Difference between revisions of "Catch rate"

Each species of Pokémon has a catch rate that applies to all its members. Higher catch rates mean that the Pokémon is easier to catch, up to a maximum of 255. When a Poké Ball is thrown at a wild Pokémon, the game uses that Pokémon's catch rate in a formula to determine the chances of catching that Pokémon. The formula also takes into account the Pokémon's current health, any status effect it may have, and the type of Ball being used.

Approximately, the probability of catching a Pokémon starts with the species' catch rate divided by 255. Then it is multiplied by the following factors:

• The health of the Pokémon (relative to its full health), which can reduce the probability to ⅓× at full health.
• The type of Poké Ball, which can augment by some ×.
• Any status ailment of the wild Pokémon, i.e. 2× increase for sleep or freeze, and 1.5× for others.

The effects stack multiplicatively — for example, a 2× and a 3× will combine to be 6×. If the calculation ends up greater than 1, the wild Pokémon is assured to be caught.

The rarity of the Pokémon (i.e. how often it appears in the wild) is totally independent from its catch rate after it is encountered. Even rare Pokémon may have high catch rates, making them relatively easy to catch in battle, such as Nosepass (catch rate 255).

Transform will change a Pokémon's catch rate to that of the target, and is the primary purpose for the existence of catch rates for species that cannot be found in the wild. However, in Generation V this is no longer true.

Poké Balls that guarantee capture (the Master Ball, Park Ball, and Dream Ball) bypass the catching formula entirely.

Capture method (Generation I)

The capture method in Generation I differs significantly from those of later generations. To determine whether a Pokémon is caught or not, the following is performed:

1. If a Master Ball is used, the Pokémon is caught.
2. If a Poké Ball is used, generate a random number from 0 to 255. If a Great Ball is used, generate a random number from 0 to 200. Otherwise, generate a random number from 0 to 150.
3. If the generated value is less than 25 and the Pokémon is asleep or frozen, the Pokémon is caught. If the generated value is less than 12 and the Pokémon is paralyzed, burned, or poisoned, the Pokémon is caught. If it is caught, skip all other steps.
4. If the previous value (the generated value less than the status amount) is greater than the catch rate of the Pokémon, the Pokémon breaks free. Otherwise, generate a random value between 0 and 255. If f is greater or equal to this value, the Pokémon is caught. Otherwise, the Pokémon breaks free. If the Pokémon breaks free, do the following:
• Compute d. If d ≥ 256, the Ball shakes three times before it breaks free.
• Otherwise, compute d × f / 255. Add 10 if the Pokémon is asleep or frozen, and add 5 if it is paralyzed, poisoned, or burned. If this value is less than 10, the Ball misses the Pokémon completely. If it is less than 30, the Ball shakes once before it breaks free. If it is less than 70, the Ball shakes twice before it breaks free. Otherwise, the Ball shakes three times before it breaks free.

The variables above are computed as follows:

• d = Catch rate × 100 / Ball Factor, where the Ball Factor is 255 for the Poké Ball, 200 for the Great Ball, and 150 for all other balls.
• f = (HPmax * 255 / Ball Factor) / (HPcurrent / 4), where all divisions are rounded down to the nearest integer (the denominator is set to 1 if it is 0 as a result). The Ball Factor is 8 if a Great Ball is used, and 12 otherwise. The resulting value may not be larger than 255, in which case 255 is used instead.

The formula thus has several curious properties that do not apply in later generations:

• The amount of times a Poké Ball shakes before it breaks free (or not at all if it misses the Pokémon) is a rough approximation of the Pokémon's catch odds. Furthermore, if a Pokémon breaks free after some number of shakes, and a subsequent attempt with all variables the same makes more shakes, the Pokémon is caught.
• Under certain situations, a Great Ball is more effective than an Ultra Ball. In particular, Pokémon with high catch rates, no status, and above ½ HP may guarantee capture with a Great Ball but fail to do so with an Ultra Ball.
• The effect of reducing HP diminishes with lower catch rates, and the effect of inflicting status diminishes with higher catch rates. Regardless of catch rate, reducing the HP does not increase chances of capture at less than ½ HP with Great Balls, and ⅓ HP with other balls.
• Inflicting a status effect gives the player a flat chance to catch the Pokémon, completely unrelated to its HP values.

Capture formula (Generation I)

Using a simulation of the capture algorithm, a general formula for catch rates was found.

The formula to give probabilities of capture in Generation I is as follows:

```Probability of Capture = p0 + p1
```

where

```p0= statusAilment / (ballMod+1)
```
• statusAilment = 12 if poisoned/burned/paralyzed, 25 if frozen or asleep, 0 otherwise.
• ballMod = 255 if using a Poké Ball, 200 if using a Great Ball, and 150 otherwise.

and

```p1= ((catchRate+1)/(ballMod+1)) * ((f+1)/256)
```
• f is defined in the above section for the Capture Method.
• catchRate (given as an integer value) is stated on each individual Pokémon's article.

(Please note that this probability is theoretical. Your own experiments may result in a different value, but over a large number of trials, any experimental probability will approach this theoretical value.)

Capture method (Generation II onwards)

The exact formula in Generation III and onwards are based on three parts: determining the modified catch rate, calculating the "shake probability" and then performing "shake checks". The formula in Generation II is similar, but the formula in Generation I is entirely different.

Modified catch rate

The modified catch rate, a, is the catch rate after various factors such as weakening the Pokémon and using stronger Poké Balls are taken into consideration. A modified catch rate may never fall to 0 (that is, render a Pokémon impossible to capture), but it may cause the modified rate to fall below its original unmodified catch rate (such as from high health, Heavy Balls, Baiting in the Safari Zone, or the dark grass penalty in Generation V). In Generation III and Generation IV, the modified catch rate may never fall below 1.

Generation II

The modified catch rate a is calculated in Generation II as follows:

a = (3 × HPmax - 2 × HPcurrent) × (rate × bonusball) / (3 × HPmax) + bonusstatus

with the final value rounded down to the nearest integer, where

• HPmax is the number of hit points the Pokémon has at full health,
• HPcurrent is the number of hit points the Pokémon has at the moment,
• rate is the catch rate of the Pokémon (which may have been previously modified from the use of the Heavy Ball modifiers),
• bonusball is the multiplier for the Poké Ball used, and
• bonusstatus is the multiplier for any status ailment the Pokémon has (10 for sleep and freeze, and 0 otherwise).
• bonusstatus was intended to equal 5 for paralyze, poison and burn, but due to a glitch, the game accidentally skips this check.

Note that in Generation II, if 3 × HPmax > 255, then both 3 × HPmax and 2 × HPcurrent are quartered (rounded down) for use in the formula; if the latter is 0, it is made to 1 instead in this case. Note that the subtraction itself may underflow, due to both values being unsigned 8-bit integers in Generation II.

Generation III-IV

The modified catch rate, a, is calculated in Generation III and Generation IV as follows:

Where

• HPmax is the number of hit points the Pokémon has at full health,
• HPcurrent is the number of hit points the Pokémon has at the moment,
• rate is the catch rate of the Pokémon (which may have been previously modified from the use of the Heavy Ball or Safari Zone modifiers),
• bonusball is the multiplier for the Poké Ball used, and
• bonusstatus is the multiplier for any status ailment the Pokémon has (2 for sleep and freeze, 1.5 for paralyze, poison and burn, and 1 otherwise).

Given this formula, the maximum value for a (if the Pokémon could have 0 HP) would be catch rate × bonusball × bonusstatus. The minimum value for a (for a Pokémon with full health) would be × catch rate.

Generation V

Generation V follows the formula in Generation III-IV, with all divisions above rounded down to the nearest multiple of 1/4096. Furthermore, two additional factors are multiplied into the above formula:

• Capture Power factor: Multiply by 1.1 if Capture Power ↑ is active, 1.2 if Capture Power ↑↑ is active, and 1.3 if Capture Power ↑↑↑, Capture Power S, or Capture Power MAX is active, and round down to the nearest multiple of 1/4096.
• Dark grass factor: This factor, multiplied into the HP factor (3 × HPmax - 2 × HPcurrent above) and then rounded to the nearest multiple of 1/4096, depends on whether or not the battle occurs in dark grass (where Double Battles may occur), and the number of Pokémon that have been caught in the Pokédex: if the battle is not in dark grass, this is 1. If it is, consult the table below.
Multiplier Number Caught
1 >600
3686/4096 (90%) 451-600
3277/4096 (80%) 301-450
2867/4096 (70%) 151-300
2048/4096 (50%) 30-151
1229/4096 (30%) <30

If the modified catch rate is greater than 255, the Pokémon is automatically caught. A critical capture check is done regardless of whether the Pokémon is otherwise automatically caught.

Shake probability

The shake probability, b, is the probability that a single shake check passes.

Generation II

Consult the following table to determine b:

 a b 0-1 2 3 4 5 6-7 8-10 11-15 16-20 21-30 31-40 41-50 51-60 61-80 81-100 101-120 121-140 141-160 161-180 181-200 201-220 221-240 241-254 255 63 75 84 90 95 103 113 126 134 149 160 169 177 191 201 211 220 227 234 240 246 251 253 255

Generation III-IV

The shake probability is calculated as follows in Generation III and Generation IV:

File:Catch formula 2.png

Generation V

In Generation V, the formula is

b = 65536 / (255/a)(¼)

where all divisions and the fourth-roots are rounded to the nearest 1/4096, and the final value is rounded down to the nearest whole number.

Shake checks

A "shake check" is done to determine whether the Pokémon is caught, and, if the Pokémon breaks free, the number of shakes that occurs before it does so.

Generation II

In Generation II, a check occurs to determine whether the Pokémon is caught outright, and shake checks are only used if this check fails to determine the number of shakes before the Pokémon breaks free. To determine if the Pokémon is caught outright, generate a random number between 0 and 255. If this value is less than or equal to a, the Pokémon is caught. To perform a shake check, generate a random number between 0 and 255, and compare it against b. Do this three times or until the check fails, whichever comes first, to determine the number of shakes before the Pokémon breaks free.

Generation III-IV

Unlike Generation II, the shake checks themselves determine whether or not the Pokémon is caught, and, if it is not, the number of shakes a Poké Ball will make before the Pokémon breaks free. Four checks are performed, and all checks must pass in order for the Pokémon to be caught, and if the Pokémon breaks free, the number of times the Poké Ball shakes is equal to the number of passed checks. To perform a shake check, generate random numbers between 0 and 65535, inclusive, and compare it against b; the checks fail if the generated value is greater.

Note that as a result of the formula, if a is 255 or greater, then b is 65535 or greater, and then the Pokémon is thus guaranteed to be caught; the game does not perform shake checks in the event of a guaranteed capture before this occurs.

Generation V

Generation V's shake checks work identically to those of Generation III and IV, except that after the critical capture check only three checks are performed in a normal capture and one in a critical capture. In a normal capture, the Pokémon breaks free without shaking if the first check fails, while the Pokémon breaks free after one shake if the second check fails. The Pokémon breaks free after three shakes (not two) if the third check fails. In a critical capture, the Ball will always shake once, and the Pokémon will break free or be caught depending on the check.

Probability of capture

Therefore, the probability p of catching a Pokémon in Generation IV, given the values a and b calculated above, is:

File:Catch formula 3.png

The second expression for p may be expanded as follows:

File:Catch formula 3 expansion.png

Since (216 - 1)4 ≈ 264, we can approximate p with the following expression:

File:Catch formula 3 approximation.png

The percentage error in this approximation approaches 0 as a approaches 255, and does not exceed 21.2%.

For a constant probability p, the probability P that a player can capture the Pokémon with no more than r tries is:

Note that this is the cumulative probability function for a geometric distribution. The expected value of r is 1/p, that is to say, on average, a Pokémon that can be caught with probability p will be caught with 1/p tries.

The inverse problem, the number of tries, r, needed to have a probability P of capturing a Pokémon is:

Poké Ball effectiveness rates

Ball Rate Notes
Poké Ball
Great Ball 1.5×
Ultra Ball
Master Ball 255× Never fails, with few exceptions
Safari Ball 1.5× Safari Zones only
Level Ball 1×, 2×, 4× or 8× 1× if the player's Pokémon is the same level as or a lower level than the wild Pokémon

2× if the player's Pokémon is at a higher level than the wild Pokémon but less than double it
4× if the player's Pokémon is more than double but less than four times the level of the wild Pokémon
8× if the player's Pokémon is of a level four times or more than that of the wild Pokémon

Lure Ball 1× or 3× 3× only if fishing
Moon Ball 1× or 4× Always 1× due to a glitchGSC
4× only if used on a Pokémon in the Nidoran♂, Nidoran♀, Clefairy, Jigglypuff or Skitty families HGSS
Friend Ball
Love Ball 1× or 8× 8× only if used on a Pokémon of the same species and gender as the player's PokémonGSC

8× only if used on a Pokémon of the same species as, but opposite gender of, the player's PokémonHGSS

Heavy Ball -20, +20, +30 or +40 -20 if used on Pokémon weighing less than 451.5 lbs

+20 if used on Pokémon weighing between 451.5 lbs and 677.3 lbs
+30 if used on Pokémon weighing between 677.3 lbs and 903.0 lbs
+40 if used on Pokémon weighing more than 903.0 lbs

Fast Ball 1× or 4× 4× only if used on a Grimer, Tangela, or MagnemiteGSC

4× only if used on a Pokémon with a base Speed of at least 100HGSS

Sport Ball 1.5× Bug-Catching Contest only
Net Ball 1× or 3× 3× only if the target is a Bug- or Water-type Pokémon
Nest Ball 1× to 4× ((40 - Pokémon's level) / 10)×, minimum 1×RSEFRLGDPPtHGSS
((41 - Pokémon's level) / 10)×, minimum 1×BWB2W2
Repeat Ball 1× or 3× 3× only if target has been caught previously
Timer Ball 1× to 4× ((number of turns passed in battle + 10) / 10)×, maximum 4× (reached after 30 turns)RSEFRLGDPPtHGSS
1× + 1229/4096× (0.3×) per turn passed in battle, maximum 4× (reached after 10 turns)BWB2W2
Premier Ball
Luxury Ball
Dive Ball 1× or 3.5× 3.5× only if divingRSE or surfing/fishingFRLGDPPtHGSSBWB2W2
Dusk Ball 1× or 3.5× 3.5× only if inside a cave or night
Quick Ball 1×, 4×, or 5× 4× only on the first turn of the battleDPPtHGSS
5× only on the first turn of the battleBWB2W2
Park Ball 255× Never fails, Pal Park only
Dream Ball 255× Never fails, Entralink only

Note: Due to a glitch in the Generation II games, the Moon Ball does not work as described in the games there, and the Love Ball only works on same-gendered (instead of opposite-gendered) Pokémon.

Examples

Most legendary Pokémon have a catch rate of 3. Assuming its HP is almost depleted and it is paralyzed, and Dusk Ball is used at night or in a cave, then the chance of catching the Pokémon with each Ball in Generation IV is approximated by 3 * 3.5 * 1.5 / 255 = 15.75/255 ~ 6.2%, resulting in about 16 Dusk Balls required to catch the Pokémon on average.

If an Ultra Ball were used instead, then the chance drops to 3 * 2 * 1.5 / 255 = 9/255 ~ 3.5%, which amounts to about 28 Ultra Balls on average.

Alternatively, if a Timer Ball were used after the tenth turn in Generation V or after the thirtieth turn prior to Generation V, the chance of capture is 3 * 4 * 1.5 / 255 = 18/255 ~ 7.1%, or about 14 or 15 Timer Balls required on average.

Critical capture

In Generation V, there is a chance of a critical capture, where the Poké Ball will only shake on the ground once before capture. When a critical capture occurs, the Poké Ball will make a high-pitched whistling sound as it is thrown, then pause in mid-air, and shudder before it drops down to the ground.

The probability of a critical capture depends of the number of Pokémon that has previously been caught in the Pokédex. First, compute the value of a (the modified catch rate), as above. Then, whether or not this value is less than 255 (above which the Pokémon is caught regardless of whether or not it is a critical capture), multiply this value by the following:

Species Caught Multiplier
>600 2.5
451-600 2
301-450 1.5
151-300 1
31-150 0.5
<30 0

A random number is generated, and if it is less than the modified value, a critical capture occurs.

Critical captures make one shake check instead of three, thus it appears to increase the odds of capture for Pokémon. Though it may create higher odds of capture, a critical capture is not a guaranteed catch; it is possible for critical captures to fail. For example, a critical capture against a full-health Pokémon with a catch rate of 3 (such as Kyurem) with a Poké Ball will still only have a 25.03% chance of success, but it is much higher compared to the normal capture's 1.57% chance. Furthermore, situations where critical capture is guaranteed will not guarantee capture.

Trivia

• Some people claim to have discovered button combinations that increase a Pokémon's catch rate; this is merely idle thought, as there is no method to improve catch rates other than the methods described above.