I wanted to know if I could really catch every single pokemon in my neighborhood. I never see many of them here. But I do in other cities. I decided to see if the math shows that it is impossible for certain pokemon to spawn in certain areas. The analysis was overkill. But it's alright. I enjoyed doing it.
For the past few months, I have done an average of about 20 sweeps of the 1KM circle around my house. On average, each sweep nets about 35 spawns, so we are talking about 600 spawns per day. Over the course of 3 months, that is 55,000 pokemon. We'll just work with 50,000 to get a conservative idea.
Here are the unevolved pokemon that have never spawned here (This is because evolved pokemon will always spawn in an area where their unevolved form does)
That's 18 pokemon to not spawn out of 50,000 spawns. Please keep in mind, I have never seen a single pokemon spawn here only once (excluding evolved forms). Chansey, Koffing, Magikarp, both Hitmons, have all spawned here at least 3 times. This data would lead us to conclude that the individual spawn rate for each one is probably less than 1/50,000. Lets try and figure out how much lower it is, and then conclude if it is low enough, the number is effectively zero.
If each one had a spawn rate of 1/50,000 in my neighborhood, what would be the probability of never seeing a single one? Well, going with that arbitrary spawn rate, the chance of never having any one of 18 different events with a probability of 1/50,000 occur in 1 trial is 18/50,000 (0.00036). This is only one trial. As said above, if each scan of the area is its own trial, 1,800 were conducted.The probability of never seeing any of these 18 pokemon in 1,800 trials is ((49,999/50,000)1800) *18
That probability is 1/17.4. Alot larger than I first calculated.
That number is, for all intents and purposes, certainly not zero.
Obviously the spawn rate for any of these guys is not 1/50,000. It is much, much lower. How much lower? Well, it is difficult to calculate a probability when an event has yet to occur. Let's use the following question to get an idea:
Assuming that all 18 of these pokemon had the same spawn rate, and that they never spawned once in 50,000 spawns, what would the individual probability need to be in order for their to be a 50% chance of this occuring?
Well, for a 50% chance in 50,000 spawns, the answer is going to be a probability of 1/100,000 (50,000/100,000) total for any 18. In other words, if the probability of seeing any of them is 1/100,000, their would be a 50% I saw at least one. This means that the hypothetical individual probability is 5.555*10-5 (assuming equal spawn rates).
Pokemon Go has 20 Million Players. Lets say each player wanted to catch an aerodactyl in their backyard, and their's has the same spawn rates as mine (obviously it will not). If each player checked their backyard as often as I did, and we ran with the 5.555*10-5 chance of seeing any one pokemon (in this case, we specifically want to find only aerodactyl), only 11 players would find him!
Errors and Assumptions
So let's discuss errors before drawing a conclusion. I am a high school student and it is very possible I made a mathematical error at some point. That's always a given. I also made several assumptions, here they are:
1.All pokemon never seen in my neighborhood have an equal spawn rate . It most certainly isn't. Obviously, magikarp should be more likely than Aerodactyl. This assumtion holds true if the probability is zero, however.
2.My scanner can detect all pokemon
3.The chosen expected spawn rate was picked in such a way that, if it were true, their is a 50% chance I would not have seen any of them. If I repeated this entire experiment over and found no new pokemon in my neighborhood but kept the spawn rate at 5.555*10-5 the probability of not seeing any would be 25%.
Alright. The claim that a spawn rate in an area is never zero is wrong. At the very least, it is so small that, at hypothetical best, only 11 out of 20 million players would find any unfound pokemon in my neighborhood. It is pretty much safe to conclude that the extremely small 1KM circle around my house is a dead-zone for certain pokemon. All pokemon that have been found have a spawn rate that has enabled them to spawn at least three times over the previous three months. None have been found once or twice. This is strong evidence that the lowest used in-game spawn rate is well above 1/50,000. I also did the math to effectively prove this.
No. A spawn rate of Zero is definitely possible and certainly exists for some pokemon in some areas. It is possibly coded into the game to never find a Grimer or Chansey in your neighborhood. Look elsewhere or hatch some eggs. Don't forget to pray to RNGsus.