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Equation 2 · The EV Formula Is an Exact Production Function Trainers Solved by Accident

What does this equation mean?

HP=⌊(2B+I+⌊E/4⌋)⋅L100⌋+L+10\text{HP} = \left\lfloor (2B+I+\lfloor E/4 \rfloor) \cdot \frac{L}{100} \right\rfloor + L + 10

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Start withL
Divide by100
This relates toHP
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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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BB

Symbol B

B is one of the signed contributions combined to compute the quantity on the left.

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II

Symbol I

I is one of the signed contributions combined to compute the quantity on the left.

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EE

Symbol E

E is one of the signed contributions combined to compute the quantity on the left.

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LL

Symbol L

L occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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fraction

fraction

Divide the expression above the line by the one below it.

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multiplication

multiplication

Multiply the quantities on either side.

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addition

addition

Add the term after the plus sign to the term or group before it.

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100100

Denominator: 100

The complete quantity below the fraction bar; it must be nonzero for this division.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

HP uses the same inner term but a different outer shell, adding the Pokémon’s level plus ten instead of multiplying by a nature: HP=⌊(2B+I+⌊E/4⌋)⋅L100⌋+L+10\text{HP} = \left\lfloor (2B+I+\lfloor E/4 \rfloor) \cdot \frac{L}{100} \right\rfloor + L + 10. At level 100 — the level Smogon’s singles tiers, including the OU tier this article draws its spreads from, are actually played at — the level term collapses to a clean multiplication by one, so every floor operation inside the level scaling vanishes and the formula reduces to simple integer arithmetic: raw score equals twice the base stat plus the IV plus the floor of EV over four, plus five, times the nature coefficient. That collapse is not incidental to this article; it is why the whole problem is exactly solvable rather than merely…
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HP uses the same inner term but a different outer shell, adding the Pokémon’s level plus ten instead of multiplying by a nature: HP=⌊(2B+I+⌊E/4⌋)⋅L100⌋+L+10\text{HP} = \left\lfloor (2B+I+\lfloor E/4 \rfloor) \cdot \frac{L}{100} \right\rfloor + L + 10. At level 100 — the level Smogon’s singles tiers, including the OU tier this article draws its spreads from, are actually played at — the level term collapses to a clean multiplication by one, so every floor operation inside the level scaling vanishes and the formula reduces to simple integer arithmetic: raw score equals twice the base stat plus the IV plus the floor of EV over four, plus five, times the nature coefficient. That collapse is not incidental to this article; it is why the whole problem is exactly solvable rather than merely well-approximated. A trainer is not tuning a continuous dial. A trainer is allocating a strictly rationed resource — at most 510 points total, at most 252 in any single stat since Generation VI [ 2 ] — against a fixed, integer-valued conversion rate, in six independent lines, one of which the nature coefficient tilts by exactly ten percent in one direction and discounts by exactly ten percent in another [ 3 ] . Two Pokémon-standard six-stat lines, one budget, hard per-line ceilings, an unambiguous conversion technology: that is a textbook constrained-allocation problem, not a metaphor borrowed from economics to dress up a hobby.

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