"PSA: Egg IV distribution"

#PokemonGO: Hello all,I've been using a bot (on an account now submitted for deletion, so please do not ask to purchase it from me, I have no interest) to do nothing but gather eggs and hatch them. After getting a sample size of 1000, I plotted the data and examined the distribution. I threw around a few simple ideas that a lot of programmers use for skewed distributions, and I'm effectively certain I've found how Egg IVs are determined - for anyone who has played Fire Emblem, this might be familiar.Here's my data-set:IMGEssentially, a caught Pokemon (barring the ATK IV glitch) rolls a "dice" of sorts, between 0 and 15, and that's the IV. However, egg Pokemon do it slightly differently. For each IV, they roll the dice 3 times, and take the highest - so, your chance of getting, say, a 15 IV in DEF is not 1 in 16, as per a wild Pokemon, but rather about 1 in 11 (because instead of having only one chance to get a 15, you have 3 chances, so your chances of missing it entirely are (15/16)3, and so your chance of getting it is 1 minus that).The mean hatched Pokemon comes out at 77.8%, but the distribution is skewed somewhat - there's a larger cluster at the upper end of the scale and then a long thin tail downwards, so the median is somewhat higher at exactly 80% (that's 36/45). Given this is literally unachievable for some wild Pokemon from what we know (e.g., no wild or nest Bulbasaur recorded to my knowledge with higher than 3 IV in ATK, therefore maxing out at 33/45 or 73.3%), this means that Eggs are actually a very good proposition, although this was always obvious.What's more interesting is that we can now figure out whether to wait for another Egg or not. For example, if your Gastly is >80%, you know it is in the top 50% of hatched Gastly. If it is <80%, you might want to wait and try for another Egg if possible.And if you're aiming for the elusive 15/15/15? Well, the odds are 0.54% - so roughly one in every 180 eggs. It's not great... but much better than the one in every 4096 you'd have to catch from the wild assuming that ATK IVs weren't glitched, and still better than the one in every 256 wild Pokemon for those with a Pokedex number approximately 120 or greater.One last cool fact? If this is right, there is a 1 in 68,719,476,736 chance of hatching a 0/0/0 Pokemon. Better hope it's not you! via /r/TheSilphRoad http://ift.tt/2ajxyFP