Teammates Statistics Further Information (January 2009)
 

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:

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

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:

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:

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.

Oh my god X-Act, this is frickin' awesome. Thank you, so so much.

KYOGRE Usage Information
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Probability of being in a team: 49.90%

I was almost positive there is a Kyogre in every match.

Yeah X-Act thats brilliant!.

cool, X-Act, check out walrein>Abomasnow for size, people!

except there are 2 teams each match. In order for it to be 100%, it would have to be on every team (like arceus will be when it comes out)

Amazing again, X-Act. Thanks.

Oh, I read that wrong, my bad.

Bah, I honestly don't think I'd make room on my team for Arceus, but I could make him whatever I want, those 120 stats don't lie.

46% of teams with a Skarmory also have a Blissey. Heh, I bet that used to be a lot higher in the older generations.

As is tradition to say, awesome job X-Act.

Another great find/creation by X-Act, well done!

Thanks X-Act!

can we stop the 'thanks x-act!' cause they are just pc+ posts.

this info is useful for seeing what combinations of pokemon people use in their teams. I've actually found some new cool combos with that information!

This is a really cool resource, but the fifth line of each block of stats is inaccurate. Instead of p_2 – p_12, you accidentally used 2 * p_2 – p_12. Example:

What I'd really be interested in seeing is some measure of correlation between the usages of two Pokémon. For instance, if p_1 and p_2 were independent, the probability that both Pokémon would be on a team together would be p_1 * p_2 = p'_12. I'd like to see the relationship between the actual p_12 and p'_12. If p_12 is higher, the two Pokémon are often used together, whereas if p'_12 is higher, they are seldom used together.

Seems like im the only one using a Smeargle+Medicham combination :/

I swept many teams with it and it isn't that hard to setup, even though Scizor can cause some problems with bulletpunch.

Actually, considering neither Smeargle (2.77%) or Medicham (1.06%) are used all that often, the two are used together quite a bit. p_12 / p'_12 = 6.33.

For comparison, the same formula for :

Walrein and Abomasnow : 41.4 (Paired incredibly often)
Skarmory and Blissey : 2.89 (Paired quite often)
Celebi and Heatran : 1.80 (Paired pretty often)
Gengar and Salamence : 1.06 (Almost unrelated)
Salamence and Dragonite : 0.369 (Not often paired ; the two are redundant)
Ludicolo and Infernape : 0.163 (Rarely paired ; they work at cross purposes)

A value greater than 1 means that the two are used on teams together more than average, whereas a value of less than 1 means they're used on teams together less than average.

Thanks for spotting this mistake. The files were just updated with the correct fifth line for each block.

I'll think more about this.