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Equation 17 · The EV Formula Is an Exact Production Function Trainers Solved by Accident

What does this equation mean?

L(x,y,λ)=(296+x4)(264+0.275y)−λ(x+y−B)\mathcal{L}(x,y,\lambda) = (296+\tfrac{x}{4})(264+0.275y) - \lambda(x+y-B)

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Inputs and operations(296+tfracx4)(264+0.275y) - λ(x+y-B)
Result or conditionL(x,y,λ)
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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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L\mathcal{L}

Symbol L

L is part of the quantity the equation computes from the expression on the right.

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xx

Symbol x

the writing.

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yy

Symbol y

y is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

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λ\lambda

Symbol λ

λ is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

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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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=

=

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

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addition

addition

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

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subtraction

subtraction

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

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How to interpret it

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What the article says around this equation

Hitting the 127-point ceiling says nothing yet about which stats should receive the investment — that answer depends on what the spread is actually for. For the Swords Dance set’s job, sweeping through a metagame’s Speed tiers with a boosted physical attack, I define a proposed measure I will call the sweep index: the product of a Pokémon’s final Attack stat and its final Speed stat. This is not an official in-game statistic; it is this article’s own construct, chosen because a physical sweeper that hits hard but moves last contributes nothing, a sweeper that moves first but hits softly contributes little, and a product (rather than a sum) captures that the two failure modes compound rather…
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Hitting the 127-point ceiling says nothing yet about which stats should receive the investment — that answer depends on what the spread is actually for. For the Swords Dance set’s job, sweeping through a metagame’s Speed tiers with a boosted physical attack, I define a proposed measure I will call the sweep index: the product of a Pokémon’s final Attack stat and its final Speed stat. This is not an official in-game statistic; it is this article’s own construct, chosen because a physical sweeper that hits hard but moves last contributes nothing, a sweeper that moves first but hits softly contributes little, and a product (rather than a sum) captures that the two failure modes compound rather than merely add. Writing x for invested Attack EVs and y for invested Speed EVs and relaxing the two internal floors to their continuous approximation for tractability, Garchomp’s Jolly-natured sweep index becomes f(x,y) = (296+x/4)(264+0.275y) , and maximizing it subject to a shared budget x+y=B through a Lagrangian L(x,y,λ)=(296+x4)(264+0.275y)−λ(x+y−B)\mathcal{L}(x,y,\lambda) = (296+\tfrac{x}{4})(264+0.275y) - \lambda(x+y-B). produces first-order conditions 14\tfrac{1}{4}(264+0.275y) = λ\lambda = 0.275\,(296+x4\tfrac{x}{4}) , which reduce, after clearing terms, to a single tangency condition independent of the budget size:

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