Number Of Different Teams Possible in Pokémon

Pokémon 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 Pokémon 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 Pokémon. 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 Pokémon 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 Pokémon 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 Pokémon 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 Pokémon cannot have two of the same moves, and you can't have two of the same Pokémon 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.

Putting that all together gives us 216,217,804,439,226,231,642. In truth, that number could have been much larger if we accounted for EVs and IVs, held items and the like, they don't change play enough to matter anywhere other than the competitive scene.

So there you have it, 216 quintillion different combinations. On the one hand it seems so unfathomably large that not every possible combination will ever be made. At the same time it seems to limit Pokémon's possibility space. Now I know its limits.

Next time, I promise I won't be talking about a big number. Probably.

You're reading Numbers, a blog on Kotaku that examines games and culture through the lens of math and statistics. To contact the author of this post, write to dancstarkey@gmail.com or find him on Twitter @dcstarkey.