Here is the system for catching Pokemon. It uses Die and the amount of HP left for your opponent. You CANNOT catch Pokemon that belong to a trainer:
1/2 or more of health remaining-
Pokeball - Roll the Catching Dice. If you roll a 1, you caught the Pokemon
Greatball - Roll the Catching Dice. If you roll a 1 or 2, you caught the Pokemon.
Ultraball- Roll the Catching Dice. If you roll a 1, 2, or 3, you caught the Pokemon.
1/3 to 1/4 of health remaining-
Pokeball - Roll the Catching Dice. If you roll a 1 or 2, you caught the Pokemon
Greatball - Roll the Catching Dice. If you roll a 1, 2, or 3, you caught the Pokemon.
Ultraball- Roll the Catching Dice. If you roll a 1, 2, 3, or 4, you caught the Pokemon.
1/5 to 1/6 of health remaining-
Pokeball - Roll the Catching Dice. If you roll a 1 , 2, or 3, you caught the Pokemon
Greatball - Roll the Catching Dice. If you roll a 1, 2, 3, or 4 you caught the Pokemon.
Ultraball- Roll the Catching Dice. If you roll a 1, 2, 3, 4, or 5 you caught the Pokemon.
1/7 to 1/8 of health remaining-
Pokeball - Roll the Catching Dice. If you roll a 1 , 2, 3, or 4, you caught the Pokemon
Greatball - Roll the Catching Dice. If you roll a 1, 2, 3, 4, or 5, you caught the Pokemon
Ultraball- You caught the Pokemon.
Lower than that
Pokeball - Roll the Catching Dice. If you roll a 1 , 2, 3, 4, or 5, you caught the Pokemon.
Greatball - You caught the Pokemon
Ultraball- You caught the Pokemon.
The Master Ball, or the site's fourth Pokeball, can catch anything with no flaw.