Every Pokémon carries a hidden layer of numbers that determines its ceiling — Individual Values, or IVs, that exist independently of training, held items, or player skill. A Pokémon with perfect IVs in a critical stat will always outperform an identical species with poor IVs, even with identical EVs, nature, and level. Understanding the stat formula turns the breeding grind from random hope into deliberate optimization.
What Are IVs? The Hidden Stats
IVs range from 0 to 31 in each of the six stats: HP, Attack, Defense, Special Attack, Special Defense, and Speed. They are assigned at the moment a Pokémon is generated — encountered in the wild, received as a gift, or hatched from an egg — and cannot be changed through normal gameplay (Hyper Training raises the calculation to act as 31 but does not change the underlying IV).
The spread across all six stats creates over 887 million possible IV combinations per species. Most casual players will never notice the difference between a 25 IV and a 31 IV in Attack because it amounts to only a few points at Level 100. Competitive battlers care deeply because a single point of Speed can be the difference between outspeeding a benchmark threat and getting hit first.
The Pokémon Stat Formula
The stat calculation differs between HP and all other stats. Both use IVs, EVs (Effort Values), Base Stats, and level as inputs.
HP Stat =
floor(((2 × Base + IV + floor(EV / 4)) × Level / 100) + Level + 10)
Other Stats =
floor((floor(((2 × Base + IV + floor(EV / 4)) × Level / 100) + 5) × Nature))
Nature multipliers: 1.1 for boosted stat, 0.9 for hindered stat, 1.0 for neutral. Nature interacts with the final flat value, not the dice inside the formula, making it consistently valuable at every level of IV investment.
Worked example — Garchomp Attack at Level 100:
- Base Attack: 130
- IV: 31, EV: 252, Nature: Jolly (neutral to Attack) → nature multiplier = 1.0
floor(((2 × 130 + 31 + floor(252 / 4)) × 100 / 100) + 5) × 1.0
= floor(((260 + 31 + 63) × 1) + 5) × 1.0
= floor(354 + 5)
= 359 Attack
With 0 IV and 0 EV instead: floor(((260 + 0 + 0) × 1) + 5) = 265 Attack. The gap between a perfect and a zero Attack IV at 252 EVs is 94 points — roughly a 35% difference that cascades through every damage calculation.
What Are EVs? Training Your Stats
Effort Values are earned through battling specific Pokémon, using Vitamins (Protein, Iron, etc.), or feeding Feathers. Each stat has its own EV counter, capped at 252 per stat. The total across all stats is capped at 510 EVs.
The conversion rate is 4 EVs = 1 stat point at Level 100. This means the maximum stat gain from EVs alone is floor(252 / 4) = 63 stat points per stat. Two stats can be maxed (252 + 252 = 504) with 6 EVs left over — enough to add 1 extra point in a third stat.
Vitamins grant 10 EVs each and are capped at 100 EVs per stat (25 Vitamins maximum before needing to battle for the remaining 152). In modern games (Sword/Shield and later), the Vitamin cap is removed in some contexts, allowing you to max a stat entirely with 25 Vitamins + 38 battles against the right Pokémon, or by using Feathers for fine-tuning.
Optimal EV Spreads by Role
Competitive EV investment follows the role the Pokémon fills on the team. Spreading EVs evenly across all six stats — 85 each — is almost never optimal because it raises every stat by only 21 points rather than maximizing the two or three stats that determine the Pokémon's function.
| Role | Primary EV Focus | Secondary EV Focus | Leftover | Reasoning |
|---|---|---|---|---|
| Physical Sweeper | 252 Attack | 252 Speed | 4 HP | Maximize damage output and outspeed threats |
| Special Sweeper | 252 Sp. Atk | 252 Speed | 4 HP | Same logic for special side |
| Physical Wall | 252 HP | 252 Defense | 4 Sp. Def | Survive physical hits; HP scales both defenses |
| Special Wall | 252 HP | 252 Sp. Def | 4 Defense | Survive special hits; HP maximizes total bulk |
| Bulky Attacker | 252 HP | 252 Attack or Sp. Atk | 4 Defense | Balance survivability with offensive presence |
| Support/Tank | 252 HP | 128 Def / 128 Sp. Def | 4 Speed | Even physical/special bulk for utility roles |
| Speed Control | 252 Speed | 252 HP or Atk | 4 remaining | Trick Room setters often flip this — 0 Speed IVs |
Trick Room setters deliberately run 0 Speed IVs and 0 Speed EVs to move last under Trick Room conditions where slower Pokémon act first.
IV Breeding: How to Get Perfect 6IV
Breeding for perfect IVs uses two items: the Destiny Knot and the Everstone.
Destiny Knot: When held by either parent, exactly 5 of the parents' combined 12 IVs (6 per parent) are passed to the offspring. The remaining stat gets a randomly generated IV. Without Destiny Knot, only 3 random IVs pass from parents.
Everstone: Guarantees the holder's Nature passes to the offspring 100% of the time.
The breeding ladder for a perfect Garchomp:
- Find a Ditto with high IVs (ideally 5–6 perfect IVs from trading) or a Garchomp with target IVs.
- Breed Ditto (Destiny Knot) + Garchomp (Everstone with desired Nature). Collect eggs, check IVs via the Judge function.
- Keep offspring that have 4+ perfect IVs. Replace the parent with the better offspring.
- Repeat until you have a 5IV parent missing only the IV in a stat you do not need (typically Sp. Atk for a physical attacker).
- Breed two 5IV parents together. The probability of a 6IV offspring from two 5IV parents with Destiny Knot is approximately 1/32 per egg — expect 30–100 eggs on average.
The probability of hatching a 5IV Pokémon from two 5IV parents (Destiny Knot, 5 IVs passed, 1 random) is roughly 5/6 × (1/32) for the perfect one = about 1 in 6.4 eggs for 5IV with the right missing stat, though the math is slightly more complex due to which IVs are inherited from which parent.
Competitive Example: Building a Perfect Garchomp
Garchomp (Gible line) is a Dragon/Ground physical attacker with Base Stats: 108 HP / 130 Atk / 95 Def / 80 Sp. Atk / 85 Sp. Def / 102 Speed. The target build is a Jolly (Speed+, Sp. Atk–) Garchomp with 31/31/31/x/31/31 IVs — perfect everywhere except Sp. Atk, which is never used.
EV spread: 252 Attack / 252 Speed / 4 HP
Final stats at Level 100:
| Stat | Base | IV | EVs | Nature | Final |
|---|---|---|---|---|---|
| HP | 108 | 31 | 4 | — | 363 |
| Attack | 130 | 31 | 252 | ×1.0 | 359 |
| Defense | 95 | 31 | 0 | — | 226 |
| Sp. Atk | 80 | 0 | 0 | ×0.9 | 139 |
| Sp. Def | 85 | 31 | 0 | — | 206 |
| Speed | 102 | 31 | 252 | ×1.1 | 333 |
The 333 Speed benchmark with Jolly nature outspeeds every non-boosted base 100 Speed Pokémon by a meaningful margin and ties with other base 102s. Adamant nature (Attack+) would raise Attack to 394 but drop Speed to 299, falling behind base 105 Speed threats like Mega Lopunny — a trade most competitive teams reject.
The IV and EV system rewards players who treat stat optimization as a calculation problem. Once you internalize the formula, breeding decisions become straightforward: identify the two stats that define the Pokémon's role, maximize both, then protect nature via Everstone, and trust the Destiny Knot to compress the IV breeding ladder from dozens of generations to a manageable handful.