APEX LEGENDS LANDING STATISTICS
You have a 1 in 3 chance of starting a bad game.

If you've never heard of it, Apex Legends is yet another battle royale first
person shooter, where typically 20 teams of 3 random people need to fight to
be the last ones standing. All teams drop from an aircraft toward the ground
and need to pick up equipment for fighting. Around every 3 months a new com-
petitive season starts. Each season a map is chosen with a certain amount of
named areas.

This introduces three big problems for every start of a round:

* Bad teammates are on your team.
* The equipment in the area may not be adequate.
* Another team has landed in the same area.

The following of the article explores the rough chances of all these events
happening individually and at once.

S 1. LONE WOLF

A "lone wolf" is someone who decides their team is a luxury which they feel is
not necessary. Since you wouldn't count yourself (I hope), this means the
following combinations of teammates is possible:

Player 2 is Good, Player 3 is Good
Player 2 is Bad,  Player 3 is Bad
Player 2 is Good, Player 3 is Bad
Player 2 is Bad,  Player 3 is Good

There are 3 of 4 scenarios where you will have a bad teammate.

S 2. WEAPONS

There are 22 guns which can be found in an area at the start. I've categorized
them (subjective) based on what I think is their strength:

~6 "weak"
~9 "medium"
~7 "strong"

In a scenario where everyone's skill is the same, strong beats everything. This
means there are 15 other weaker weapons which you are likely to come across, or
15/22 chance.

S 3. PLACEMENT

Season 7 (2020-11) introduces a new map: Olypmus. This map has 16 named areas.

Each area has a 1 in 16 chance of a team landing on it. If you land in an area,
there is a 15 in 16 chance they will not land in the same one since there are 15
other possible areas to go to.

Since there are 19 other teams, and each has a 15/16 chance of not landing in
your area, we need to multiply this 19 times: (15/16)^19 which is approximately
0.29, or 29% chance they don't land in the same area. That's pretty bad news for
your team, since there is a (about 2/3) 71% another team will land with you.

S 4. ALL TOGETHER

Now let's combine it all together:

* 3/4 chance of a wolf on your team
* 15/22 chance of getting a bad weapon
* 2/3 chance of another team landing with yours

3/4 * 15/22 * 2/3 = 15/44 (34%) chance of all bad things happening to your team, or
about 1 in 3 games.

S 5. OTHER CONSIDERATIONS

Of course a big factor here are incentives. Because of how the points system
works, there is incentive to kill other teams early on. There is also incentive
for teams to land in certain areas for the particular equipment which is spawned
there. This means there is some game theory at play here, skewing and
influencing where teams will end up. Our chances of survival are much greater if
we ignore these incentives since they don't contribute to survival - only points
gained.