (forward  “go” or “take” to the jump that comes of the hind end being fully engaged at the canter). 

Many horses learn to canter on a long stride by reaching out in front and going fast. This is not very comfortable and can feel like you are running over the jumps. We have all seen horses at shows that have this way of going. Whenever I see this, I think “the hunter is clean and within the time allowed.”  Most of the time, the spectators are at least as terrified as the rider at this approach to a course. This is a clear indication of a rookie rider or an uneducated trainer. They are desperate to “make the stride” but don’t know how to produce the right canter. 

We try to teach all of our horses that their “normal” canter rhythm is a 12’ stride (or less, if they are a  pony), achieved through an engaged hind end and relaxation through the back and in to the bridle. While we don’t want to spend a ton of time practicing shorter or longer strides, your horse – and you – need to know how to collect (to a shorter stride) or lengthen (to a longer one). On course, we still strive for that evenness of stride (equine algebra!) – at whatever length works for the lines that are set. 

Good examples of striding challenges are the shows with smaller indoor arenas or with poor footing. When the ring is small or the footing questionable (or both), the lines should be set a bit shorter. Most horses don’t like the feeling of opening up their stride in a small space, with walls coming at them very quickly when they land off a jump. In addition, iffy footing will make a horse want to shorten their stride to protect their front feet and legs. So at that show, we often elect to add in the lines in any classes under 3’, to make our horses feel more comfortable. Riders at 3’ or above should be ready for the  challenge of making the step in less than ideal conditions. 

Conversely, many shows held in large outdoor arenas will add length to lines. Horses are more than willing to gallop a bit in a wide open area and usually the footing is pretty quality in those venues. So, a five stride line may be set at 73.5 feet, instead of 72 feet. The stride-ier horses or the more educated riders end up the winners. 


Most of you have heard me say that the eight most important things that go into putting together a perfect course are track and pace and pace and track and track and pace and pace and track. If you don’t get the joke, come see me after class. Our Equine Algebra talks mostly about PACE. Now, we get to TRACK. 

When we are riding a course, we have to take into account the geometry of the ring and the geometry of the course. Some rings have very square corners, some very round. Some rings are big, some small. Some rings are wide, some narrow. You get my drift. Each will require you to adjust your TRACK in order the make the course FLOW and to find the jumps at an even hunting PACE. 

A good hunter course designer takes the ring geometry into account in their courses and designs turns that flow from one line into another. They will try to avoid tight turns (less than 90°) and short take-off or landing tracks. A good jumper course will ask difficult pace, track, and striding questions without being “trappy.” 

Tight turns on a hunter course make it VERY DIFFICULT to maintain your quality canter. You will almost  surely lose pace in those turns and be in the position of having to ask your horse to go more forward (trying to reestablish your canter) while you’re heading for the next jump. If you can’t get your canter back, you’re going to add. If you CAN get your canter back, you are likely to be going too forward at that point and miss a distance or need to make a major canter adjustment once you jump in to the line. Both will be major deductions to your score.  

The course designer can be your best friend, or your worst enemy. For the most part, hunter courses should be simple and inviting – again, encouraging that lovely FLOW through the course from a quality canter. Courses that disrupt that flow, with difficult tracks (turns), incorrect striding distances, or too many obstacles that make it hard to weave your way through to the next jump, are NOT good courses. Sometimes designers try to show how much they know by crowding the ring with jumps and hard turns. They are really just showing you how much they DON’T know. 

We don’t walk hunter courses, but we school and have warm-up classes that allow us to ride the course and find the best tracks. Distances are required to be posted right on the courses. In the jumpers, we are allowed to walk the course to determine track and distances best for our horse, but we cannot school and distances are not listed. In the jumpers, your horse’s stride should be foremost in your mind as you walk the course and determine distances and tracks.


Once we learn the SIMPLE ARITHMETIC of striding, we apply that to creating an EVEN HUNTING PACE  over our course using our EQUINE ALGEBRA. Finally, our TRACK GEOMETRY shows us the perfect track to follow so that we FLOW EVENLY throughout the course, find the jumps, and may get a good ribbon. 

None of that is possible without a RHYTHMIC canter that has IMPULSION through the hind end and CONTROL through the bridle. Some horses (including some of our lesson horses and ponies) are not able to achieve this type of perfect canter due to their physical limitations. In those cases, we strive for rhythm in the canter, which almost every horse is capable of producing. Rhythm is the basis of a good canter, and in most situations, over lower jumps, rhythm will produce the right kind of look for your ride. RHYTHM will allow you to find the jumps, even without a great hind end. But, without at least some rhythm, you can’t be the winner.