So I see this on numerous smallholding/homesteading/permaculture forums so i thought I'd throw in my two cents from family experience.
I see lots of people complaining goats are impossible to contain with fencing. Goats are usually naturals when it comes to finding a way over obstacles to get what they want, this includes your fences. The key here is what they want.
So why are goats jumping your fence? To get to the other side
But really, there is something outside your fence which it wants, which means it requires something which you have not provided it. Water, shelter (goats do not do well in the rain), company (especially Bucks/Billys), boredom (usually for kids or overly small yards) or most often food.
Goats by nature are browsers, not grazers. You can pen then animal in or stock them too densely and force them to eat what is there, but as usual if you go against nature you will encounter problems. Goats eat a variety to balance nutrition (grasses have shallow roots so unless your feilds have perfect mineral balance....) and to avoid parasites (a natural reason they enjoy eating things above ground level).
The other considerable factor to this problem seems to stem from the new craze over dwarf goats. Consider, smaller goats are more agile. Growing up we had saanens, toggenburgs, anglo nubians and boers (full size breeds). Once mature only the billys could/would clear a 4ft fence (their pen was 5ft 7-9 strands mixed hot/cold electric). All others could climb, but never escaped from their partially silvopastured rotational yards, and why would they want to (internal fences were 2 strand electric, perimeter fences were 3ft woven topped with 2 strand electric).
TLDR: If your goats are escaping:
- Pygmy goats are smaller and more agile, larger goats are slightly less agile.
- If your goats are escaping you are probably not adequately providing for all its needs. Usually they lack company or do not have diverse enough feed options - try offering a nontoxic tree or shrub branch - preferably hang it above the ground for them or even better plant fodder trees/bushes in their feed yards and allow them to grow big enough to survive the goats