When thinking about a saddle one of the most important, but least thought about, details is the rigging of the saddle. The rigging basically determines where the saddle will sit on the horses back.
Rigging is the metal (occasionally leather) hardware that attaches directly to the tree or is build into the skirts. It’s the place where the latigo and rear billet cinch straps attach that in turn go under the horses belly and fasten on the other side. If there is only a front latigo it’s called a single rig saddle and if there is a rear cinch it’s called a double rig. Most cowboys ride with double rigs because it helps keep the saddle in place during roping.
A brief aside. Mexican and later California cowboys at first used only a single rig because they dallied the rope which gave them a lot of control over the tension because they would slip the rope keeping the cow under control gradually. Texans being Texans tied the end of the rope directly to the horn. When they roped and the cow moved away the rope would become tight and jerk the saddle hard causing the back to move rapidly up and sometimes throw the cowboy off. Thus the invention of the back rig.
Rigging position (where the front cinch hardware is placed) is measured from the back of the saddle. Center rigging places the hardware halfway between the fork (think of the horn) and the cantle (the part that sticks up by your back). Center or Center Fire rigging was the way saddles were constructed in the old days. By contrast full rigging is directly under the center of the fork. There is 3/4 rigging and 7/8 rigging in between those two.
The majority of cowboys I know use 7/8 and a few less 3/4. It really depends on the shape of your horses back but somehow I feel more secure with 7/8.
One of the best books I know about the details of western saddles is Saddle Savy by Dusty Johnson. Dusty works out of his Pleasant Valley Saddle Shop and School southwest of Loveland, Colorado. The book seems to be out of print but you can still find some copies at Alibris by clicking HERE.