>>23328610Ditto. I did the math once before to find that is it just overall easier to toss balls until you catch something instead of weakening it first. Puting the Pokemon to sleep is the most you should ever do and if it is a common mon then you can even skip that much. Of course exceptions exist for Pokemon with moves that allow them to leave battle or kill themselves but generally with enough save scumming you can even catch those in normal Pokeballs as well.
Lot of people aren't aware but ultra balls only give you like 10% higher chance at best and that would seriously be pushing it.
Status (~10% chance increase) >>> Health reminding (~1% chance increase) > Ball type which range from anywhere to not even a full percent increase to slightly less then 10% increase depending if you already went all out beforehand. This is for the 1st gen mind you.
For the newer games they balanced out status effects to the point where you need to do literally everything just so each thing alone would be worth using in the first place. Alternately you can just take the easy way and toss balls even skipping the part you put them to sleep as that is now useless.