why torkoal is a nuke

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In competitive Pokémon (VGC double battles), the fire tortoise Torkoal is generally considered to be a nuke when positioned properly.

But looking at its base stats, it really doesn't seem like it should be.

Torkoal is a special attacker, which just means it uses its special attack (Sp. Atk) stat to do damage. At a measly 85 base Sp. Atk, Torkoal is significantly outclassed by new-gen special attackers like Flutter Mane (135 base Sp. Atk) and Gholdengo (133 base Sp. Atk). It even has less base Sp. Atk than Indeedee-F (95 base Sp. Atk), a support Pokémon not known for doing all that much damage, and Gastly (100 base Sp. Atk), an unevolved Pokémon from Generation I.

is Torkoal's Sp. Atk really that bad?

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But, okay, maybe base stats aren't everything. After all, training your Pokémon is the whole point, and maybe the best training ever can help Torkoal overcome Flutter Mane's 50 point lead.

Here's how Pokémon games actually calculate damage:

$$\text{damage} = \underbrace{(\text{stat} \times \text{base power} + 2)}_{\text{base damage}} \times \text{spread penalty}\times \text{multipliers} \times \text{type effectiveness}.$$

Type matchups depend on the particular Pokémon involved, so $\text{type effectiveness}$ is a little less relevant to understanding why Torkoal does so much damage in general. We'll ignore it for the rest of this post for the sake of brevity.

Now, the parameter $\text{stat}$ is the part of the damage that depends on a Pokémon's stats, defined by

$$\text{stat} = \dfrac{2\times \text{level} +10}{250} \times \dfrac{\text{attack}}{\text{defense}}.$$

The $\text{attack}$ and $\text{defense}$ are the effective attacking and defending stats of the Pokémon involved. These effective stats depend on a Pokémon's base stats, level, and training. In our case, since Torkoal is a special attacker, $\text{attack}$ is Torkoal's effective Sp. Atk stat, and $\text{defense}$ is the effective Sp. Def stat of the defending Pokémon.

Competitive Pokémon battles take place at level 50, and at this level, maximal special attack training gets Torkoal to an effective Sp. Atk of 150. Unfortunately for Torkoal, even a Flutter Mane with no special attack investment will have an effective Sp. Atk stat of 155.¹ In practice, a Flutter Mane wanting to do damage will maximize special attack for an effective Sp. Atk of 205.

What does this mean for damage? A maximally-invested Torkoal gets a $\text{stat}$ of

$$\text{stat} = \dfrac{2\times 50 +10}{250} \times \dfrac{150}{\text{defense}} = \dfrac{66}{\text{defense}}.$$

Compare that to a maximally-invested Flutter Mane, who gets

$$\text{stat} = \dfrac{2\times 50 +10}{250} \times \dfrac{205}{\text{defense}} = \dfrac{90.2}{\text{defense}}.$$

On base stats alone, Flutter Mane is doing ~35% more damage than Torkoal. How can Torkoal ever keep up?

Eruption is kinda broken

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The first of Torkoal's unique gifts is the move Eruption. It is a Fire-type spread move (hits both Pokémon on the opposing side of the field) and has a huge base power of 150…with a catch, which we'll cover later.

This really is huge. Most consistent (i.e. not wildly inaccurate) single-target moves have base power 80-100, with spread moves often being weaker than that. For example, Flutter Mane's highest base power move is usually the single-target move Moonblast, which has 95 base power.² Its highest power spread move is Dazzling Gleam, which is about half as strong as Eruption at 80 base power.

In fact, the absurd base power of Eruption helps narrow the gap between Torkoal and the rest of the field. Recalling our $\text{stat}$ values from earlier, we can see that Torkoal using Eruption has a $\text{base damage}$ of

$$\text{base damage} = \text{stat}\times \text{base power} +2 = \dfrac{66}{\text{defense}}\times 150 +2 = \dfrac{9900}{\text{defense}} + 2.$$

For Flutter Mane using Moonblast, we have

$$\text{base damage}= \dfrac{90.2}{\text{defense}} \times 95 + 2 =\dfrac{8569}{\text{defense}}+2$$

and when using Dazzling Gleam,

$$\text{base damage} = \dfrac{90.2}{\text{defense}}\times 80 + 2 = \dfrac{7216}{\text{defense}} + 2.$$

It seems like Torkoal's knocking it out of the park now, but there is one additional thing we have to consider: the $\text{spread penalty}$. When calculating the damage each opposing Pokémon takes, spread moves get a 0.75x penalty, while single-target moves get a 1x, unaffected. Therefore, Torkoal is dealing

$$\text{base damage} \times \text{spread penalty} = \left(\dfrac{9900}{\text{defense}}+2\right)\times 0.75 = \dfrac{7425}{\text{defense}}+1.5$$

to each opposing Pokémon with Eruption, and Flutter Mane is dealing

$$\text{base damage} \times \text{spread penalty} = \left(\dfrac{7216}{\text{defense}}+2\right)\times 0.75 = \dfrac{5412}{\text{defense}}+1.5$$

to each opposing Pokémon with Dazzling Gleam.

Now it's clear—Torkoal is actually knocking it out of the park with Eruption, doing something like ~30-35% more damage compared to Flutter Mane's Dazzling Gleam.³

In addition, even though Torkoal's Eruption does slightly less damage to each individual Pokémon compared to Flutter Mane's Moonblast, we have to keep in mind that Torkoal is doing that damage to both opposing Pokémon. This loosely doubles the damage output. Torkoal then outdamages Flutter Mane by ~70%.

But now for the catch: Eruption's base power is that huge 150 only when Torkoal is at full HP; the lower Torkoal's HP is, the lower the base power of the move. This is a huge catch, of course, but Torkoal is still a nuke, it just needs to be positioned properly.

multipliers are also pretty broken

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But ultimately, Torkoal only deals huge damage because of how multipliers scale. Multipliers are exactly what they sound like—other conditions that scale the damage a Pokémon does. There are many of them, and the most common ones include

• STAB (Same-Type Attack Bonus): 1.5x if the Pokémon shares a type with the move it's using.
• Item: Power-boosting items usually give boosts in the range of 1.2-1.5x, with higher power items coming with some kind of cost.
• Weather: In sun, Fire-type moves get a 1.5x multiplier, while Water-type moves get a 0.5x multiplier. Vice versa in the rain.

Torkoal uses all three of these to great effect. As a Fire-type, it gets a 1.5x STAB boost to the Fire-type move Eruption. It almost always runs a power-boosting item like Charcoal(1.2x for Fire moves) or Choice Specs (1.5x). With its ability Drought, it automatically sets up the sun for another 1.5x boost.

Damage boosts from STAB and item choice are available to virtually all Pokémon, but a weather-setting ability is far harder to come by. In fact, of the 500 or so fully evolved Pokémon that exist as of Generation IX, only 4 of them have access to the ability Drought. But it's precisely Drought that pushes Torkoal over the edge. Without it, Torkoal gets

$$(1.5{\small\times} \text{ from STAB}) \times (\text{1.2-1.5}{\small\times} \text{ from item}) = \text{1.8-2.25}{\small\times} \text{ total},$$

which is respectable. But with the sun boost, Torkoal gets

$$(1.5{\small\times} \text{ from STAB}) \times (\text{1.2-1.5}{\small\times} \text{ from item}) \times (1.5 {\small\times}\text{ from sun})= \text{2.7-3.375}{\small\times} \text{ total}.$$

Because multipliers scale, well, multiplicatively, Drought takes Torkoal from doing double damage to doing triple damage. This is massive, given that Torkoal was already doing a respectable amount of damage due to the base power of Eruption.

tl;dr

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How much damage a Pokémon does is largely determined by three things:

1. its stats,
2. the base power of the moves it uses, and
3. applicable multipliers.

While Torkoal is cooked in the stats department, the high base power of Eruption and its access to an extra multiplier through Drought make up for it.

appendix

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There are things I did not mention here for simplicity. For example, the fact that Fire is a good offensive type is surely paramount to Torkoal's viability—I can't imagine Torkoal doing much damage if Eruption was a Bug-type move (even if Torkoal was a Bug-tortoise and sun was, I don't know, spider ballooning or something). I also didn't mention Terastallization, which is another multiplier Torkoal likes to use.

footnotes

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1. Technically, you can get Flutter Mane to have a lower special attack stat of 137 by using a hindering nature, but you would never do this in practice. ↩

2. quite high for a move that doesn't miss! ↩

3. The exact number here depends on the defense stat of the defending Pokémon, because of the linear +1.5 term. I've gone with 100-200 as a reasonable range for the defending Pokémon's effective Sp. Def stat. ↩