Pokémon
Type Elo

Pokémon Introduction

Pokémon, for those that do not know, are a fictional species of collectible monsters, each having unique designs, skills and powers. Pokémon have one of 18 possible types. Each type has weaknesses, resistances and immunities against the other types. It is essentially like rock, paper, scissors but with 18 possible hand shapes.

Here are a few Pokémon and their types:

Fire

Ground

Psychic

Fire is weak to Water, meaning a Water attack will do double damage to a Fire Pokémon.
Dragon resists Grass, meaning a Grass attack will do half damage to a Dragon Pokémon.
Flying is immune to Ground, meaning a Ground attack will do no damage to a Flying Pokémon.

Elo Introduction

One way to competitively rank similar competitors is by using the Elo rating system. In its most famous incarnation it is used to rank chess players, but it can be used to rank any zero-sum game. We are going to use it to rank Pokémon types. A simple explanation of how Elo works is that winning matches increases your rating, and losing matches decreases your rating. The points you gain or lose depend on the relative rating difference of the opponents.

I like to visualise it in 4 different examples:

• If I am much better than my opponent and I win, I increase my rating, but not by much.
• If I am much worse than my opponent and I win, I increase my rating by a lot.
• If I am much better than my opponent and I lose, I decrease my rating by a lot.
• If I am much worse than my opponent and I lose, I decrease my rating, but not by much.

Pokémon Type Elo

Below is a calculator which can run a simulation of Pokémon type battles. Every type starts out with the same Elo rating, and after every battle the ratings get updated.

Pokémon with Multiple Types

Unfortunately, Pokémon is a bit more complicated than this. Pokémon can have 2 types, which is equivalent to playing rock, paper, scissors with both hands at the same time. This also means both types are factored into the weaknesses, resistances and immunities calculations.

Here are a few Pokémon with multiple types:

Rock

Water

Ghost

Poison

Bug

Flying

Both Fire and Rock are weak to Water, meaning a Water attack will do quadruple damage to a Fire Rock Pokémon.
Both Dragon and Poison resist Grass, meaning a Grass attack will do quarter damage to a Dragon Poison Pokémon.
Fighting resists Dark, and Ghost is weak to Dark, meaning a Dark attack will do neutral damage to a Fighting Ghost Pokémon.

Pokémon Types Elo

Below is a calculator which can run a simulation of Pokémon type battles. It is similar to the previous calculator, except now for every season there are 14,535 distinct battles (compared to 153 battles per season with 1 type).