Damage Dealt At Level 5 Compared to Damage Dealt At Level 100

[X-Act]

I have a Totodile versus a Bronzor. Suppose I match them up at Level 100. Then I take the same exact Pokemon (same EVs, IVs, natures, etc.) but match them up at Level 5. In which scenario is the most damage dealt if the same moves are used?

The answer is: it depends.

After working it all out (mathematical details are left for a later post if people are interested), this is what I found out:

If the attacking stat of the attacking Pokemon is smaller than or equal to the defensive stat of the Pokemon taking the damage, and the Pokemon taking the damage has 20 HP or more at Level 5, then the Level 5 Pokemon will deal more damage (as a percentage) than the Level 100 version.

If the attacking stat of the attacking Pokemon is larger than or equal to the defensive stat of the Pokemon taking the damage, and the Pokemon taking the damage has 20 HP or less at Level 5, then the Level 5 Pokemon will deal less damage (as a percentage) than the Level 100 version.

If the attacking stat of the attacking Pokemon is equal to the defensive stat of the Pokemon taking the damage, and the Pokemon taking the damage has 20 HP at Level 5, then the Level 5 Pokemon will deal the same amount of damage (as a percentage) that the Level 100 version dealt.

In all other cases, the damage dealt cannot be known so easily.

However, the above sentences can still provide us with interesting conclusions.

The first sentence is basically telling us that if you're dealing damage against a Pokemon with high Defense and HP (i.e. a tank), the damage dealt at Level 5 is greater. This means that tanks are less effective in Little Cup (are dealt more damage) than in the other metagames.

The second sentence is telling us that if you're dealing damage against a Pokemon with low Defense and HP (i.e. you're sweeping), the damage deailt at Level 5 is smaller. This means that sweepers are less effective in Little Cup (deal less damage) than in the other metagames.

So it all kinda balances out in the end!

 

[eric the espeon]

Interesting, I had always wondered about if it was the Level that played a major part in LC being so offensive or if it was just that first stage Pokemon tended to get more aggressive stat spreads. I would love to see the math you used to come up with this, and see how large an affect this has.

 

[X-Act]

I would love to see the math you used to come up with this, and see how large an affect this has.

Okay.

The stat of a Pokemon is

Stat = (2*B + 31 + EV) * Level/100 + X

where B is the Base Stat, EV is the EVs, and X is 10 + Level if the Stat is HP, and 5 otherwise.

This means that the HP stats, at Level 5 and Level 100, are:

HP_5 = (2*B + 31 + EV) / 20 + 15
HP_100 = (2*B + 31 + EV) + 110

This means that

HP_5 = (HP_100 - 110) / 20 + 15
20*HP_5 = (HP_100 - 110) + 300
20*HP_5 = HP_100 + 190
HP_5 = (HP_100 + 190) / 20

For all other stats, we have

Stat_5 = (2*B + 31 + EV) / 20 + 5
Stat_100 = (2*B + 31 + EV) + 5

This means that

Stat_5 = (Stat_100 - 5) / 20 + 5
20*Stat_5 = Stat_100 - 5 + 100
20*Stat_5 = Stat_100 + 95
Stat_5 = (Stat_100 + 95) / 20

Note that the above formulae ignore rounding downs, but that's not very consequential in our arguments.

Now the damage dealt is simplified as

((2*Level / 5) + 2) * A * P / (50 * H * D)

where A is the attack stat, P is the move power, H is the opponent's HP, and D is the opponent's defense stat.

At Level 5, ((2*Level / 5) + 2) simplifies to 4, while at Level 100, it simplifies to 42. Thus:

Damage at Level 5 = 4 * A_5 * P / (50 * H_5 * D_5)
Damage at Level 5 = 0.08 * A_5 * P / (H_5 * D_5)
 
Damage at Level 100 = 42 * A_100 * P / (50 * H_100 * D_100)
Damage at Level 100 = 0.84 * A_100 * P / (H_100 * D_100)
Damage at Level 100 = P * (A_100 / D_100) * (0.84 / H_100)

But by the formulae above, A_5 = (A_100 + 95) / 20, D_5 = (D_100 + 95) / 20 and H_5 = (H_100 + 190) / 20. Hence we have

Damage at Level 5 = 0.08 * ((A_100 + 95) / 20) * P / (((H_100 + 190) / 20) * ((D_100 + 95) / 20)))
Damage at Level 5 = 0.08 * (A_100 + 95) * P / ((H_100 + 190) * ((D_100 + 95) / 20)))
Damage at Level 5 = 0.08 * 20 * (A_100 + 95) * P / ((H_100 + 190) * (D_100 + 95))
Damage at Level 5 = 1.6 * (A_100 + 95) * P / ((H_100 + 190) * (D_100 + 95))
Damage at Level 5 = P * ((A_100 + 95) / (D_100 + 95)) * (1.6 / (H_100 + 190))

So let's start comparing these two formulae:

  Damage at Level 5 = P * ((A_100 + 95) / (D_100 + 95)) * (1.6 / (H_100 + 190))
Damage at Level 100 = P * (A_100 / D_100) * (0.84 / H_100)

Both formulae multiply by P, so the move power neither increase nor decrease the damage.

We now need to ask: when is (A_100 + 95) / (D_100 + 95) greater than A_100 / D_100? The answer is simple: when A_100 < D_100. And if A_100 > D_100, then (A_100 + 95) / (D_100 + 95) would be smaller than A_100 / D_100.

We also ask: when is 1.6 / (H_100 + 190) greater than 0.84 / H_100? The answer is: when H_100 > 210. And if H_100 < 210, 1.6 / (H_100 + 190) would be less than 0.84 / H_100.

So we have that if A_100 < D_100 and H_100 > 210, then the damage at Level 5 is greater than the damage at Level 100, while if A_100 > D_100 and H_100 < 210, the damage at Level 5 is less than the damage at Level 100. Now A_100 < D_100 means that the attacking stat is less than the defensive stat. H_100 < 210 means that the HP stat at Level 100 is less than 210. Since H_5 = (H_100 + 190) / 20, we have that H_100 = 20*H_5 - 190, and hence:

20*H_5 - 190 < 210
20*H_5 < 400
H_5 < 20

so "The HP stat at Level 100 is less than 210" means the same as "The HP stat at Level 5 is less than 20".

That's how I got the arguments in the original post.

 

[sbc]

Very interesting stuff there X-Act, thanks. I'm still surprised that sweepers deal less damage relatively although the changes in base stat due to evolutions may explain this.

 

[little gk]

thanks for this X-Act, i would've never thought sweepers have a harder time here than lv. 100 play

 

[X-Act]

Maybe I didn't put the words correctly. What I meant to say is that if we were only allowed to use Little Cup Pokemon but at Level 100 instead of at Level 5, sweepers would deal more damage but tanks would tank better. Maybe the different Base Stats of the Pokemon used in Little Cup make the metagame more offensive than the Base Stats of the Pokemon used in Standard. I didn't consider this in my arguments at all.