When adding caster to right front spindle you increase the amount the tire goes down when turning right, and amount it goes up turning left.
It takes a stiff chassis (or one that duplicates the same amount flex each time it's turned) to make the best use of this. Upon entering a typical oval turn while turning left the right front goes up (when using 90 deg. spindles: this is multiplied when using 7,10,13 or any degree spindle,unless installed upside down- I've seen this on a very fast, ill handling twin) and more importantly unloading the rear left tire allowing the mower to turn left easier (loose). While turning left as the rear starts coming around, you turn right to prevent spinning out ( more importantly lowering the right front and loading the left rear for enough traction to run through entire turn with out letting of the gas, while in control with minimal turning of steering which slows momentum) if cross is set correctly for your driving style.
As far as the amount caster, the more you have ( in general ) the
less you have to turn the wheel to steer.
From what I've seen and applied ( with solid axle ) is to only turn slightly right through turns (entering with quick release of throttle
with correct stagger sets itself up and follow with slight steering to the right to trim slide).
The tracks always change, when set right it appears the driver is not even turning the wheel and turning the best times at full throttle.
Opinions vary, this is how I use and see caster being applied, and it is only part of a good front end set up.
Butcher.