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#### Silph Study: **#005**

##### Published:

**12.01.2016**

# PokeStops and Egg Distances

We are often asked, *"Do some PokeStops give out different egg species?"* or *"Do some PokeStops give out more 10km or 2km Eggs?"*

Because of the difficulty in gathering this data, the world has been in the dark regarding PokeStop egg drop rates and distributions. We still don't know all the answers, but today we get to share a new, significant finding!

26 Silph Researchers undertook a grueling task: **each researcher collected and hatched 50 eggs from a single Pokestop**, allowing us to analyze whether different Pokestops gave different eggs. Nearly all 26 researchers managed to acquire the target 50, and some managed to get up to 180. In total **1,841 eggs** were hatched, and the contents have been recorded and analyzed.

###### Summary

After analysis, we are confident that not all Pokestops award eggs from the same distribution.

In other words, **we witnessed some travelers receiving significantly more 2k eggs and others receiving significantly more 5k eggs from their PokeStop of choice!** We can't yet say why, but the fact that not all PokeStops were observed to give out the same egg odds is a big deal. Look forward to more research as we continue learning about PokeStops and Eggs.

Now for the fun part: how we arrived at our conclusions!

###### Analysis

First, we examined the distribution of egg-distances (ie, 2km, 5km, or 10km) for eggs from each PokeStop. One important reason for starting with this is because the distance is already determined at the PokeStop and the hatching location cannot have any influence on it. The distribution for each researcher is given in the following table:

## Eggs Received from 1 PokeStop

Immediately, we suspected that not all PokeStops are awarding egg-distances from the same distribution. Here is a look at the ratio of 2km eggs to 5km eggs:

## Ratio of 2km to 5km Eggs

We decided to run a **chi-squared** test for independence on the data. This test checks whether it's plausible that the distance distribution is independent of PokeStop. We unfortunately obtained very few **10km eggs**, so we are unable to include these in the test *(See Note 1)*. So we looked only at the distribution between 2km and 5km eggs. This left a total of **1,715 eggs** to analyze, 669 2km eggs and 1,046 5km eggs.

The first step of the chi-squared test is to calculate the expected number of 2km and 5km eggs for each researcher, based on their total number of hatches and the egg distribution of all trainers. Then we will test whether these expected counts differ significantly from the observed (actual) counts.

## Example:

Researcher jFarr hatched a total of 169 eggs (not including 10km eggs). The expected counts are 169 x 669 / 1715 = 65.925 2km eggs and 169 x 1046 / 1715 = 103.075 5km eggs. Next we take the square of the difference between the expected and observed count and divide it by the expected count. In our example, jFarr got 67 2km eggs and 102 5km eggs, so we get values (67 - 65.925)^2/65.925 = 0.0175 and (102 - 103.075)^2/103.075 = 0.0112. These values give a measure of how much the expected and observed counts differ from each other.

We add up the values for all trainers, and come up to a total of **43.905**. If the egg distribution were independent of PokeStop, this total would follow a chi-squared distribution with 25 degrees of freedom. The number of degrees of freedom is calculated as:

(#researchers - 1) x (#egg types - 1) = 25 x 1 = 25

We can now calculate the p-value, this is the probability that a random variable following a chi-squared distribution with 25 degrees of freedom is 43.905 or larger. The result is:

p = 0.0111

This is *lower* than the 0.05 threshold for significance, so we have concluded that **the hypothesis that distance distribution is independent of PokeStop has been refuted** *(See Note 2)*.

###### Further Testing (Species Distribution, etc.):

We continued by looking at the individual species hatched. It is believed that the contents of an egg are already determined upon receiving it at a PokeStop (largely due to the fact that Pokemon with legacy movesets were hatched after global moveset changes, among other compelling reasons). Under the assumption that this is true (most importantly: hatching location is not important) we can research the contents of the eggs. The counts for individual species are too low to do any meaningful testing, so we had to group different species together. One way to do this is to compare the distribution between Water and non-Water Pokemon from 5km eggs. It's important that we look at 5km eggs only; if we looked at all eggs, a difference in species distribution could be caused by the difference in distance distribution we just discovered.

We ran a chi-squared test similar as before to the counts of Water and non-Water Pokemon from 5km eggs. This test gave a p-value of p=0.1728, which means we did **not** find a significant difference in the contents of 5km eggs of the different researchers. Other ways of grouping up species have also been tried, but none gave a significant result.

Despite not getting a result here, we are still very interested in the distribution of individual species from eggs and we will be running further, more specific, experiments in the future.

###### Notes

**Note 1:**

The chi-squared test requires that no more than 20% of the expected counts are lower than 5. If we included 10km eggs, this would not be the case.

**Note 2:**

Strictly speaking, we can only conclude that the researchers obtained egg distances from different distributions. It could theoretically be the case that this is caused by something other than PokeStop location (such as time of day, level, etc.). More research is planned to help confirm/isolate factors affecting egg drop distributions.

###### Publication

This finding was shared on our subreddit on Dec. 1, 2016.

###### Notable Researchers

Contributions to this project were made by 26 Silph Researchers. This was a tough experiment to see through to completion. It meant never spinning a PokeStop while out and about if you had an empty egg slot. It also meant either intense walking, or intense incubator purchases. We all owe these good travelers a lot for making this research possible:

- jFarr
- bakanoitte
- Phaazoid
- GCBill
- thehighknight
- samaraner
- ux
- Rabiiiii
- Chris
- epicification
- ZoltanSnarf
- Memnoich
- Antithesis
- Marfnet
- izzytdi
- SDWeasel
- toon_leader_bacon
- coolblueflame
- killem2
- patman9
- Hendy2322
- LilxDRUMMERxBoy
- thesquideye
- Astraldebri
- b1LLybLaz3
- Nguyeezus