As all of you should know, the Pokémon games use various formulas for everything!
Capture Rates
This section applies to all games. Whether or not one captures a Pokémon is determined by inputting a random integer between 0 and 255 and testing to see if it is less than the current capture rate.
The actual formula goes as follows: PokeballEffect (((( 4 * Max HP - 2 * HP ) * Catch Rate ) / Max HP ) + Status + 1 ) / 256 The Capture Rate is a value defined for each Pokemon between 3 and 255, which determines how likely you are to capture the Pokemon. This also happens to be something you could've figured out by yourself. The Ball Modifier relates to the current type of Pokéball used. A Pokéball has a modifier of 1, therefore there would be no change. A Great Ball has a modifier of 1.5, however, and so, one would multiply that by 1.5. Not particularly difficult as long as you know what each ball does.
Normally, a Pokémon's Status is 1. If it is paralyzed, poisoned, or burnt, Status is 6. If the Pokémon is asleep or frozen, Status is 11. This is almost certainly to ensure that one may always capture a Pokemon if they try hard enough.
A Pokémon at full health will be caught if the random integer is below 2 times the capture rate times the ball modifier.
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