# Quantifying the Change in Damage from Attacking and Defensive EVs

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## Introduction

Every player knows that effort values (EVs) in Attack or Special Attack allow a Pokemon to deal more damage. Likewise, EVs in HP, Defense or Special Defense decrease the damage dealt to that Pokemon.

This article provides an insight into by how much this damage is increased or decreased. We are first going to provide the results immediately. Afterwards, comments on these results are provided, and finally, their derivation is given for those people who would like to know from where the equations were found.

## Results

Providing E EVs to HP, Def or SpD arriving to an HP, Def or SpD stat S after applying the EVs decreases the damage dealt to the Pokemon by 25 × E ÷ S %.

Providing E EVs to Atk or SpA while having an Atk or SpA stat A before applying the EVs increases the damage the Pokemon deals by 25 × E ÷ A %.

If a Pokemon has a nature that boosts Def or SpD, the damage dealt to it is decreased by 9.09%. If a Pokemon has a nature that hinders Def or SpD, the damage dealt to it is increased by 11.11%.

If a Pokemon has a nature that boosts Atk or SpA, the damage it deals is increased by 10%. If a Pokemon has a nature that hinders Atk or SpA, the damage it deals is decreased by 10%.

The important thing to remember is that, for HP, Def and SpD, the stat you need to divide is the one that you would have after applying the EVs, while the stat you need to divide for Atk and SpA is the one you would have before applying the EVs.

Let’s provide an example. Say we have a Heracross that, so far, has no EVs in any stat apart from Speed. That means that its stats are currently:

```HP: 80 × 2 + 141 = 301

Atk: 125 × 2 + 36 = 286

Def: 75 × 2 + 36 = 186

SpA: 40 × 2 + 36 = 116

SpD: 95 × 2 + 36 = 226```

Suppose we give 252 EVs in Attack. The increase in physical damage would be (25 × 252 ÷ 286) % = 22.03%. If Heracross is Adamant, this increase would be larger by 10%, i.e. it would become 22.03 + 2.20 = 24.23%.

Now suppose we decide to give Heracross 252 EVs in SpA to see what happens. The increase in special damage would be (25 × 252 ÷ 116) % = 54.31%. Notice how the SpA stat would increase by a much larger percentage than would the Atk stat given the same EVs. This is because the SpA stat started much smaller than the Atk stat, and hence adding 63 to the SpA stat by giving it 252 EVs results in a much larger percentage increase than that of the Atk stat.

Now let’s give Heracross 252 EVs in HP. The HP stat would become 301 + 63 = 364 after providing the EVs. Hence, the decrease in damage that it would take from both physical and special moves would be (25 × 252 ÷ 364) %, or 17.31%, i.e. Heracross would take 82.69% of the damage it would have taken if it had no EVs in HP.

Giving 252 EVs in Def would make the Def stat 186 + 63 = 249, and hence the decrease in damage that it would take from physical moves would be (25 × 252 ÷ 249) %, or 25.30% (meaning Heracross would take 74.7% of the damage it would take if it had no EVs in HP). This means that if you want Heracross to be more physically defensive, 252 EVs in Def would be better than 252 EVs in HP. However, 252 EVs in HP would be better if you want to protect Heracross from both physical and special moves, as it would provide 17.31% less damage for both, instead of a decrease of 25.3% for physical moves only.

For one final example, giving 252 EVs in SpD, the SpD stat would become 226 + 63 = 289. The decrease in damage that it would take from special moves would be (25 × 252 ÷ 289) % = 21.80%. Furthermore, a boosting nature in SpD would increase this protection even further by 9.09%, which would make the overall decrease in damage 1.0909 × 21.80 = 23.78%.

## Derivations

We’ll start from the derivation for the attacking stats first.

Consider a Pokemon having an attack or special attack stat equal to A, and E EVs are going to be provided to that stat. The damage that would deal with the original stat A is equal to

where P is the move power of the move used and H and D are the HP and Def/SpD stat of the foe respectively. The formula used here is a very good approximation of the damage formula.

After giving E EVs to the attacking stat, it becomes equal to A + (E ÷ 4). Hence, the damage dealt after the EVs are given would be

The difference in damage dealt is

The fraction percentage of this increase in damage with respect to the original damage is

as given in the previous section.

Now let’s work out the percentage change in damage given a boosting or hindering nature. The attacking stat when it is boosted is equal to 1.1 × A. Hence the difference in damage is

The fraction percentage of this increase in damage with respect to the original damage is

as given in the previous section. The case for the hindering nature is treated similarly. Now we tackle the defensive stats, starting from HP.

Consider a Pokemon having an HP stat of H and E EVs are going to be provided to that stat. The damage that would be dealt with the original stat H is equal to

where P is the move power of the move used by the foe, A is the attacking stat of the foe and D is the Def/SpD stat of your Pokemon.

After giving E EVs to the HP stat, it becomes equal to H + (E ÷ 4). Hence, the damage dealt after the EVs are given would be

The difference in damage dealt is

We now consider the underlined part. The least common multiple of the denominators is H × (H + E ÷ 4), so we have the underlined part equal to

Hence the difference in damage dealt is

The fraction percentage of this decrease in damage with respect to the original damage is

But (H + E ÷ 4) is just the HP stat after the EVs are allocated, which we shall call S. Thus we finally have that the decrease in damage is by (25 × E ÷ S) %, as given previously.

The same exact argument can be used when giving EVs to Defense or Special Defense.

Finally we work out the percentage change in damage given a boosting or hindering nature.

The defensive stat when it is boosted is equal to 1.1 × D. Hence the difference in damage is

The fraction percentage of this decrease in damage with respect to the original damage is

as given previously.

For a hindering nature, the defensive stat would be 0.9 × D. Hence the difference in damage is

The fraction percentage of this increase in damage with respect to the original damage is

as given previously.

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