In one of our courses a member asked a question about crookedness. She wanted to know which exercises to ride on the hollow side and the stiffer side to combat the symptoms of crookedness. There is unfortunately not a simple, straightforward answer to this because crookedness leads to imbalance on several different levels, such as:
left to right balance
front to back balance
a difference of muscle strength between the left and the right hind leg
an imbalance between the flexor muscles (carrying power) and extensor muscles (pushing power) in each hind leg
a difference in stride length between the right and left hind leg
a difference in body awareness and coordination between the left side and the right side of the body
a difference in flexibility of the muscles on both sides of the body
a difference in lateral mobility of the shoulders
a difference in lateral mobility of the hindquarters
a difference in lateral mobility of the spine
That’s why you may have to ride some of the same exercises in both directions, but perhaps for different reasons or to address a different set of issues.
The legs on the stiffer/convex side have to support more weight than the legs of the hollow/concave side.
The front leg of the stiffer side carries the largest share of the weight.
The hind leg on the hollow side carries the smallest share of the weight.
The hind leg on the stiffer side pushes more, but doesn't flex enough because it tends to lag behind so it never steps enough under the body. Its extensor muscles are stronger than its flexor muscles.
The hind leg on the hollow side neither really flexes/supports nor extends/pushes because it's always off to the side.
The hind leg of the stiffer side tends to move more slowly and take shorter steps because the hind leg of the hollow side doesn't stay on the ground long enough, forcing the hind leg of the stiffer side to touch down too early.
Both hind legs have to be strengthened and made more flexible. In order to be able to do this, both hind legs have to be brought under the body first because the hind leg of the stiff side is too far out behind, and the hind leg on the hollow side is off to the side. Only when a hind leg steps underneath the center of gravity can you use the body mass to strengthen and supple it vertically.
Once the hind leg of the stiffer side is underneath the body, you can strengthen its flexor muscles with down transitions, turns, and half halts.
Once the hind leg of the hollow side is underneath the body, you can strengthen its extensor muscles by lengthening the strides or asking for a more powerful push, and through up transitions, and you can strengthen its flexor muscles with down transitions, turns, and half halts.
You also have to develop the horse's mobility equally in both directions.
The shoulders tend to drift towards the stiffer side. Turning in the opposite direction tends to be more difficult.
The haunches tend to drift towards the hollow side. Yielding towards the opposite side is often more difficult.
The spine tends to bend better towards the hollow side because the majority of the weight usually rests on the legs of the stiffer side. Getting a good bend towards the stiffer/convex side is often difficult, if not impossible. And it doesn’t improve until the horse learns that he has two perfectly healthy legs on the hollow/concave side that are capable of supporting the body mass. As soon as he trusts his legs on the hollow side to support the weight, he can start bending towards the stiff/convex side.
In other words, in order to straighten the horse we have to teach him to turn his shoulders equally easily towards the hollow side as towards the stiff side.
We have to teach him to move his haunches equally easily towards the stiff side as towards the hollow side,
and we have to teach him to support his weight equally easily with the legs of the hollow side as with the legs of the stiff side, so that his spine is free to bend towards the stiffer side. This entails rocking the weight back and forth between the left and right pair of legs.
For these reasons it is too simplistic to say e.g. that we only ride shoulder-in in one direction and haunches-in in the other direction. We need to ride all movements in both directions, but for slightly different reasons and perhaps with a different focus, or a different emphasis.