Number Of Different Teams Possible in PokĂ©mon

PokĂ©mon is endlessly fascinating to me. It has layers of complexity that keep it that keep it both accessible to younger players and interesting for adults. While on a very long and boring plane ride this past week, I got to wondering just how many different PokĂ©mon teams you could make, and the number was paradoxically both bigger and smaller than I thought it'd be.

The question is interesting to me because it reflects the emergent nature of PokĂ©mon. The game itself is superficially simple. Capture creatures, train them, and compete to see who's got the best team. Everyone is limited to a team of six, though and each of those creatures can have up to four moves. That sounds simple, but it turns out that there are billions and billions of ways to arrange your squad.

For my calculations, I took the 719 total number of PokĂ©mon and assumed you wouldn't be using any of them twice. I know some folks do, but I think that would needlessly inflate the final figure. That in mind, I took 719*718*717*716*715*714 to reflect that while your first pick can be any of the 719 possible monsters, your next will have to exclude whomever you picked first.

For moves, I used a bit of statistics so I wouldn't have to look up how many possible moves each and every PokĂ©mon can learn. With a confidence level of 95% and a confidence interval of 20, I found that I'd only need to look up the move pools of 15 monsters. Or, in simpler terms, I'm 95% sure that the averages I found were within 20 of the real value.

Using a random number generator, I was able to calculate the mean and median move pool size, which are 72.5 and 74 respectively. The number of different techniques you could choose for any given PokĂ©mon is, therefore, remarkably consistent. That gives me a lot of confidence in my final results as well.

Taking all of that together, I used combinations to figure up the total. All that really means is that I'm mathematically accounting for the fact that a given PokĂ©mon cannot have two of the same moves, and you can't have two of the same PokĂ©mon in a party. If we were allowing multiple pokemon of the same species, then we'd use 719^6, but since we're using combinations, it is written as (719 choose 6). That's the same as saying 719*718*717*716*715*714, just shorter.