Guide: Pokemon Math for Dummies

[Armando]

This is a work in progress. This guide is aimed at the casual player and is meant to help simplify and interpret certain mathematical aspects of the game. All math in Pokemon is simple. If there's something you don't understand, the problem isn't you, it's how I explained things; so don't be afraid to ask questions.

Stat Formulas

Stats are the heart of a Pokemon; to understand a given Pokemon's potential and compare it to others, you need to understand how stats work. All stats other than HP are calculated using the same formula. The formulas for Pokemon of any level are:

HP = Level + 10 + [Base HP * 2 + IV + (EVs/4)] * Level/100
Other Stats = [5 + [Base Stat * 2 + IV + (EVs/4)] * Level /100] * Nature

For level 100 Pokemon, the formulas simplify to:
HP = 110 + Base HP * 2 + HP IV + (HP EVs/4)
Other Stats = [5 + Base Stat * 2 + IV + (EVs/4)] * Nature

Where
* (EVs/4) should always be rounded down
* Nature is 1.1 for a beneficial nature, 0.9 for a negative nature and 1 otherwise
* The end result should always be rounded down if you get a decimal

We can observe a couple of things from these formulas: for starters, a Pokemon's Base Stats contribute twice their value to your Pokemon's stats at level 100. So if one Pokemon has 80 Base Special Defense and another has 100 Base Special Defense, their actual Special Defense stats differ by 40 points, not 20. We also see that IVs contribute exactly their value, and every 4 EVs contribute 1 point. Since IVs range from 0 to 31 and you can have up to 255 EVs in a single stat, IVs and EVs contribute up to 31 and 63 points respectively.

It's also important to realize that because of the constants in the formulas and the IVs, a Pokemon with 50 Base Stat does NOT end up with half the stats as a Pokemon with 100 Base Stat even if they have 0 EVs; it ends up with more than half. This is especially true for HP, which has a very large constant in the equation.

For more information: Stats in DP (D/P) - Smogon University

The Damage Formula

The game's damage formula is a bit long and cumbersome, but if we ignore a small constant and do a little bit of algebra, we get a much simpler formula that approximates the real thing closely. Additionally, by dividing the damage formula by the opponent's HP, we obtain the % of HP the opponent loses, which is a much more meaningful number than the damage alone. Doing both of these things we get:

HP% Lost = (Base Power * Attack)/(HP * Defense) * (Level/125 + 0.04) * Random

Since the formula depends on the attacker's level, a Level 20 Pokemon always does less damage than a level 30 Pokemon even if they have identical stats and moves.

When the attacker is level 100, the formula simplifies to:
HP% Lost = (Base Power * Attack)/(HP * Defense) * 0.84 * Random

Where
* Base Power is the power of the attack used, and is multiplied by x1.5 if the attack's Type matches either Type of the attacker. This bonus is called STAB - Same Type Attack Bonus
* Special Attack and Special Defense are used instead of Attack and Defense when using special attacks
* Random is a random number between 0.85 and 1 inclusive, with a mean of 0.92.

By substituting these values of Random into the formula above, we get these three variations of the formula:
Minimum HP% Lost = (Base Power * Attack)/(HP * Defense) * 0.714
Average HP% Lost = (Base Power * Attack)/(HP * Defense) * 0.7728
Maximum HP% Lost = (Base Power * Attack)/(HP * Defense) * 0.84

Taking a close look at the formulas reveals that that your damage is directly proportional to the two stats in the numerator (Base Power and Attack) and inversely proportional to the two stats in the denominator (opponent's HP and Defense.) So boosting your Attack by X% you'll also boost your damage by that much, and if the opponent boosts his defense by X% then your damage is reduced by 1/X%.

An equally useful detail is the fact that the (Base Power * Attack) and (HP * Defense) products give us a way to directly compare the damage and ability to take hits of different Pokemon. For example, if we have these Pokemon:

Pokemon 1
HP = 300
Defense = 250

Pokemon 2
HP = 200
Defense = 400

Then Pokemon 1's HP * Defense = 75k and Pokemon 2's HP * Defense = 80k, revealing that Pokemon 2 is better at taking physical hits; in fact, Pokemon 1 takes 80/75 = 1.06667 = 6.667% more damage. The same calculations could be repeated with their Special Defenses to find which one is better at taking Special hits. When investing EVs into defenses, you'll generally want to maximize your HP * Defense, and this is accomplished by boosting the lower of the two stats. However, sometimes it's worth investing points in HP even when it's higher than your Defenses; your EVs are limited, and boosting HP reduces damage from both physical and special hits simultaneously.

For more information see: The Complete Damage Formula for Diamond & Pearl (D/P) - Smogon University

Stat Boosts and Drops

Stat boosts are yet another critical gameplay element that every serious trainer must understand. Sweepers usually need Attack and/or Speed boosts to do their jobs, and some tanks and walls boost their defenses to take hits better; it's obvious that knowing how each stat change increases or decreases stats is useful. The main 5 combat stats (Attack, Defense, Special Attack, Special Defense, and Speed) all behave the same way when it comes to boosts and drops:

Attack, Defense, Special Attack, Special Defense, Speed
Level......Multiplier
+6........Stat * 8/2 (4)
+5........Stat * 7/2 (3.5)
+4........Stat * 6/2 (3)
+3........Stat * 5/2 (2.5)
+2........Stat * 4/2 (2)
+1........Stat * 3/2 (1.5)
±0........Stat * 2/2 (1)
-1.........Stat * 2/3 (0.6667)
-2.........Stat * 2/4 (0.5)
-3.........Stat * 2/5 (0.4)
-4.........Stat * 2/6 (0.3333)
-5.........Stat * 2/7 (0.2857)
-6.........Stat * 2/8 (0.25)

In-game, when a stat increases or decreases by 1 level, the game simply reports that the stat rose or dropped. When a stat increases or decreases by 2 levels, the game reports that it rose sharply or dropped sharply.

For positive stat levels, each level represent a 50% increase. This means that Swords Dance (+2 Attack) and Nasty Plot (+2 Special Attack) double your physical or special damage, while Dragon Dance (+1 Attack and Speed) boosts your damage and speed by 50%. The value of these moves suddenly becomes obvious; in a single turn, the user becomes a serious threat.

Notice, also, that the positive boosts are the reciprocal (the inverse fraction) of the negative ones. Since the damage formula involves multiplying by Attack and dividing by Defense, then -1 Attack has the same effect on damage as +1 Defense, and vice-versa. I.e. -1 Attack means your damage is multiplied by 2/3, while +1 Defense means your damage is divided by 3/2 which is the same as multiplying by 2/3. Likewise -1 Defense means dividing by 2/3, which is the same as multiplying by 3/2, which is what boosting Attack 1 level would do. This is why Intimidate is such a powerful ability; since it drops the opponent's Attack by 1 level when your Pokemon switches in, it's as if your Pokemon has 50% more Defense until the opponent switches.

Although seldom used (due to the ban on Double Team and Sand Attack variants), Accuracy and Evasion can also be increased and decreased, though their boosts and drops are a bit different from the other 5 stats'.

Accuracy
Level......Multiplier
+6........(Move Accuracy) * 9/3 (3)
+5........(Move Accuracy) * 8/3 (2.6666)
+4........(Move Accuracy) * 7/3 (2.3333)
+3........(Move Accuracy) * 6/3 (2)
+2........(Move Accuracy) * 5/3 (1.6666)
+1........(Move Accuracy) * 4/3 (1.3333)
±0........(Move Accuracy) * 3/3 (1)
-1.........(Move Accuracy) * 3/4 (0.75)
-2.........(Move Accuracy) * 3/5 (0.6)
-3.........(Move Accuracy) * 3/6 (0.5)
-4.........(Move Accuracy) * 3/7 (0.4285)
-5.........(Move Accuracy) * 3/8 (0.375)
-6.........(Move Accuracy) * 3/9 (0.3333)

Evasion
Level......Multiplier
+6........(Move Accuracy) * 3/9 (0.3333)
+5........(Move Accuracy) * 3/8 (0.375)
+4........(Move Accuracy) * 3/7 (0.4285)
+3........(Move Accuracy) * 3/6 (0.5)
+2........(Move Accuracy) * 3/5 (0.6)
+1........(Move Accuracy) * 3/4 (0.75)
±0........(Move Accuracy) * 3/3 (1)
-1.........(Move Accuracy) * 4/3 (1.3333)
-2.........(Move Accuracy) * 5/3 (1.6666)
-3.........(Move Accuracy) * 6/3 (2)
-4.........(Move Accuracy) * 7/3 (2.3333)
-5.........(Move Accuracy) * 8/3 (2.6666)
-6.........(Move Accuracy) * 9/3 (3)

Note that being at +1 Evasion drops the attacker's chance to hit by 25%. Two stages will drop it by 40%. This, coupled with the fact that almost every single Pokemon can learn Double Team, and the fact that Whirlwind and Roar (the main ways of forcing your opponent to lose his stat boosts) can miss, are the main reason Double Team and Sand Attack variants are banned from competitive play.

The most noteworthy use of an Evasion modifier in competitive play is the move Gravity, which besides rendering Flying and Levitate Pokemon vulnerable to Ground moves, also reduces everyone's Evasion by 2 stages as long as Gravity is in effect, meaning that all attacks are 66.666% more accurate. This means that any move with 60% Accuracy or better becomes 100% accurate, while 50% Accuracy moves become 0.5 * 5/2 = 83.333% accurate.

For more information see: Stats in DP (D/P) - Smogon University

Status Ailments

Status ailments in Pokemon are very potent and can change the flow of battle drastically. However, a Pokemon can only be afflicted by 1 status ailment; any attempts at inflicting a new one or reapplying the old one will fail. Click here for the list of all true status ailments and what they do.

Dealing with Status ailments

There are a couple of different ways of dealing with status ailments. The most basic way is to predict a status and switch in something that's either immune or doesn't mind being afflicted. Besides the type immunities listed above, some abilities also provide immunities or even advantages when afflicted. For example, Will-O-Wisp will trigger Flash Fire, and Thunder Wave will trigger Volt Absorb and Motor Drive. Pokemon with Guts can switch into Will-O-Wisp and get a free Attack boost. Pokemon with Synchronize will automatically inflict aggressors with any status ailments they receive, which can be extremely useful when the opponent's trying to put you to sleep. Pokemon that already have a status ailment (including Rest's self-inflicted sleep) can also be used to block status attempts.

If you don't have Pokemon that are immune or gain an advantage from switching into a specific status, you can switch in something that isn't hurt that much by it. Pokemon with Natural Cure, Rest or Refresh can rid themselves of status ailments one way or another, so they can afford to take one for the team. Special Attackers don't mind being burned nearly as much as other Pokemon, since they don't lose their offense. Slow Pokemon don't mind Paralysis as much as others. RestTalkers (Pokemon that use Rest + Sleep Talk) can switch into Sleep without being helpless. In the absence of that option, the opponent is only entitled to sleeping 1 of your Pokemon, so if you suspect a Hypnosis or Sleep Powder, you can switch in something that you can afford to have sleeping - usually a tank or wall that can last enough turns to wake up and can still sponge hits for others while it sleeps.

Another approach is to have a Pokemon with Heal Bell or Aromatherapy; these moves cure your entire team of status ailments. With a cleric on your team, even if one or more of your Pokemon is severely crippled, you can salvage the situation. Common clerics include Miltank, Blissey, event Dragonite, Shaymin, and the Eevee evolutions.

There is one other reliable way of protecting against status ailments - holding a Lum Berry. This berry will automatically heal the first status ailment that Pokemon is afflicted with. The opportunity cost of using this is very high, since you forego other terribly useful items to protect against something the opponent might not use against you. However, it can be useful for some leads that have most of their bases covered but can be crippled by faster leads with status ailments (usually Sleep.) It's also very rarely used to get a one-time full heal out of Rest, since the berry will cure Rest's sleep instantly.

Pseudo-Status

These don't count as status ailments (they can exist alongside a true status ailment) but are still adverse effects. Any lingering pseudo-status is cured if the Pokemon switches, much like stat changes.

Confusion
When a Pokemon is affected by Confusion, there's a 50% chance that when it tries to attack, it'll hit itself with a 40 Base Power typeless physical move instead. This can be very painful when used against a Pokemon with high Attack and low Defense, especially if its Attack has been boosted. Confusion lasts 2-5 turns as measured by the number of times the message "[Pokémon] is confused!" Confusion is sometimes used in conjunction with Paralysis in order to reduce the chances of the opponent attacking successfully to 37.5%, a strategy referred to as Parafusion. The most common way of inflicting confusion is the move Confuse Ray.

Flinching
When a Pokemon flinches, it fails to attack that turn. Flinching can only happen if the defender is hit by a move that can cause flinching before it has a chance to attack. Because of this, Paralyzing your enemies is important when abusing Air Slash with Togekiss or Iron Head with Jirachi.

Infatuation
When a Pokemon is infatuated, there's a 50% chance it'll be too infatuated with the enemy to attack. Infatuation lasts for as long as both Pokemon remain on the field. Infatuation only works against Pokemon of the opposite gender, and doesn't work on genderless Pokemon. These drawbacks, combined with the lack of self-damage, makes infatuation very impractical.

Leech Seed
Pokemon affected by Leech Seed have 1/8th (12.5%) of their max HP drained by their opponent at the end of each turn. Since the amount of HP drained depends on the target, not the user, seeding high HP enemies is very advantageous. Leech Seed will stay in play even if the user switches (though it does disappear if the target switches, as usual.) Leech Seed doesn't work on Grass Pokemon, and seeding Pokemon with the ability Liquid Ooze will cause you to lose HP instead of drain it.

Taunt
Prevents the target to use damaging moves for 3-5 turns. Useful for preventing Pokemon from using support moves or stat boosts, and prevent walls from recovering.

Torment
Prevents the target from using the move it used on the previous turn. When used against Choice users, they will be forced to use Struggle every other move.

Mean Look
Prevents the foe from switching through means other than Baton Pass or U-Turn. The effect ends if the user switches; however, this effect can be Baton Passed so the user can switch while keeping the foe trapped. If the foe uses Baton Pass to escape, the Pokemon it switches to will be trapped instead.

Encore
The foe automatically repeats the last selected move for 4-8 turns as long as they choose not to switch. Used to render the opponent defenseless and force switches, especially when it's forced to repeat a non-damaging move.

Trapping attacks: Whirlpool, Fire Spin, Magma Storm, Sand Tomb, Bind, Clamp, Wrap
Besides the damage of the attack, these moves prevent the opponent from switching for 2-5 turns, dealing 1/16th of their max HP in damage at the end of each turn that they remain trapped. Effect ends if the user switches out.

Curse (when used by Ghosts)
User sacrifices 50% of their max HP to curse the target. Target loses 25% of their max HP at the end of each turn until they switch out or die.

Disable
Prevents the target from using the last move it used prior to being hit by Disable for 4-7 turns. Only 1 move can be disabled per opponent.

For more information see: Status in DP (D/P) - Smogon University

Scouting - Winning the information war

In every battle, your opponent possesses a few key Pokemon that will prevent you from executing your winning strategy. For example, you won't be able to sweep with a Nasty Plot Azelf as long as the opponent has a Blissey in good health; there are very few special attackers with the power to eliminate Blissey. If the opponent becomes aware of your Azelf's existence and conceals his Blissey, it's possible that you'll sacrifice all your physical attackers throughout the course of the fight. Once that happens, it's very likely that you won't be able to win. Evidently, the less you know about your opponent's team, the more vulnerable you are to being put in a checkmate. Even if you can avoid this, lack of knowledge about your opponent's team can force you to switch if you mispredict an attack, especially if you're using a Choice Scarf/Specs/Band Pokemon. Not only is giving your opponent a free turn to set up costly, frequent switching will quickly rack up damage from Stealth Rock and Spikes. This section of the guide explains how certain moves can be used to "scout" the opponent's team safely (note that many of these moves have other uses as well.)

Baton Pass and U-Turn
Both of these moves allow you to switch out to another Pokemon. What makes them valuable for scouting is the fact that if the opponent decides to switch on the same turn you use either of these, the opponent switches first, and then, after having seen what he chose, you switch. This allows you to check what counter your opponent has for your Pokemon while being able to switch to something that'll scare the counter away, potentially revealing another of your opponent's Pokemon and buying yourself a free turn. For example, suppose your opponent has Swampert out. You predict an Earthquake and switch to Azelf, who's not only immune, it outspeeds Swampert and can easily OHKO with Grass Knot. Obviously the opponent will switch to something that can handle Azelf, so you U-Turn.

Substitute
By creating a Substitute when the opponent switches, you're protected for at least 1 turn from whatever your opponent sends; it virtually impossible for the opponent to KO you. Additionally, the substitute will block any attempts to reduce your stats (such as Intimidate) or inflict status ailments. Even if you still find yourself in a bad match-up, you're still guaranteed 1 shot at your opponent and can safely take one of its attacks, giving you insight about its move set. Additionally, if you have Baton Pass you can switch out of bad match-ups safely. If your Baton Pass goes second,the Substitute simply takes the hit and your next Pokemon switches in scott-free. If the Baton Pass goes first, you still pass the sub, but if you predict the opponent's attack correctly there's the possibility that the sub won't break and your next Pokemon will be able to hide behind it. Recycling the previous example above: suppose you have Jolteon out and create a subsitute while the opponent switches in Swampert. Jolteon Baton Passes the Substitute to Azelf. If Swampert chose to use Earthquake, Azelf will switch in with substitute intact, giving it 2 free turns instead of 1 (one while the opponent switches, and another while the get rid of your sub.) Even if Swampert doesn't fall for the bait and uses Surf or Stone Edge, the substitute will take the hit for Azelf and he'll still get in safely.

Protect
Although it's seldom used alone (it's usually used in conjunction with Wish), Protect allows you to scout the opponent's moves very similarly to Substitute - it allows you to protect yourself against the opponent's attack, giving you a good idea of what the opponent's got at his disposal. However, you must exercise caution when using Protect: if the opponent predicts that you'll use it, he gets a free turn to switch or set up. This is especially problematic when using the Wish+Protect combo.

Roar and Whirlwind
These moves are identical except for the fact that Roar doesn't work against Soundproof Pokemon. They always go after other attacks (even Focus Punch) and force the opponent to switch to a random Pokemon. They're mainly used to force the opponent to lose its stat boosts or to rack up Stealth Rock/Spikes/Toxic Spikes damage. Since the opponent's next Pokemon is chosen randomly, these moves can reveal Pokemon the opponent had been concealing.

Further reading: Articles (D/P) - Smogon University
I highly recommend these:
Introduction to Competitive Pokémon
Move Priority
Deconstructing: A Guide to Wallbreaking
Opening the Door: A Guide to Entry Hazards
Providing Team Support
Overused Speed Tiers
Underused Speed Tiers

Credits: Most of this info is basically Sparknotes versions of the far, far more thorough articles in Smogon.com.

[DakAttack]

Re: Guide: Pokemon Math for Dummies

Which name do you like better: Mathmando, or Armathdo?

[Feba]

Re: Guide: Pokemon Math for Dummies

definitely Armathdo, flows better, less obvious at first glance.





Yes, I just decided for him.

[Armando]

Re: Guide: Pokemon Math for Dummies

I agree, I prefer Armathdo.

Revamped the first 3 sections and added a section on status ailments.

[Feba]

Re: Guide: Pokemon Math for Dummies

I agree

YOU'D BETTER.

[Van'derfel]

Re: Guide: Pokemon Math for Dummies

Do you really need math in Pokemon though? I always just go with "RAWR overpowered Charzard kill!"

[Armando]

Re: Guide: Pokemon Math for Dummies

If you're just going to play against NPCs, no.

If you're going to play against other people, the more you know, the better you'll do. Same thing applies to pretty much any multiplayer game, really.

[Armando]

Re: Guide: Pokemon Math for Dummies

Bump. Added a bit more info about dealing with status ailments, a section on scouting, and other useful guides.
EDIT: Expanded the list of pseudo-status ailments.

[Rostum]

Re: Guide: Pokemon Math for Dummies

Thanks Armando! I'm still just playing through the game battling gym's and stuff at the moment, but this will come in handy once I start battling other people.

[Armando]

Re: Guide: Pokemon Math for Dummies

No prob :D