IV probabilities for non-bred Pokemon

[lostRD]

I've been doing some mathematics with the help of Wolfram Alpha (WA) and it seemed interesting enough to share.

Pokemon have 6 IVs that range from 0-31 which is 32 possible values per stat. If we had 6 dice of 32 sides each, we could roll them to get valid IVs - provided we subtract 1 from each dice value at the end because dice start from 1, not 0.

Tell WA to "roll 6 32-sided dice" and it will tell you many things. The most interesting to me is that the distribution looks to be a typical normal distribution with mean value of 99 and standard deviation of 22.6 (variance of 511.5).

Ask WA for "normal distribution mean = 99, variance = 511.5" and it will give us even more useful information. Look to the bottom at Percentiles and you'll see that the bottom 10% of Pokemon caught (not bred) will have a combined IV total of 64 or worse (70 minus 6 because each stat must be decreased by 1 as I noted earlier and there are 6 stats) and the top 10% of Pokemon will have a combined IV total of 122 or better. Those numbers average out to about 11 and 20 per stat. This means that 80% of Pokemon will have an average IV between 12 and 19. Who wants those though?

Let's look more into Pokemon that are worth having. WA tells us that the top 1% of Pokemon will have an IV total of 145 or better which is an average of 24 per stat. If you catch a Pokemon with stats that good, you have a 1%er.

Want to find out how good your poke's IVs really are? Simply input your IV total into the CDF (cumulative distribution function) of the distribution to find our the percentage of Pokemon that yours is better than by asking WA for "x=145 CDF of normal distribution mean = 99, variance = 511.5" and changing 145 to your total but add 6 so if your total is 100 then use 106 instead. Take WA's answer, multiply by 100 to get the percentage, subtract it from 100 to get the percentage that is equal or better than your poke and voila, you can brag accurately!

Edited April 27, 2015 by lostRD

[Kiliminati]

Man, I'm so proud of myself for actually understanding everything you just wrote

Thank you statistics

[londark]

>WA

>Not Matlab

[lostRD]

>WA
>Not Matlab

Because everyone has access to Matlab, right? /s

Snark aside, Wolfram Alpha is a fantastic free resource.

[londark]

There is a poverty version around....don't remember the name tho

 

Worst case there is always R for statistic and probability 

 

Altho WA is indeed usefull

[londark]

Also, that is a pretty cool example of  the Central limit theorem

[PandaJJ]

However, since breeding is obviously a much more efficient way of acquiring usable comps than catching, all you really care about is catching pokemon that can be used for breeding. In which case, the IV total is irrelevant. The only thing you care about is how likely it is to have one or more IVs of X-31, where X is the minimum IV you are willing to accept on your final product. I like your attitude, though.

[lostRD]

Also, that is a pretty cool example of the Central limit theorem

It sure is! I had forgotten what the theorem was called. With a bit of time and some basic scripting I could compare the normal distribution to the actual distribution to see just how close the approximation is.

However, since breeding is obviously a much more efficient way of acquiring usable comps than catching, all you really care about is catching pokemon that can be used for breeding. In which case, the IV total is irrelevant. The only thing you care about is how likely it is to have one or more IVs of X-31, where X is the minimum IV you are willing to accept on your final product. I like your attitude, though.

My math is bad, see next post

The maths is considerably more simple for catching pokes with 31s. The chance of each 31 is 1/32 and each poke has 6 chances so the total is 6/32 or about 20%. For 2x31, the chance is (6/32) * (5/32) which simplifies to 30/1024 or about 3%. 3x31 is (6*5*4)/(32^3) or 120/32768 or about 0.4%.

If every fifth Pokemon I caught had a 31, I would be so happy... Edited April 26, 2015 by lostRD

[PandaJJ]

The chance of each 31 is 1/32 and each poke has 6 chances so the total is 6/32 or about 20%.

 

The bolded statement is wrong. By that logic, all pokemon will have at least one IV of 25 or higher, since the chance of one stat being 25 or higher is 6/32, which makes the chance of any stat being this 36/32 (as you can see, this doesn't even make sense).

 

The proper chance is 1 - (31/32)⁶, i.e. the chance that not all your IVs are smaller than 31. This is about 17,34%, which is much closer to 1 in 6 than 1 in 5.

Edited April 26, 2015 by PandaJJ

[lostRD]

The bolded statement is wrong. By that logic, all pokemon will have at least one IV of 25 or higher, since the chance of one stat being 25 or higher is 6/32, which makes the chance of any stat being this 36/32 (as you can see, this doesn't even make sense).

The proper chance is 1 - (31/32)⁶, i.e. the chance that not all your IVs are smaller than 31. This is about 17,34%, which is much closer to 1 in 6 than 1 in 5.

Well now I feel silly. My results did feel wrong, I'd been out of school too long to remember why though. Oops. This is why I let Wolfram do the thinking.

[PandaJJ]

Well now I feel silly. My results did feel wrong, I'd been out of school too long to remember why though. Oops. This is why I let Wolfram do the thinking.

 

Haha, no problem, we all make mistakes. Of course, the rest of your argument is also invalid, as the chance of encountering a pokemon with at least two IVs of 31 is only about 1,34%. This is the reason why many people breed for 25+ instead - the chance of encountering a pokemon with at least one IV being 25+ is about 77,27%, while the chance of encountering a pokemon with at least two IVs being 25+ is about 39,06%.

[axx]

Because everyone has access to Matlab, right? /s

There is a poverty version around....don't remember the name tho

http://www.scilab.org/

tho, not having access to matlab... *shivers*

[Magikarpisamaze]

My head exploded. 

[londark]

http://www.scilab.org/
tho, not having access to matlab... *shivers*

Was actually talking about Octave, but that one looks poverty enough as well