"A big-picture look at my rather typical shiny hunting results"

#PokemonGO: tl;dr – Each shiny release is a chance to be lucky, average, or unlucky. For the data set considered, I am actually slightly luckier than average with only 43% of trainers expected to have more luck in finding shinies than me. Buried in that “average” experience are some exciting highs and frustrating lows that we can all relate to. As the number of shiny opportunities continues to increase, it is only natural that each player will experience some of those extremes.Approach: For about a year I have tracked my shiny success. I use pokedex screenshots before and after shiny events. Pokemon storage sorted by date verifies the number of shiny I found (never transfer). I only used events for which I made 100% manual encounters. The data sets generally reflect a total event effort; they aren't truncated because I quit looking after getting a shiny. Absol is the only one for which I essentially quit hunting after getting a shiny.The shiny rates are taken from the Silph Road published rates. I used 1:450 for wild, 1:20 for feebas (Americas), 1:75 for Absol, 1:35 for Mawile, 1:19 for Kyogre and Groudon (assuming Lugia & Ho-Oh rate applies), 1:25 for Community Day, 1:60 for Aerodactyl, and 1:10 for Zapdos day.I have with 24 shiny experiences that I can confidently use to quantify my performance. I have solid records of encounters and a published shiny rate.I use the binomial distribution to assess my experience. The probability mass function gives the probability of X successes (shiny) in a total of Y experiments (encounters). I sum a portion of that mass function to quantify the percentage of the population that will have had luck better than me. Said a bit differently, if I had a pool of thousands of trainers that made the same number of encounters as me, the sum is the percentage that would end up having more shiny than me.Example: Zapdos raid day. I found 3 on 31 encounters. For 31 encounters at a 1:10 rate, the expected distribution is: 0 shiny (4%), 1 (13%), 2 (22%), 3 (23%), 4 (18%), 5 (11%), 6 (5%), 7 (2%). The fraction of the population that was more lucky than me (% LTM) is 18% + 11% + 5% + 2% = 36%. Note that the distribution does not stop at 7 shiny; extending the series to the full range of possibility (31 shiny) produces a sum of 38%.Findings: I knew my notable high going into this effort. I found my shiny absol within 3 raids (0.05% of the population does better than that). Aerodactyl is my notable low with only 1 on 214 encounters (87% of the population does better than that).The average of my % LTM values is 43%. Before we rush to suggest that there could be some bias in certain trainers finding shiny, I think it important to remember that I am drawing from just 24 shiny experiences.I took a look at the distribution of my results, expecting a normal distribution. The discrete nature of the metric and the number of samples are insufficient to aggregate into meaningful bins, so I choose not to share that data here.What Next: Dig deeper for additional data sets (shiny & total encounters). The 24 were my easiest to grab data points. Add data sets once shiny rate is published or found (Shinx, Psyduck, Ingress Prime, Plusle/Minun, Wingull). Continue to lament my lack of shiny hat Pikachu.DataSpeciesEncounters# Shiny% LTMSpeciesEncounters# Shiny% LTMDuskull233110%Fragment Pikachu633075%Poochyena216038%Kyogre13115%Houndour220039%Groudon41164%Witch Pikachu203036%Drowzee11113%Drifloon547070%Beldum2051112%Santa Pikachu538070%Cyndaquil204757%Delibird600138%Totodile3151072%Snorunt70037%Larvitar111638%Feebas41161%Zapdos31338%Absol310.1%Aerodactyl214187%Mawile44136%Charman.139632%Mareep128289%Bulbasaur160562%​ via /r/TheSilphRoad http://bit.ly/2WX0cCX