## FANDOM

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This is primarily about spinoffs, not the core Pokémon series and the Dexit controversy. Despite this, I still managed to write a paper.

## The "problem":

Many recent Pokémon spinoffs don't implement the full National Pokédex, but instead, cap things off at the original 151. It's a decent cutoff point, but does it make for an ideal selection of Pokémon?

Well, Kanto has some oddities that might affect the balancing for games that include elements of the battle system. For instance, the Poison type is significantly overrepresented among Pokémon introduced in Gen I, compared to those introduced in other generations.

I could go on like that, and let my anti-Kanto bias seep further into my admittedly cherry-picked arguments…

## …or, I could prove my anti-Kanto bias with math.

Statistically speaking, this selection is "probably not ideal" beyond any shadow of a doubt. There are currently 896 known species of Pokémon. Assuming we keep the roster size at 151, we can perform a combination to find the number of possibilities.

In other words, we want to calculate how many possible Pokédexes we can get by choosing 151 of the 896 Pokémon species. Below is that calculation. It probably goes well off your screen.

${896\choose151}=\frac{896!}{151!(896-151)!}\\=10896424544605561301351266465331910860664204684218050656743381112791385331060482499548324977203374431318152505906985425703059118462226805459792961694373519869191856521764847360$

If my math's correct, the chance that these spinoffs' developers lucked out and got the ideal set of 151 Pokémon is $\approx\frac{1}{10.9*10^{175}}$. That's virtually nothing, and it will decrease further whenever new Pokémon are introduced. Ergo, we should really expect to see Pokémon in the ideal 151 that aren't from Gen I.

We can see evidence for this in practice. While several Kanto Pokémon are considered emblematic of the series or are heavily merchandised, various Pokémon introduced in other regions are comparably popular. Only 5 of the top 30 worldwide results for 2020 Google Pokémon of the Year are from Kanto. Seems like there's room for improvement.

That's all assuming these spinoffs need to be 151 Pokémon strong, when in their respective contexts, the significance of this 151 doesn't apply. It's totally arbitrary. They could include 150, 152, even just 15. Take that, number.

## What is the ideal Pokémon roster, then?

The Pokémon franchise's managers should have data to suggest a better answer than "Gen I", and we probably don't even have all of that data. We also aren't brute-forcing that multiseptenquinquagintillionth. But rather than saying "Who knows for sure?", I figured it'd be more interesting to open this question to all of you, and leave you to your own devices in answering it from here on out.

You can base your list on whatever you want, be it personal taste, other statistics, or whatever other metrics you think would make for a decent ideal (or truth), with any level of research behind it. I don't care. It's a fanon blog comment on a fanon wiki.

You can also choose any reasonable size you want: Operating under the assumption that it's already been decided to use a subset of the National Pokédex, do stay significantly below the full 896. I'd recommend trying to minimize the number of Pokémon while still including enough for some decent variety, but the resulting sizes will vary between people, and you can totally flout the suggestion if you so desire.

Finally, please consider using a format that makes your list convenient to scroll through. With that, I look forward to seeing your results and strategies!

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