Catching Pokémon

Chance to catch a Pokémon affected by:-

Throw Object roll of the catcher.
Pokémon's size and movement (affects Throw skill)
Health of the Pokémon.
Status of the Pokémon.
Catch Rate of the Pokéball being used.

i: Character makes a Throw Object skill roll (either unskilled, skilled, or Speciality Skill: Pokéball)

ii: Throw result modified by target size and movement (speed, dodging, flying, swimming, hiding etc.)

If successful, Pokémon has a chance to escape. This attempt may be made up to three times, and each attempt is half the chance of the previous attempt. Should the attempt result in a natural 99-100 roll, then the Pokémon is automatically caught and no further attempts are made even if available. Minimum chance to escape is always 1% (unless the Pokéball specifies otherwise) and a result of a natural 1 roll means the Pokémon automatically escapes, and no further attempts are required, even if available.

iii: Base chance to escape is 100 minus the Difference modifier.

Difference Modifier
Difference of maximum Life Points and the current Life Points modifier round down):-
[Take max Life Points # and divide by current Life Points #. Then divide 100 by this number. (I.e. 145÷50 = 2.9 then 100÷2.9 = 34.5. OR 210÷120 = 1.75 then 100÷1.75 =57)]

<10 = 90 (thus 100 - 90 = 10% for 1st escape chance, 5% for 2nd, and 2% for 3rd)
11-25 = 75 (thus 100 - 75 = 25% for 1st escape chance, 12% for 2nd, and 6% for 3rd)
26-50 = 50 (thus 100 - 50 = 50% for 1st escape chance, 25% for 2nd, and 12% for 3rd)
51-75 = 25 (thus 100 - 25 = 75% for 1st escape chance, 37% for 2nd, and 18% for 3rd)
76-90 = 15 (thus 100 - 15 = 85% for 1st escape chance, 42% for 2nd, and 21% for 3rd)
>90 = 5 (thus 100 - 5 = 95% for 1st escape chance, 47% for 2nd, and 23% for 3rd)

iv: This is further modified by Status of the Pokémon:

Frozen or Asleep = -50% of chance
Paralyzed = -25% of chance
Burned or Poisoned = -10% of chance

v: Then Catch Rate of the Pokéball being used modifies this again:-

Pokéball = No change
Great Ball = -25%
Ultra Ball = -50%
Master Ball = -100%
Safari Ball = -25%
Level Ball = no change, -25%, -50%, or -75%
Lure Ball = no change, -33%, or -66%
Moon Ball = no change or -50%
Friend Ball = no change
Love Ball = no change or -75%
Heavy Ball = dependent on weight of poke'mon +40, +20, +0, -10, -20, -30, or -40
Fast Ball = no change or -50% if used on Magnemite, Grimer, Tangela, or has DEX of at least 90
Premier Ball = no change
Repeat Ball = no change if new, or -50% if caught before
Timer Ball = -5 per Round in battle before throwing Timer Ball
Nest Ball = no change, or -50%
Net Ball = no change, -33%, or -50%
Dive Ball = no change, or -50% if diving/surfing/fishing/swimming
Luxury Ball = no change
Heal Ball = no change
Quick Ball = no change, -50% if used in 1st Round of battle
Dusk Ball = no change, -33% if in cave or at night.
Cherish Ball = no change
Sport Ball = -25%
Park Ball = -100%
Dream Ball = -100%
Beast Ball = +10, or -75% if used on an Ultra Beast

All the pokeballs above are dependent on many conditions see https://bulbapedia.bulbagarden.net/wiki/Catch_rate for details