How Catching Pokemon Works...

You weaken a pokemon as normal in combat, but instead of it fainting and becoming uncatchable like the game, when reduced to 0 they flee and you cannot stop them nor catch them. Assuming that goes well however, when you throw a pokeball, you roll a 1d20, and add any one of the following modifiers Note: a 1 does not automatically fail:

+2 for Pokeball
+4 for Greatball
+6 for Ultraball
+8 for Netball when used on Bug or Water type pokemon
+8 for Diveball, but you must have used the dive ability of a pokemon, and only when used underwater
+60 for Masterball
+2 for a status effect

The following modifiers only a storyteller will add to the final roll. They will still tell you your final result however, including the following if they apply:

+2 for at Half life
+4 for 3/4th
+6 for 5 hp or less

Your roll attempts to beat a set number the storyteller has set for a pokemon. Assuming you do everything correct, and are using ultraballs, you could have a total of +14 to a roll.

-For every 5 balls thrown, the pokemon gets tired, and you gain a miscellaneous +1 on catch rolls