Mind you.The catch rate is fixed.
What I mean by that is for example,you're on turn 1,you failed a Pokeball,no matter how many savestates you tried,the results will still turn out the same in that exact moment.
Let's say you're catching a legendary Pokemon,if it's in full health and you randomly chugged a Pokeball and it actually worked,it will still work on that exact moment if you replay it using the savestates on the moment before you throw the ball.
Or let's say the ball is all like "Aww.It appeared to be caught."It will stay the same on that exact turn no matter the savestates.SO,how do I catch some Mons without wasting the first 5 balls is testing out if the first one works,if it doesn't,I load the savestate(before I catch a mon)and use it the second turn.If it still doesn't work,I will just do what I did earlier,load the savestate where you haven't use it,stall it until later.