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# Teammates Statistics Further Information (January 2009)

Discussion in 'Pokémetrics' started by X-Act, Feb 8, 2009.

1. ### X-Actnp: Biffy Clyro - Shock Shock

Joined:
Feb 17, 2006
Messages:
4,675
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.
2. ### twash

Joined:
Dec 26, 2007
Messages:
2,342
Oh my god X-Act, this is frickin' awesome. Thank you, so so much.
3. ### MatthewI love weather; Sun for days

Joined:
May 26, 2008
Messages:
4,214
KYOGRE Usage Information
------------------------

Probability of being in a team: 49.90%

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

Joined:
Jan 2, 2009
Messages:
51
Yeah X-Act thats brilliant!.
5. ### IceTime

Joined:
Aug 8, 2008
Messages:
168
cool, X-Act, check out walrein>Abomasnow for size, people!
6. ### RBGTrying to get my Smods back D:

Joined:
Jan 27, 2008
Messages:
3,407
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)
7. ### bobbycat

Joined:
Dec 15, 2008
Messages:
47
Amazing again, X-Act. Thanks.
8. ### MatthewI love weather; Sun for days

Joined:
May 26, 2008
Messages:
4,214
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.
9. ### Aquamentus

Joined:
Jan 13, 2009
Messages:
186
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.
10. ### Shelcario

Joined:
Nov 25, 2007
Messages:
1,421
Another great find/creation by X-Act, well done!
11. ### Vrolok

Joined:
Oct 13, 2007
Messages:
141
Thanks X-Act!
12. ### Thorns

Joined:
Feb 17, 2007
Messages:
4,612
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!
13. ### TheMaskedNitpickerTriple Threat

Joined:
Dec 5, 2007
Messages:
1,031
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.
14. ### TekkenStorm

Joined:
Apr 13, 2008
Messages:
203
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.
15. ### TheMaskedNitpickerTriple Threat

Joined:
Dec 5, 2007
Messages:
1,031
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.
16. ### X-Actnp: Biffy Clyro - Shock Shock

Joined:
Feb 17, 2006
Messages:
4,675
Thanks for spotting this mistake. The files were just updated with the correct fifth line for each block.

I'll think more about this.