Distribution of wild Pokémon by total IVs

Zanesc · June 24, 2023

Today, a catching event was held in Eterna Forest and while participating in it, I started wondering what are the actual chances of winning it, which in turn got me thinking about the probability of finding a wild pokémon that has over 170 total IVs or something like that. Since there are probably other people who wonder about these things, I got your curiosity covered.

I compiled the information of all of my wild catches in my PC and their respective IV total. Excluding alphas and bred pokémon I was left with a total of 306 wild catches (sample size) each with their own IV total, I also never released any of my caught Pokémon. so I knew this dataset was decently trustworthy for selection bias since I don't throw away bad Pokémon. I had a hunch that this probably followed a normal (gaussian) distribution so I plotted the data from my wild catches on a histogram.

On the x axis, are the IV values separated by intervals of 10. On the y axis, lies the number of pokémon whose IV total lies in the specified interval. As you can see, it indeed does follow roughly the trend of the normal distribution, so by taking the liberty of assuming this behaved exactly like a normal distribution, I was able to compile some interesting information.

Firstly, given the dataset, the mean value of total IVs for a random pokémon was calculated to be approximately 93.52, which made sense since 93 is 186/2. The standard deviation, also based on the dataset values was calculated to be approximately 21.5, and by using this value together with the assumption that the mean value was exactly 93, the following normal distribution of total IV values was created:

image.png.adff1bde7a59b00db9a17f19fe0bfc79.png

By using an online tool, one could calculate the probability of a random wild caught pokémon to have an IV total belonging to an arbitrary interval, which was given by the area under the gaussian curve limited by the desired starting and ending points of the interval. Doing so, I could find out the chances of finding a wild caught pokémon that belonged within a certain IV total range. Here are the findings:

in "Lower than" or "Higher than" format, in intervals of 10:

< 10 IVs = 0.01%
< 20 IVs = 0.03%
< 30 IVs = 0.17%
< 40 IVs = 0.68%
< 50 IVs = 2.28%
< 60 IVs = 6.24%
< 70 IVs = 14.24%
< 80 IVs = 27.27%
< 90 IVs = 44.45%
> 90 IVs = 55.55%
> 100 IVs = 37.24%
> 110 IVs = 21.46%
> 120 IVs = 10.46%
> 130 IVs = 4.26%
> 140 IVs = 1.44%
> 150 IVs = 0.40%
> 160 IVs = 0.09%
> 170 IVs (quite plausible win in a catching event) = 0.02%
> 175 IVs (very likely winning a catching event) = 0.01 %

The > 90 interval has a greater frequency than < 90 because the mean happens to be at 93. This means that excluding the pokémon who have exactly 93 total IVs, 50% of them will have more than 93, while the other 50% will have less than 93. I could've picked an interval that was a divisor of 186 in order to avoid this asymmetry but I think the intervals of 10 are easier to convey.

So the probability of any given wild pokémon that you catch being the event winner, assuming that victory happens for catches of 170 IVs and above, hovers around 1 in 5k to 1 in 10k. Since the victory prize is usually a shiny and shiny rate is 1 in 30k it can be a better method for obtaining shinies depending on what hordes are avaliable, and you can even choose the IVs on your shiny, so make sure to participate in catching events I guess, they can be a very good deal, lol

Some fun facts:

Since the mean is 93 IVs, the starters and gifted mons with their 6x15 90 IV total are officially slightly below average and not actually average. Essentially an overcomplicated way to say that 15 is slightly less than 31/2
The top 1% of wild catches are those with 143 IVs and above
The probability of finding a wild pokémon with total IVs equal to or greater than 180 is, rounded to 3 significant figures, 0.00% lol
This is made under the assumption that the IVs of a pokémon can assume any real value in between 0 and 186, this is of course not the case as it can only assume integer values. This may or may not have an effect on the probabilities and wether or not the intervals should be inclusive or exclusive, but I think this is enough overthinking over a pokémon game and also I have no idea how to take that into account.