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Equation 19 · Part 2 · The EV Formula Is an Exact Production Function Trainers Solved by Accident

Symbol x

y−x=224y - x = 224
xx

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the writing.

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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)\mathcal{L}(x,y,\lambda) = (296+x4\tfrac{x}{4})(264+0.275y) - λ(x+y−B)\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: y - x = 224 The unconstrained-by-caps answer, in other words, wants Garchomp’s invested Speed to run 224 points ahead of its invested Attack — a gap wider than the entire 252-point ceiling on either stat individually.

The passage around this formula

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: y−x=224y - x = 224. The unconstrained-by-caps answer, in other words, wants Garchomp’s invested Speed to run 224 points ahead of its invested Attack — a gap wider than the entire 252-point ceiling on either stat individually. That single number is the whole explanation for why the observed spread looks like a blunt “max both” instinct rather than a delicate balance: a 224-point desired gap cannot fit inside a box only 252 points wide on a side, so the interior tangency point is infeasible, and…

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