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Hello there!
Ever since I started to play this game, which has been only as a solo player so far, I noticed a certain bias for me to be put into the yellow team. After browsing Reddit, this seemed to be a thing for many players. So I wanted to take a look if there is more to it and eventually started to track my 3 team games. Sadly I didn't tracked all my games and didn't include a screenshot at first, so I only gathered my last 54x 3 team games. I've took a screenshot at the beginning of each game, with names displayed (Sometimes I was to slow and you can't see my name clearly <.<).
Link to album: https://drive.google.com/drive/folders/1KcWr2bi0gU2t0tWxesOqRAaxObzeJCz5?usp=sharing
Or summarized in a table:
Table 1: Tracking of 3 Team Games
This comes down to:
Now that we have some data, we can test a hypothesis.
Let the null-hypothesis be that every player is assigned randomly to any of the 3 teams with an equal chance of 33%.
Let out hypothesis be that (for me) the chance to join the yellow team is not 33%.
The easiest way to test this would be to say this is a sequence of independent experiment with a boolean-valued outcome (yes/no). So we simply ask "Are we in the yellow team?".
The null-hypothesis suggests that this should happen 33% of the time. 66% of the time, we should find me in either the red or blue team.
So p = 0.33 and 1-p = 0.66. As for the number of experiments, we have a total of N = 54.
The expected value of the number of games in the yellow team is simply N*p, so we find:
E(yellow team) = 54 * 0.33 = 18.
The standard deviation is given by the sqrt(N*p*(1-p)). It tells us something about the random spread of the number of games that we can expect.
So let's calculate that and call it S.
S(yellow team) = sqrt(54*0.33*0.66) = sqrt(12) ~ 3.5
So the expected value is 18 games and the standard deviation is about 3.5 games.
How many standard deviations is our observed value away from the expected value or simply:
40 = 18 + Z * 3.5 , find Z.
-> Z ~ 6.3
So we find that our observed value is more than 6 standard deviations away from the expected value (Mind that this is a binomial distribution and not a normal distribution, but we will approximate it with a normal distribution because I don't want to calculate it.)
So taking a look at the wiki page of the standard deviation, we can scroll down to the table under
Rules for normally distributed data:
https://en.wikipedia.org/wiki/Standard_deviation
| Confidence interval | Proportion within (Percentage) | Proportion without (Percentage or Percentage Fraction) |
|---|---|---|
| 6σ | 99.9999998027% | 0.0000001973% or 1 / 506,797,346 |
Mind that this is not exact for simplicity! Anyways, it tells us that our observed value and our expected value with the associated standard deviation is not really compatible with one another. That or I got as unlucky as you can possibly be.
The conclusion from that is that the null-hypothesis is false, or in other words the chance for me to get into the yellow team is significantly higher than 33%.
And there we go. Discuss.
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