Mathematically, the odds of catching a Ditto with at least one perfect 31 IV are about 1 in 6 (18.75% to be exact), so on average you will need to capture about 36 Dittos to acquire one with a perfect IV for each stat. That's a little over a full PC box.
When I saw this, I was about to go off to start catching Ditto, since it didn't seem like too much work, even though I'm just a casual player. But it seemed too easy. Thinking about it... the calculation done here shows that 36 Dittos are required to get six with an
arbitrary perfect IV, not six with
distinct perfect IVs as claimed. For example, when you have one such Ditto already, then there is a 1/6 chance that the next such Ditto will have the same perfect IV as the first. When you have three perfect IV Dittos, there is a 50% chance that the next such Ditto will have the same perfect IV as one of the first three.
So to find the
actual average number of Dittos that you'd need to catch:
First Ditto with one perfect IV: 6/32 = 3/16 chance to find in any particular encounter (nearly 1/5 chance). So we'll say you need five Dittos to get to this point on average.
Second Ditto: 3/16 chance to find one with any arbitrary prefect IV, but also 1/6 chance that this is the same as before, which we need to exclude. So we have only a 5/32 (3/16 * 5/6 = 5/32) chance of finding this second Ditto in any given encounter. That's close to 1/6, so we'll say you need six more Dittos to get to this point on average... 11 Dittos total so far.
Third Ditto: 1/3 chance that the arbitrary perfect IV is the same as before. 3/16 * 2/3 = 1/8 chance of finding your third Ditto in any given encounter (much less than 1/5, where we started). So 19 Dittos needed so far.
Fourth Ditto: 50% chance that the arbitrary perfect IV is the same. 3/16 * 1/2 = 3/32 chance to find the Ditto. Close to 1/11, so 30 Dittos needed so far.
Fifth Ditto: 2/3 chance that the arbitrary perfect IV is the same. 3/16 * 1/3 = 1/16 chance to find the Ditto. 46 Dittos needed so far.
Sixth Ditto: 5/6 chance that the arbitrary perfect IV is the same. 3/16 * 1/6 = 1/32 chance to find the Ditto (as expected, since this is the chance that the Ditto has a perfect in any particular stat).
Therefore, an average of
72 Dittos (or any Pokemon) must be caught to get a Ditto with one perfect IV in each of the six stats, over twice the claim in this article. I'm no mathematician so I suppose I might be doing this completely wrong, but I think that's right.