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Pokemon Mechanics and Mathematics

Ever wondered how to get the perfect Pokemon? How much damage your opponent's going to take? Well, this prezi has your definitive answer right here! Watch through, and see how it's done! :D
by

Hollis Pierman

on 14 June 2016

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Transcript of Pokemon Mechanics and Mathematics

By Hollis Pierman
Mechanics that will help you in your Pokemon Journey
Introduction
What are the factors?
Examples
Ever since Pokemon has been invented, one of main reasons why its here has
remained ever since the 1st Generation of games; attack your opponent until
they're KO'ed, earning your Pokemon experience points. How much damage does your opponent need to sustain before it's knocked out? How is every Pokemon that we know of different in its own way? Well, with these simple formula and a simple understanding of middle/high school algebra, you shall know all there is to know about calculating these two vital essentials!
How does it work?!
X_X
All you need is this simple formula for damage:
There are a ton of factors that go into calculating damage.
For example, there's the attacking Pokemon's stat; Attack for Physical moves, and Special Attack for Special moves.
Let's start off with something basic;

Rattata's Tackle against a Pidgey:

Rattata is Level 50 and has: Pidgey is Level 50 and has:
- 118 Attack - 106 Defense
- STAB Bonus
This is:
THE DAMAGE FORMULA and INDIVIDUAL VALUES...
AND HOW THEY COINCIDE!
Damage = ((((2 * Level / 5 + 2) * AttackingStat * AttackPower / DefStat) / 50) + 2 * STAB * Weakness/Resistance * Random# / 100
In Gen III onwards, this is how to calculate damage. This formula is used for EVERY move you use (except for moves that don't do damage, duh).
For one-hit KO moves, there really is no need for calculations; the game says, "Fuck math, now you die!"
DynamicPunch is a Physical move, so which do you think will get factored in, smart one?
Let's take a look at a few examples.
Damage = ((((2 * 50 / 5 + 2) * 118 * 50 / 106) / 50) + 2) * 1.5 * 1 * 85 / 100 = 33 = 22%

Damage = ((((2 * 50 / 5 + 2) * 118 * 50 / 106) / 50) + 2) * 1.5 * 1 * 100 / 100 = 39 = 27%
Individual Value Calculation
INDIVIDUAL VALUES? EXPLAIN!
Individual values, or "IVs" in Pokemon, refer to the fact that
ALL Pokemon are different in one way or another. And this fact holds true; while one Rattata can have higher Attack, one can have higher Speed than the first.
Rattata 1: Rattata 2:
HP: 21 HP: 18
Attack: 13 Attack: 12
Defense: 6 Defense: 7
Sp. Attack: 7 Sp. Attack: 6
Sp. Defense: 8 Sp. Defense: 8
Speed: 9 Speed: 11
As you can see, Rattata 1 has higher Attack, Sp. Attack and HP. However, it has less Defense and Speed. Rattata 2 on the other hand, has higher Defense and Speed. Although Rattata 1 can land decent hits on Rattata 2, Rattata 2 will go first when using Tackle.
The Formula
There are two different IV calculations; one for Health Points, and another for all other stats. Both follow the same format, but use slightly different values at certain points. Here are both formulas:
HP = [IV + (2 * Base) + EV/4 + 100] * Level
-------------------------------------------- + 10
100
Other stat = ([IV + (2 * Base) + EV/4] * Level )
{------------------------------------- +5} * Nature
( 100 )
Since health isn't
affected by nature
boosts, it gets a +10
boost at the end of
the equation.
However, since other stats are affected by a nature boost, they must either be multiplied by 1.1 or 0.9, depending on what the boost or hindrance is.
The end result is that in one hit, Pidgey gets dealt less than a quarter to more than a quarter of its health in one hit, with S.T.A.B.*
* = S.T.A.B. is an acronym for "Same Type Attack Bonus". When a Pokemon uses a move of its own type, that move gets a 1.5x damage boost automatically.
This image depicts the 28 forms of Unown; each one different from the rest. A-Z, and ! and ?
More Examples and Factors
First off, weather is a crucial factor that gives certain moves "buffs"*. Hold items also give off buffs for stats or moves, as well as Abilities. To get a better understanding of all this nonsensical, but yet real gibberish, let's look at a few more examples.
We have left out many factors, and I feel I must mention them.
* = Buffing, in this context, means that you're giving a stat or move type a boost of some sort. "Nerfing" is the polar opposite of this, as it is lowering stats or powering down move types.
VS.
Lucario:
Level 100
Fighting/Steel-type
Aura Sphere (Attack) (S.T.A.B)
- 90 Base Power
- Categorized as "Special"
Life Orb (1.3x)
361 Special Attack
Blissey:
Level 100
714 HP
405 Sp. Defense
Normal-type
Damage = ((((2 * 100 / 5 + 2) * 361 * 117 / 405) / 50) + 2) * 1.5 * 2 * 85 / 100 = 228 (32%)
Damage = ((((2 * 100 / 5 + 2) * 361 * 117 / 405) / 50) + 2) * 1.5 * 2 * 100 / 100 = 268 (37%)
Being that it has the highest Base HP in the game, Blissey will be tough to defeat with just a Lucario, so Special moves are not recommended, but I just wanted to show this to you. Now we'll factor in weather in the next example.
VS.
Floatzel
Level 100
Water-type
339 Attack
Rain in Effect
Waterfall (S.T.A.B.) (Rain Boost)
- 80 Base Power (120 after Rain)
- Physical Move
Entei
Level 100
Fire-type
434 HP
295 Defense
Damage = ((((2 * 100 / 5 + 2) * 339 * 120 / 295) / 50) + 2) * 1.5 * 2 * 85 / 100 = 300 (69%)
Damage = ((((2 * 100 / 5 + 2) * 339 * 120 / 295) / 50) + 2) * 1.5 * 2 * 100 / 100 = 353 (81%)
Definitely an improvement; in the rain, against a Fire-type, Floatzel did a great amount of damage to the legendary dog... or cat... whatever this is based upon! Now that we've taken into account weather, let's take into account Abilities in the next example.
VS.
Porygon-Z
Level 100
Normal-type
405 Special Attack
Tri-Attack
- 80 Base Power
- "Special" Move
- S.T.A.B. Bonus
"Adaptability"* = Ability
Milotic
Level 100
Water-type
394 HP
383 Sp. Defense
Damage = ((((2 * 100 / 5 + 2) * 405 * 80 / 383) / 50) + 2) * 2 * 1 * 85 / 100 = 124 (31%)
Damage = ((((2 * 100 / 5 + 2) * 405 * 80 / 383) / 50) + 2) * 2 * 1 * 100 / 100 = 146 (37%)
Well now, that didn't do very much, did it?
Even though we had a 2x S.T.A.B. bonus,
it still didn't help the fact that Milotic has
amazing bulk, and can take 3 Tri-Attacks,
in order to set up.
Now that we've covered every factor of everything that modifies this equation, we can now put it all together in our grand finale example!
VS.
* = Adaptability is an ability which modifies the user's S.T.A.B., so instead of giving it a 1.5x damage boost, it now doubles the attack power of a move of a corresponding type!
The Pokemon that just so happens to have the eighth-highest Defense rating in the game is Deoxys' Defense Forme, obtainable only in Pokemon LeafGreen, but can be transferred over to future games.
Crawdaunt's Dream World ability just so happens to be Adaptability, which means that makes this finale even more special!
Crawdaunt
Level 100
Water/Dark-type
372 Attack
- Rain is in effect
- Adaptability
- Choice Band*
Crabhammer
- 90 Base Power
- Physical Attack
Deoxys-D
Level 100
Psychic-type
460 Defense
304 HP
Damage = ((((2 * 100 / 5 + 2) * 372 * 180 / 460) / 50) + 2) * 2 * 1 * 85 / 100 = 211 (69%)
Damage = ((((2 * 100 / 5 + 2) * 372 * 180 / 460) / 50) + 2) * 2 * 1 * 100 / 100 = 248 (81%)
Wow! What a close call! Deoxys-D has managed to survive a Crabhammer
with Choice Band, Adaptability, and boosted Rain! Even with the lot of
boosts, this was still not enough to OHKO** the bulky behemoth.
* = Choice Band is an item introduced in the 3rd Generation (Ruby/Sapphire/Emerald). It allows the use of only one move until the user is switched out, but the user's Attack stat is increased by 1.5x (however, I took it into account in the move's power, which is still perfectly legitimate).
** = OHKO is an acronym for the term "one-hit KO". There are certain moves which bypass all mathematics, and automatically lower the opponent's HP in one hit, hence the term one-hit KO. However, this can also to apply for Pokemon who've had massive stat boosts.
In all the excitement while I was writing this, I had completely forgotten about moves that boost stats! So let's do an extra bonus sample where we combine all of the elements, literally!
VS.
Kingler
Level 100
Water-type
788 Attack
-1 Swords Dance boost
-Rain is in effect
-Life Orb
-Sheer Force*
Crabhammer
-90 Base Power
-Physical Attack
* = Sheer Force is an ability introduced in Gen V (Black and White). It boosts moves with secondary effects by 33%, but the move loses its secondary effect (recently, it's been discovered that you could put a Life Orb on a Sheer Force Pokemon, and it will remove the recoil you get from Life Orb).
Regirock
Level 100
Rock-type
548 Defense
364 HP
Passho Berry*
* = Passho Berries were introduced in the 4th Generation (Diamond/Pearl), and they have the ability to absorb the damage of a super-effective Water-type attack by 50%.
Damage = ((((2 * 100 / 5 + 2) * 788 * 164 / 548) / 50) + 2) * 2 * 2 * 85 / 100 = 680 (186%)
Damage = ((((2 * 100 / 5 + 2) * 788 * 164 / 548) / 50) + 2) * 2 * 2 * 100 / 100 = 800 (219%)
We just OHKO'ed one of the most defensive Pokemon in the game! If this were Crawdaunt doing this, it would've been even more humiliating for the Regirock, due to the fact that Crawdaunt has Adaptability, but this is just astounding!
Now that we've REALLY covered every aspect in this, we can now move on to Individual Values, and how they work in their own way.
*EVs, also known as Effort Values or Stat EXP, are numbers that show how much a stat has been improved on. Strategically, it is possible to put only 510 EVs on one Pokemon (508 is a legitimate amount).
Effort Values (a.k.a. EVs)
are still around, just in a completely different way. Here's how EVs work in the games now:
EVs have been around ever since Red/Blue, and
Assuming that your Pokemon has a perfect IV value of 31, every 4 EVs in a stat you gain will raise that stat by 1 point. Strategically, the maximum amount of EVs you can put in one stat is 252. You can then put 252 in another stat, and 4 more for a maximum of 508 EVs, which is the legal amount of EVs to put on a Pokemon (with cheats and hacks, you can put all of a Pokemon's EVs at maximum, and the game will accept it).
Going back to the IV equations, it asks for this variable: EV / 4 (in the equations, it looks like EV over 4). Again, assuming that one stat has perfect 31 IVs, for every 4 EVs you gain, your stat goes up by 1. 252 / 4 = 63, which means now that you add 63 in those equations.
Thanks for watching!
Equations and other information courtesy of:
http://bulbapedia.bulbagarden.net

:D
EXPERIENCE FORMULAS
Pokemon have been gaining experience ever since the mid-90's, and that has never changed. But how can one be so bold as to find out how to find out how experience thresholds work? I will show you why!
First off, you should know that every Pokemon is separated into different experience receptacle thresholds. Each Pokemon experience threshold is separated into how many experience points the Pokemon can earn, from Erratic, to Fluctuating (coincidentally, no Pokemon can have either Erratic or Fluctuating, but it was programmed into Ruby/Sapphire/Emerald). Correction: there are in fact, several Pokemon that have been programmed with Erratic and Fluctuating growth rates.
Here's the formula for Pokemon with Erratic and Fluctuating growth rates on Gogle Docs:

https://docs.google.com/document/d/1RlkOVj-QpuUd64ymiA4JlLy-qh91iHoiZ4Sr7ToFGy8/
(images courtesy of Bulbapedia)
The others are pretty easy to do!

Fast: 4n(cubed)
EXP= -------------
5
Medium Fast: n(cubed)
Medium Slow:

6
EXP = --n(cubed) - 15n(squared) + 100n - 140
5
Slow:
5n(cubed)
EXP = ------------
4
Erratic = 600,000 EXP
Fast = 800,000 EXP
Medium Fast = 1,000,000 EXP
Medium Slow = 1,200,000 EXP
Slow = 1,400,000 EXP
Fluctuating = 1,640,000 EXP
Please consider this: all Pokemon are
different in their own way. Such is with certain Pokemon who can now Mega-Evolve, the process in which a fully-evolved Pokemon can evolve during battle, which gives it a cool new appearance, and boosted stats.
Full transcript