"Egg tiers and RNG - what to expect"

#PokemonGO: tl;dr random=/=uniform(I hope /u/neovex9 doesn't mean I steal this from the comment section)The biggest misconception encountered when looking at random data is to assume that a random event of equal chance occurs the same number of times.But isn't this what random is about? Read again the first paragraph - now read the following: A random event of equal chance occurs the same number of times on average.Did you spot the difference? I just slipped in one single word. But lets try to show it with a picture: http://ift.tt/2s2oxdZ is the data for the graph.HatchesXtra-rareUltra-RareRareUncommonCommon4159351001.512.140.180.010.0011.474.170.710.110.0020.724.071.390.430.0030.232.641.811.120.0040.061.281.762.210.0050.010.501.373.460.0160.000.160.894.520.0370.000.040.495.040.0780.000.010.244.910.1490.000.000.104.240.25100.000.000.043.290.39110.000.000.012.320.56120.000.000.001.490.73130.000.000.000.890.88140.000.000.000.490.99150.000.000.000.251.03160.000.000.000.121.00170.000.000.000.050.92180.000.000.000.020.79190.000.000.000.010.64200.000.000.000.000.5020+0.000.000.000.001.05What does the graph and the numbers mean? I calculated the odds (using binominal distributions and the odds given in the latest research from us) to hatch n pokemon of a given species assuming a total of 500 eggs hatched (the golden breeder badge). I then multiply the chance with the number of pokemon that are common (9), uncommon (35) etc. I have included the ultra-ultra-rare - even if we can't yet prrof they exist.If you follow the link, you notice that the curves are pretty flat. And they overlap. Actually we have 3 curves overlapping around 4 hatches - the ultra-rare, rare and uncommon. This means if you hatched 500 eggs and got 4 of a certain species (say a Scyther) then it could belong to any of the three classes. It might be most likely to be rare - as the rare distributions peaks at this point - but ultra-rare and uncommon represent more pokemon and therefore it could be this class as well.Another way to look at the data. At 500 hatches you still have an 18% chance for a rare not to have hatched - as well as a 5%+ chance of a rare to have hatched 10 times or more often.Now if player A is the unlucky one who didn't hatch pokemon X and player B is the 'lucky' one who hatched it 10+ times then from RNG point of view this isn't special. From a psychololical point of view it means - surely - this can't be true. There must be a biome dependence, there must be a player dependence, something else is happening here.To repeat: A random event of equal chance occurs the same number of times on average - individual outcomes will vary - sometimes by a lot. via /r/TheSilphRoad http://ift.tt/2qJ9hCH