The Leaping Dragon maneuver makes you jump as a Swift Action, as described here:
The initiator may make an Acrobatics check to jump as a swift action, and he gains a +10 competence bonus to his Acrobatics check and is treated as if he had a running start.
Meaning you're able to jump and then do any combination of Standard and Move, or a single Full-Round Action, like jumping in close to an enemy and doing a full round of attacks.
Now, recovering a maneuver you have used when you have the feat Martial Training 1 is a Full-Round Action, and I will quote:
You may recover one maneuver by expending a full round action to recover it
So adding all of this together, shouldn't I then be able to recover Leaping Dragon as a Full-Round Action, and then instantly use it to jump as a Swift Action in the same round?
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It would be usefull if you want to climb a montain without having ranks on climbing skill. Otherwise, it is pointless, since usualy you move faster making two moves rather making one jump. And you can also run, moving 4 times your land speed.
So, if you have a move of 30 ft., you can run 120 ft. in one full round. The CD to jump 120 ft (with running start) is 120 (110 if you consider your +10 bonus).
You can't jump more than your movement speed.
That being said, jumping 20'-30' as a swift action can set up some good pounce scenarios.
I am failing to see the benefits of using the swift action jump, then recovering the maneuver, and doing it again... unless you're in really specific niche circumstances. At which point you should probably be using methods of flight rather than leap-frogging around.
Not fully related with the original thread, but, as VoodistMonk mentioned,
No jump can allow you to exceed your maximum movement for the round.
However, with some set of bonuses to jump, it would be hard, but possible, you exceed this limit. If it happens, what do you guys think that is better:
a) The character lands on its maximum jump distance
b) The character spend a full round jumping, and use part of the next round actions (move, standard or both) to finish the jump?
A 20th level character with max Acrobatics ranks (20 ranks), Skill Focus (Acrobatics) and Acrobatic feat (+10 bônus), using a Improved Ring of Jumping (+10 competence bonus) under the effect of jump spell (+30 enhancement bônus) and Dex 24 (considering level increments and magic itens) will have +80 to its jump check (considering Acrobatics as a class skill).
In this scenario, it would be possible to move 110 feets (10 feets for runing start plus 100 feets on a 20 on d20).
Six Mythic tiers and the right build will let you jump 1000 miles... jump. So it can be done, but why?
The feat in question is essentially just pounce via jumping.
The leapfrog shenanigans do not make any sense to me, whatsoever. I don't see a mechanical advantage it would ever provide in juxtaposition to literally every other method of movement in the game.