Combat

Combat runs in real time, not in turns. Every hit in the game — hunting, delves and duels alike — goes through the one formula below, so what you read here is what the server does.

The damage formula

Attack is the attacker's Attack for a physical move and Sp. Attack for a special one; Defense is the defender's matching stat.

ratio  = (Attack ÷ Defense) ^ 1.0 × (stages) ^ 0.4
base   = floor((2 × Level ÷ 5 + 2) × Power × ratio ÷ 50 + 2)
damage = round(base × STAB × Type × Random × 0.34)

Attack: Your effective Attack or Sp. Attack, after IVs, quality, nature and stages.
Defense: The defender's matching defensive stat, computed the same way.
Power: The move's base power, listed on every move's row in the Moves page.
STAB: Same-type attack bonus — applied when the move's type is one of the attacker's own.
Type: Type effectiveness against the defender's type or types.
Random: A small random roll, rolled fresh on every single hit.

The exponent 1.0 on the ratio is the part most people miss: your Attack does not enter the formula directly, its ratio against the defender's Defense does — and that ratio is square-rooted. Doubling your Attack does not double your damage.

What your Attack is actually worth

Hyper Beam (power 450), thrown by a level 50 attacker at a defender with 100 Defense, before any type bonus. Only the attacking stat changes down the table.

Attack	Damage	vs. reference
60	38	×0.47
80	50	×0.62
100	63	×0.78
130	81	×1
160	100	×1.23
200	125	×1.54

Notice the shape: the damage climbs, but far more slowly than the stat does. Because of the 1.0 exponent, multiplying your Attack by four is what it takes to double the damage — which is why type matchups and stacking a buff usually beat chasing raw Attack.

…and what the defender's Defense does

The same hit at 130 Attack, with the defender's Defense swept instead.

Defense	Damage	vs. reference
60	136	×1.68
80	102	×1.26
100	81	×1
130	63	×0.78
160	51	×0.63
200	41	×0.51

What multiplies the result

These stack on top of the number the formula produced — 81 for the reference hit above. They are where the big swings live.

Modifier	Multiplier	When it applies
STAB	×1.51	The move's type is also one of the attacker's types.
Type effectiveness	×0 · ×0.25 · ×0.5 · ×1 · ×2 · ×4	From the type chart. A dual-typed defender multiplies both of its types, which is where 4× and 0.25× come from.
Critical hit	×1.5	About 6% of hits, higher on high-crit moves. A crit also ignores the attacker's own negative stages and the defender's positive ones. Focus Energy stacks up to 3 times, taking a plain move to about 63%.
Burn	×0.5	A burned attacker deals half damage with physical moves. Special moves are unaffected.
Random roll	×0.85–1.00	Rolled per hit, so the same move on the same target varies a little. The tables above use the average roll.

A hit that connects always deals at least 1 damage; only a 0× type immunity deals none.

Buffs and debuffs (stat stages)

Moves like Swords Dance and Growl move a stat between −6 and +6 stages. The middle column is what happens to the stat; the right-hand column is what happens to your damage — and they are not the same number, because the stat only reaches damage through the square-rooted ratio.

Stage	Stat becomes	Your damage becomes
+6	×4	×1.74
+5	×3.5	×1.65
+4	×3	×1.55
+3	×2.5	×1.44
+2	×2	×1.32
+1	×1.5	×1.18
0	×1	×1
-1	×0.67	×0.85
-2	×0.5	×0.76
-3	×0.4	×0.69
-4	×0.33	×0.64
-5	×0.29	×0.61
-6	×0.25	×0.57

So a maxed +6 buff is worth double damage, not quadruple. Stages wear off after a while and reset when the pocket monster leaves the fight.

Where your stats come from

Base is the species' own value, from its Pokédex entry. IVs are rolled at capture, EVs are trained afterwards with vitamins, and quality and nature scale the result.

HP   = floor(((2 × Base + IV + EV÷4) × 0.66 + 450) × Level ÷ 100) + Level + 10
Stat = floor((2 × Base + IV + EV÷4) × Level ÷ 100) + 5

IVs: 0 to 31 per stat, rolled when the pocket monster is caught and fixed for life.
EVs: Effort Values — the trained half. Up to 252 in one stat and 510 across all six, raised only with vitamins. Every 4 EVs add 1 to the base-and-IV term, so a fully trained stat is worth 63 of it.
Quality: Scales every stat together, from ×0.9 at the worst roll to ×1.1 at the best.
Nature: Raises one stat by 10% and lowers another by 10%. Five of the 25 natures are neutral. HP is never affected.
Shiny: A shiny pocket monster gets ×1.05 on all six stats, HP included — and can never be caught below Refined quality.

For example: a base stat of 100 with that stat's IV at its maximum of 31, at level 50, untrained, gives 120 — before quality and nature.

How level, IVs and quality scale a stat

The three do not scale the same way. Level multiplies the base-and-IV term, so one IV point is worth Level ÷ 100 of a stat point — you can read that straight off the formula above, and it is why at level 1 a perfect IV and a zero IV give exactly the same stat. Quality is applied last, to the finished number, so its ±10% grows with everything that went into it. Both tables below use a base-100 stat, that stat's IV at 0 and at its maximum of 31, and a neutral nature.

Attack, Defense, Sp. Atk, Sp. Def and Speed

Every stat other than HP runs this same curve. The two middle columns are the same pocket monster with that stat's IV at 0 and at 31; the last column is what quality alone moves, on the one with 31 IVs.

Level	IV 0	IV 31	What 31 IVs add	What quality moves
1	7	7	0	−1 … +1
10	25	28	+3	−3 … +3
25	55	62	+7	−6 … +6
50	105	120	+15	−12 … +12
75	155	178	+23	−18 … +18
100	205	236	+31	−24 … +24

At level 50 the whole IV range is worth 15 points while quality swings ±12 — so an unlucky quality roll cancels perfect IVs outright, and a lucky one is worth more than they are.

HP

HP runs a deliberately flatter curve so that fights last longer: the base-and-IV term is scaled to ×0.66 and a flat 450 is added to it before the level scaling.

Level	IV 0	IV 31	What 31 IVs add	What quality moves
1	16	17	+1	−2 … +2
10	78	80	+2	−8 … +8
25	180	185	+5	−18 … +19
50	351	361	+10	−36 … +36
75	521	536	+15	−54 … +54
100	692	712	+20	−71 … +71

That flat term dilutes IVs, and it cannot dilute a multiplier: at level 50 the whole HP IV range is worth 10 points while quality swings ±36 — about 3.6× as much. On HP, quality is the number to care about.

IVs and quality are both rolled when the pocket monster is caught and never change afterwards, so level and EVs are what you can still move — and levelling makes everything else matter more, not less. Nature is applied after quality and moves one stat up and another down; stat stages come after that and last only for the fight.

Speed, cooldowns and damage over time

Speed does not enter the damage formula at all. It buys you time: everything a pocket monster has to wait for gets shorter as it gets faster. That is one number, and it moves four things at once — the global cooldown that locks all of your moves after any cast, each move's own cooldown, the wind-up on moves that charge, and how often the poison or burn you inflict deals its damage. Past 300 — about a level-100 Electrode — Speed keeps helping, but each point buys less than the one before it. Moves that raise Speed, like Agility, ride that same curve: the first cast is worth by far the most, and a full stack is worth about an eighth more actions.

Speed	Global cooldown	Hyper Beam	Poison tick
0	1.00s	11.00s	2.00s
75	0.94s	10.31s	1.88s
150	0.88s	9.63s	1.75s
225	0.81s	8.94s	1.63s
300	0.75s	8.25s	1.50s
400	0.70s	7.70s	1.40s
500	0.68s	7.42s	1.35s

Wild pocket monsters get the same treatment, off their own Speed — a fast one really does hit you more often. Two things are deliberately left alone: how long a status condition lasts, and moves that channel like Recover. And because faster ticks fit more of them into the same poison, a fast attacker's damage over time adds up to more in total, not just sooner. Since damage per second is what actually kills things, a cheap fast move often beats a slow heavy one.