Capture Mechanics
The third Game Mechanics section will concern how the game determines whether an attempted Pokémon capture will be successful.
Please note that the Pokémon games round all numbers down. This will not be specifically included in the mathematical formulas on this page, but whenever you perform any action within a particular formula that results in a non-integer, round it down before performing the next action in the formula if you want to get a perfect result.
This section applies to the Advance games onwards.
The Catch Rate Formula
While incorrect versions have been floating around for a while, the true catch rate formula looks like this:
X = (((3 * M - 2 * H) * (C * B)) / (3 * M)) * S
Explanations of all the variables follow.
X (Final Capture Rate)
X is not the chance that you will capture the Pokémon; it is a number representing the success rate of this particular capture, which is then plugged into a second formula:
Y = 1048560 / √(√(16711680 / X))
The game then generates four random integers between 0 and 65535 (inclusive) and compares them to Y. Y could be said to represent the strength of the Pokéball relative to the Pokémon, while each random number could be said to represent one attempt by the Pokémon to break out of the ball; the Pokémon will be captured if and only if the ball holds (that is, the random number is less than or equal to Y) on all four attempts. On the screen, each unsuccessful attempt the Pokémon makes to break out of the ball is represented by one shake of the ball. If it does not shake at all (resulting in a message to the effect of, "Oh no! The Pokémon broke free!"), Y was less than all four random numbers; if it shakes once ("Aww! It appeared to be caught!"), one of them was less than Y; if it shakes twice ("Argh! Almost had it!"), two of them were less than Y; and if it shakes three times before breaking ("Shoot! It was so close, too!"), all but one of the random numbers were less than Y, meaning you really were as close as the message suggests. The chance of success when you throw an individual ball (that is, the chance that all four random numbers are less than or equal to Y) is thus equal to 100 * ((Y / 65535)4)%.
If you do the math, you will find that if X is 255 or more, then Y is at least 65535, resulting in an always guaranteed capture; there is therefore no need to go through the second formula if X >= 255.
M (Max HP)
The maximum HP of the Pokémon being captured, the only part in the formula where the Pokémon's actual strength enters into the equation. You may have noticed that it appears twice in the formula - if you wrote it out as a fraction, it would in fact be both above and below the line, but it can easily be rearranged:
X = ((3 * M * (C * B) - 2 * H * (C * B)) / (3 * M)) * S
X = (C * B - ((2 * H * (C * B)) / (3 * M))) * S
This means that a greater M will result in a lesser value for (2 * H * C * B) / (3 * M) and thus, counterintuitively enough, a greater value (since (2 * H * C * B) / (3 * M) is negative in the formula) for X and therefore a more likely capture if all other values are static. (Note that H, the current HP, also needs to be static for this to apply, which changes things when dealing with a full-health Pokémon - but not with one False Swiped to 1 HP, for example, which will be easier to capture if it has higher max HP.)
As the max HP approaches infinity, provided the current HP stays static, X approaches C * B * S.
H (Current HP)
The current HP of the Pokémon being captured. Interestingly, for a full-health Pokémon, H will equal M, and then we can simplify the formula for X and in fact remove both M and H from the equation altogether:
X = (((3 * M - 2 * M) * (C * B)) / (3 * M)) * S
X = ((M * (C * B)) / (3 * M)) * S
X = ((C * B) / 3) * S
This means that all full-health Pokémon with the same capture rate, regardless of level, power, etc., are equally likely to be caught with a given ball and status. We can also determine, as noted above in the max HP section, that at one current HP, a Pokémon with high max HP is easier to capture than one with low max HP and the same capture rate.
We can also see here that if the Pokémon is at full health, X is roughly (barring rounding errors) (C * B * S) / 3, or a third of the maximum theoretical catch rate for the same Pokémon at one HP.
C (Capture Rate)
The capture rate of the Pokémon whose capture is being attempted. This is a number that is set for every individual species of Pokémon, just like base stats, and represents just how elusive this Pokémon is: early-game common Pokémon such as Caterpie and Pidgey might have a capture rate of 255, while legendary Pokémon have a capture rate of 3, and others can be various values in between. A higher catch rate obviously yields a higher X and thus a greater chance of a successful capture. Unfortunately, this set value that cannot be modified is also the most influential value in the formula, as it is a direct multiplier with a very great range. Capture rates for individual species can be found in various online Pokédexes, such as Veekun.
B (Ball Modifier)
A value depending on the Pokéball that you are using, whose efficiency in turn tends to depend on various situational factors and aspects of the Pokémon you're attempting to capture. (int(something) stands for rounding down, or just cutting off everything after the decimal point; I noted at the beginning of this section that the Pokémon games always round down, but here I felt obligated to include it specifically to avoid confusion.)
- Poké Ball, Premier Ball, Luxury Ball, Heal Ball, Cherish Ball
- B = 1.0
- Great Ball, Safari Ball
- B = 1.5
- Ultra Ball
- B = 2.0
- Master Ball, D/P Park Ball
- Capture is always successful, so there is no need to use a formula.
- Net Ball
- B = 3.0 if one of the Pokémon's types is Water or Bug; B = 1.0 otherwise
- Nest Ball
- B = int((40 - Pokémon's level) / 10), minimum 1.0
- Dive Ball
- B = 4.0 when underwater in R/S/E or fishing/surfing in D/P; B = 1.0 otherwise (not certain of this; will test as soon as possible)
- Repeat Ball
- B = 3.0 if the Pokémon is already registered as caught in the Pokédex; B = 1.0 otherwise
- Timer Ball
- B = int((number of turns passed in battle + 10) / 10), maximum 4.0
- Quick Ball
- B = int((25 - number of turns passed in battle) / 5), minimum 1.0
- Dusk Ball
- B = 4.0 at night or in a cave; B = 1.0 otherwise
While the fourth root (square root of a square root) in the formula that derives Y from X will yield a value for Y that is not nearly twice as high for an Ultra Ball as for a Poké Ball, this is evened out thanks to there being four random numbers calculated, and the final chance does end up being affected about as much by the ball modifier as one would expect from looking at them, though the rounding changes this slightly.
S (Status)
We all know that Pokémon are easier to catch when, say, asleep or paralyzed. This is entered into the formula here, with the status modifier. Basically, if the Pokémon is asleep or frozen, S = 2; if the Pokémon is poisoned, paralyzed or burned, S = 1.5; and otherwise, S = 1. As with the Pokéballs, this does reasonably accurately make the Pokémon this much easier to catch.
Catch Rate Calculator
To approximate your chances of catching any Pokémon, enter the appropriate information into this form. Note that the calculation could be slightly inaccurate as it assumes an HP IV of 15 for the wild Pokémon, while it could be anything from 0 to 31; this obviously cannot be helped, but thanks to all the rounding down in the formula, it tends not to matter very much. The number of balls needed is rounded up from the strict average, but you should of course bring more balls than that for safety.
Page last modified February 22 2010 at 03:39 GMT
