Catch Rates of Poke Balls

It's all probability. You can catch a full-strength Mewtwo with a single pokeball if you get lucky; you can miss with 100 duskballs in a row if get really unlucky. Picking the outlier cases from 50-100+ hours of gameplay is going to give you weird results almost by definition.

Regarding an untouched Azelf in a single quick ball, the gap between 4x and 5x isn't really that much of a windfall anyway: it's 1.6% at 4x and 2.0% at 5x.

As for the Gligar, I'm not sure how weakened is weakened, but at max HP the odds are 80/256 and at min 240/256. If you had it at totally minimum HP and/or inflicted with status then something may be amiss, but anything above 1/4 HP and you have an unlikely but very possible (if frustrating) situation.

Really the only time you can say anything conclusive is when you either set up a situation in which a certain outcome MUST occur (ie, the first time a Quick Ball fails to catch a 190-200 you know it must be <4x, because it should have a 100% catch rate at 4x) or you do a whole bunch of attempts to thin out short-term probabilitistic screwing/blessing. And all of this is making the assumption that those formulas are correct.

Rolken said:

Assuming all this is correct, it can be massively simplified. Make a slight round from 16711680 -> 16777216 and 1048560 -> 1048576 (both powers of 2 - I'm inclined to say that those are the real numbers and somebody screwed up somewhere, but who knows), and the second formula magically folds down to...

Click to expand...

Hold on right there.

First of all, the final probability shouldn't be divided by 65536.

The number generated by the ball-catching formula is a number between 0 and 65535 inclusive. The random number generator throws a two-byte number at random 4 times. If, in the four times, the number generated by the formula is less than or equal to the random number generated, the Pokemon is caught.

That means that if the number is 65535, the probability is not 65535/65536, but it is 1. So we need to actually divide by 65535, not 65536.

Secondly, those numbers in the formula are correct.

16 711 680 = 256 * 256 * 255
1 048 560 = 65 535 * 16

If the rate is 255, here's what will happen:

Probability = ( 1 048 560 / ( sqrt( sqrt( 16 711 680 / 255 )))) / 65 535

Since 16 711 680 = 256 * 256 * 255, then 16 711 680 / 255 = 256 * 256. sqrt (256 * 256) = 256, and sqrt (256) = 16.

Hence Probability = (1 048 560 / 16) / 65535

Since 1 048 560 = 65 535 * 16, then (1 048 560 / 16) / 65 535 = 1. So the Pokemon will be certain to be caught if the rate is 255 or more.

Now, and this is the important point:

(( 1 048 560 / ( sqrt( sqrt( 16 711 680 / Rate )))) / 65 535) ^ 4

= ( 1 048 560 / (( sqrt( sqrt( 16 711 680 / Rate ))) * 65 535)) ^ 4

= ( 16 / (( sqrt( sqrt( 16 711 680 / Rate ))) * 65 535) ^ 4

= 65536 / (16711680 / Rate)

= Rate / 255

It simplifies considerably.

Hence, probability to catch a Pokemon reduces to:

((( MaxHP * 3 - CurHP * 2 ) * CatchRate * BallRate ) / ( MaxHP * 3 )) * Status / 255

Now, if the HP is maxed, then MaxHP = CurHP, and this reduces to:

((( MaxHP * 3 - MaxHP * 2 ) * CatchRate * BallRate ) / ( MaxHP * 3 )) * Status / 255
= (( MaxHP * CatchRate * BallRate ) / ( MaxHP * 3 )) * Status / 255
= (( CatchRate * BallRate * Status ) / 255 ) / 3

This means that if BallRate * Status is 3 or more, then a Pokemon with a catch rate of 255 can be ALWAYS caught. (For example, a sleeping Pokemon with a Great Ball: BallRate = 1.5 and Status = 2. 1.5 * 2 = 3, so the 255 catch-rate Pokemon is always caught. This is extremely useful when catching Ditto with a Repeat Ball that has Transformed to a Magikarp, since the BallRate for the Repeat Ball is 3.)

If HP is 1, then CurHP = 1, and this reduces to:

((CatchRate * BallRate * Status) / 255) * (3 * MaxHP - 2) / (3 * MaxHP)

As Rolken said, (3 * MaxHP - 2) / (3 * MaxHP) is very near 1, especially if MaxHP is large, so it reduces to

~ ((CatchRate * BallRate * Status) / 255)

This means that a Pokemon with a catch rate of 255 will have a huge probability (depending on the MaxHP) to be caught by a Poke Ball (the higher the MaxHP, the better, actually).

To summarise:

Probability to catch a Pokemon whose HP is maxed = (( CatchRate * BallRate * Status ) / 255 ) / 3 (exact)
Probability to catch a Pokemon whose HP is 1 ~ (CatchRate * BallRate * Status) / 255 (approx)

So what Rolken said is basically true, except for the 256 bit. :]

I have a question, and it may be a stupid one. Is the amount of times a Pokemon "shakes" in a ball before either breaking out or being caught an indicator of anything?

This has happened to all of us - you throw a ball and it shakes twice then breaks out, and if you keep throwing balls without attacking it it will just break out without shaking at all. Does this mean that it will never be caught in the current situation and that a better ball/more damage must be dealt, or just perhaps that the probability of catching it is very low?