"[Detailed Analysis] Probability of finding various IVs from both wild Pokémon and hatched/raid Pokémon (with some beautiful graphs)"

#PokemonGO: TLDR: Look at the graphs at the end of the post to see the difference in probability of finding high IVs for wild Pokémon, and hatched/raid PokémonI decided to do some in-depth analysis to work out the probability of finding high IV Pokémon, in both the wild, and through egg hatching and raids. This is completely just for fun, but I thought I would share just in case anybody else was interested.For this analysis, I have assumed that every IV combination has the same chance of appearing, for example, 15/15/15 has the same chance of appearing as 1/0/11I started off by writing down all the different combination of possible IVs. There are three stats, HP, Attack and Defence, each with a possible IV between 0IV and15IV. That makes a total of 163 = 4096 different combinations. The table below shows:• The possible IV combination totals• The number of times each total is calculated• The percentage chance of each total• The chance of finding a Pokémon that is over each IV total.IVCountChanceChance of ≥IV010.024%100.000%230.073%99.976%460.146%99.902%7100.244%99.756%9150.366%99.512%11210.513%99.146%13280.684%98.633%16360.879%97.949%18451.099%97.070%20551.343%95.972%22661.611%94.629%24781.904%93.018%27912.222%91.113%291052.563%88.892%311202.930%86.328%331363.320%83.398%361503.662%80.078%381623.955%76.416%401724.199%72.461%421804.395%68.262%441864.541%63.867%471904.639%59.326%491924.688%54.688%511924.688%50.000%531904.639%45.313%561864.541%40.674%581804.395%36.133%601724.199%31.738%621623.955%27.539%641503.662%23.584%671363.320%19.922%691202.930%16.602%711052.563%13.672%73912.222%11.108%76781.904%8.887%78661.611%6.982%80551.343%5.371%82451.099%4.028%84360.879%2.930%87280.684%2.051%89210.513%1.367%91150.366%0.854%93100.244%0.488%9660.146%0.244%9830.073%0.098%10010.024%0.024%I always knew that the most common IVs (for wild Pokémon) would be 49 and 51, but I never knew the exact figures, and now I do. There is 4.688% chance (around 1 in 21 chance) that a wild Pokémon will have 51IV (the same applies to 49IV). On the flip side, there is just 0.024% chance (1 in 4096 chance) that a wild Pokémon will have 100IV (the same applies to 0IV). This is a huge difference, you are 192 times more likely for find a 51IV Pokémon, than a 100IV Pokémon in the wild.Some other interesting metrics are as follows:The chance of finding 80IV or more is 5.371%The chance of finding 85IV or more is 2.051%The chance of finding 90IV or more is 0.854%The chance of finding 95IV or more is 0.244%As you can see, as you increase the IV that you’re aiming for, your chances of finding a Pokémon in the wild with desired IVs will decrease exponentially.I also did the same for egg hatches and raids. In this case, again there are three stats, HP, Attack and Defence, each with a possible IV between 10IV and 15IV. This makes a lower total of 63 = 216 different combinations. I then worked out the exact same metrics as I did for wild Pokémon.• The possible IV combination totals• The number of times each total is calculated• The percentage chance of each total• The chance of finding a Pokémon that is over each IV total.IVCountChanceChance of ≥IV000.000%100.000%200.000%100.000%400.000%100.000%700.000%100.000%900.000%100.000%1100.000%100.000%1300.000%100.000%1600.000%100.000%1800.000%100.000%2000.000%100.000%2200.000%100.000%2400.000%100.000%2700.000%100.000%2900.000%100.000%3100.000%100.000%3300.000%100.000%3600.000%100.000%3800.000%100.000%4000.000%100.000%4200.000%100.000%4400.000%100.000%4700.000%100.000%4900.000%100.000%5100.000%100.000%5300.000%100.000%5600.000%100.000%5800.000%100.000%6000.000%100.000%6200.000%100.000%6400.000%100.000%6710.463%100.000%6931.389%99.537%7162.778%98.148%73104.630%95.370%76156.944%90.741%78219.722%83.796%802511.574%74.074%822712.500%62.500%842712.500%50.000%872511.574%37.500%89219.722%25.926%91156.944%16.204%93104.630%9.259%9662.778%4.630%9831.389%1.852%10010.463%0.463%The most common IVs in egg hatches and raids are 82IV and 84IV. There is 12.5% chance (1 in 8 chance) that a wild Pokémon will have 84IV (the same applies to 82IV). On the flip side, there is just 0.463% chance (1 in 216 chance) that a wild Pokémon will have 100IV (the same applies to 67IV). This is a smaller difference than wild Pokémon, but you are still 27 times more likely for find an 84IV Pokémon, than a 100IV Pokémon from egg hatches and raids.I gathered the same metrics as I did for the Wild Pokémon, but for egg hatches/raids instead:The chance of finding 80IV or more is 74.074%The chance of finding 85IV or more is 37.500%The chance of finding 90IV or more is 16.204%The chance of finding 95IV or more is 4.630%As you can see, as you increase the IV that you’re aiming for, your chances of finding a hatched/raid Pokémon with desired IVs will decrease exponentially, however the chances look much more appealing than wild Pokémon.In conclusion to this, I have created some graphs, which I feel is a beautiful visual representation of the difference between IVs chances for wild Pokémon, and IVs chances for hatched and raid Pokémon. This first graph below shows the percentage chance of IVs for wild Pokémon, and hatched/raid Pokémon.% Chance of IVsThe second graph, below, shows the chance of finding IVs above x, for wild Pokémon, and hatched/raid Pokémon.% Chance of IVs above xYou can see that hatched/raid Pokémon are a lot more likely to have better IVs. Data is beautiful!As I mentioned at the beginning of the post, we all know that hatched/raid Pokémon are more likely to have better IVs than wild Pokémon, but I wanted to dive a little deeper into this subject, purely because I find it very interesting. Pokémon and stats, what’s not to like?! via /r/TheSilphRoad http://ift.tt/2xZxarY