"Egg hatching and RNG - explaining what to expect"

#PokemonGO: I have done a lot of research trying to show the different egg rarity classes. I will try to slowly publish some of it - now that TSR has published the main finding. The bit below was done pre-Gen2. Some of it should be re-written - chances at the time where 1/295 for ultra rare - now 1/315 - but it won't influence the data too much and I rather publish as is as not at all.Explaining observations on the Silph RoadHumans like to add patterns into random events. Who hasn’t read the story of the player hatching 500 eggs and who still hasn’t hatched a Lapras. Having a model which predicts the likelihood of an event allows us now to the likelihood of such events. This part will show that these stories are in line with what we should expect from a random model with some very small chances to hatch ultra rare Pokémon. Chances to hatch a certain Pokémon The following table shows the chances to hatch a specific common, uncommon, rare or ultra-rare Pokémon when reaching the silver breeder medal (100 hatches) or the gold breeder medal (500 hatches). The numbers are generated by using the predicted chances from part 1 pre-Valentine and calculating the chance to hatch a certain Pokémon.Hatched eggs Chance to hatch at least one of a specific PokémonBreeder Medalcommonuncommonrareultra rare10093.5%74.3%49.2%28.7%50099.9999%99.9%96.6%81.6%Table 1: Chances to hatch specific Pokémon when reaching the silver and gold breeder medalThe same data can also be displayed in a graph showing the total number of different Pokémon hatched. - Alas - not sure how best to integrate the graph here - sorry ...Graph 2 (missing) : Number of different Pokémon hatched depending on total eggs hatchedThe graph predicts that even with a gold breeder medal (500 eggs hatched) that random predicts that you hatch ‘only’ 65 out of 68 possible Pokémon. The three missing Pokémon are most likely some of the ultra rare ones. The prediction for 1000 hatched eggs is 67.5 different species – this means around half the players still won’t have bred one specific Pokémon after they hatched 1000 eggs.Here is an alternative view – predicting the fraction of players who hatch a certain number of ultra rare or rare Pokémon after hatching 500 eggs:Number hatched Fraction of players hatching a certain number of a specific PokémonNumberultra rarerare018.41%3.37%131.21%11.47%226.40%19.46%314.85%21.98%46.26%18.58%52.10%12.54%60.59%7.04%70.14%3.38%80.03%1.42%90.01%0.53%100.00%0.18%Table 4: Variation in eggs hatched for a player achieving the golden breeder meda l Keep in mind there are 9 rare and 14 ultra rare Pokémon. Every player should therefore expect at least one Pokémon who spawned a lot more than expected and one who spawned a lot less. So, while we should expect 18% of players to hatch not a single Lapras (replace with any other ultra rare if you want) in the first 500 eggs we can as well expect 9% of players to hatch 4 or more Lapras (replace with any other ultra rare if you want) when reaching the golden breeder medal.Final note: I used these calculations also to look for biome specific trends in egg hatching between researchers as well as reanalysing the original research about single stops - I couldn't find any non-random signal that would show biome deprendency. But more about this in a different article. via /r/TheSilphRoad http://ift.tt/2lLWopj