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# How do I find the chance of catching a Pokemon with a catch rate of 5?

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Hey, I'm making a fakemon, and I want to know the probability of catching it, and how to calculate it myself. Assume that it has full health and a normal PokeBall is used (like how PokemonDB lists the chance on its Pokedex pages).

edited
We also need to know the HP stat of the Pokemon.
The base stat hp is 120
What level do you want it to be caught?
Probably level 48, gen 8  This, however, has a quantity, a, that is unknown. I don't know much about your Pokemon, so unfortunately, some assumptions are compulsory. Let's figure this out, shall we? First, let us find A. I am assuming that you don't have any status. I am also assuming it's level 100. Here's the Math.

((3 * 381 (See 1) - 2 * 381) * 5 * 1)/(3 * 381) = (381 * 5)/(381 * 3) = 4/3
So let's try and find B.

655356/(255/a)^0.1875 = 24472.574545454...

Alright, so how does this = a percent? Well, let's see this now.

"So what is a Shake Check? Basically, a random number is generated in between 0 and 65535. That number is compared to your b value, which is your shake probability. If your b value is smaller or equal to the random number generated, than your Shake Check fails, and you DO NOT catch the Pokemon. 4 Shake Checks are performed, and if you pass all 4 then the Pokemon is caught." Sempi (See 2)

Based off of this, we need to see the probability that your number is greater than 24473 (just rounded it). So, we can do (65535 - 24473)/65535 to find the probability of you getting a greater number, as 24473 represents all numbers less and equal to this number. We get 0.6266 (approximately), however, we are not done. Here's the thing. We haven't calculated the four chances of actually even getting the actual Pokemon. This event happens 4 times. This thing is not affected by previous events (Thank god, that would make this a hot mess). These events are all independent events, as it is known in the stats world. Now, take this as an example. Say you have a dice. You have to roll it 4 times. What is the probability of getting a 6 each time? So, you have a 1/6 chance the first time, and you are doing it six times. Thus, you want to raise this number to a power. So, 1/6 1/6 1/6 * 1/6 would be your answer, because that is 1/6 to the power of 4. This results in a very small number. 0.0007716049383, or .07716049383%.

So, with that outlined, let's get our final answer: 0.6266 ^ 4 = 15.4% Now, this seems awfully high. It is quite high, however, the main killer is simply the rate. We can see a correlation of the higher the HP, the higher the catch rate. Now, the other difference is level matters. Hope this helps!

1: The HP stat with Max IVs, No Evs: I utilized a stat calc for cresselia, 'cause it has base 120 HP
2: The question that I got the quote from

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omg maths
agreed. Mafs

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