Doug's latest ladder statistics contained information about Pokemon that are commonly paired with other Pokemon in teams. I used this to find further information regarding these paired Pokemon using quite a simple probability technique.

Suppose Pokemon 1 has probability p_1 of appearing in a team and Pokemon 2 has probability p_2 of appearing in a team. Furthermore, let the probability that both Pokemon are in the same team be p_12. Then:

Code:

Probability that Pokemon 1 is in a team but Pokemon 2 is not = p_1 - p_12
Probability that Pokemon 2 is in a team but Pokemon 2 is not = p_2 - p_12

The above is obvious. Perhaps the following is a little less obvious:

Code:

Probability that Pokemon 1, Pokemon 2 or both are in a team = p_1 + p_2 - p_12

This results from the fact that if the above happens, then either Pokemon 1 is in the team but Pokemon 2 isn't (p_1 - p_12), or Pokemon 2 is in the team but Pokemon 1 isn't (p_2 - p_12) or both Pokemon 1 and Pokemon 2 are in the team (p_12). Adding these all up gives us p_1 + p_2 - p_12.

Hence we can also say that:

Code:

Probability that neither Pokemon 1 nor Pokemon 2 are in a team = 1 + p_12 - p_1 - p_2

This is simply 1 minus the probability that either or both Pokemon 1 and/or Pokemon 2 are in a team.

Finally, we can also find the probability that either Pokemon 1 or Pokemon are in a team, but not both at the same time:

Code:

Probability that either Pokemon 1 or Pokemon 2 are in a team, but not both = p_1 + p_2 - 2 * p_12

This is simply the addition of the two equations that I started with.

Armed with the above equations, I found the probabilities of all the teammate Pokemon that Doug listed in his statistics, for the Standard, Suspect, UU and Uber ladders.

Before the probabilities are given, I also provide the top 100 teammate Pokemon. If Pokemon 1 is used in so many teams, what percentage of these teams also contain Pokemon 2? I provide the highest 100 probabilities for each ladder.

The stats generated by my program are here:

Further Standard Ladder Teammates Information

Further Suspect Ladder Teammates Information

Further UU Ladder Teammates Information

Further Uber Ladder Teammates Information

Hope you find these additional statistics useful.