# Gotta plot ’em all

While surfing the Internet and gasping for tidbits of fun here and there, I stumbled upon this April’s Fool post from my Duke colleagues. Extracting Pokemon data from Bulbapedia, he put together some revealing plots. Motivated by grad school to play quite a bit of Pokemon this last year, I saw more potential and thus decided to totally steal the idea and dig a little deeper.

A Pokemon has 5 stats: HP, Attack, Defense, Special, and Speed. I haven’t learned how to plot 5-D yet, so let’s do a Principal Component analysis to reduce the dimensionality a bit.

The biplot below shows how we reduce Pokemon’s 5 stats into 2 dimensions–principal component 1 (PC1) and PC2. The five red arrows demonstrate how each stat can be expressed in terms of the two PCs.

All 5 stat vectors point to the positive side of PC1 (x-axis), meaning that we can interpret PC1 as a sort of “Overall strength.” On the other hand, Speed/Special (Brain) diverge from HP/Attack/Defense (Brawn) in terms of PC2 (y-axis), meaning that we can interpret PC2 as a measure of emphasis on Brain over Brawn.

A graph to explore the relationship between pokemon stats

Let’s plot all 151 Gen I Pokemon according to these two principal components.

The plot makes sense. Mewtwo is clear outlier in all regards. Notice the next in line in terms of overall strength are the three legendary birds (Zapdos, Moltres, Articuno) and 2 dragons (Gyarados and Dragonite). This graph pretty much validates my all-time favorite team: Arcanine, Snorlax, Articuno, and Hypno.

It’s a bit hard to spot all Pokemon in the cluttered plot above, so here is the same idea disaggregated across types (which helps greatly to pick the best Pokemon within a type). Choosing a Psychic is a tough decision–I have always wavered between Hypno and Kadabra, for the former has less Brain but more solid overall stat.

Grass type clutters tightly at the middle of PC2, meaning that all of them are average in terms of Speed/Special. On the other extreme, Ground is mostly brawn and Psychic mostly brain (no surprise there).

Just to self-congratulate again on a well-picked team, this graph zooms in the Fire type, showing that Arcanine is the best of the lot (not counting the legendary Moltres).