A team is evaluating extended thinking for a supply chain optimization problem that requires Claude to evaluate 50+ variables across 12 supplier constraints. They are debating what budget_tokens value to set. What principle should guide the thinking budget calibration?

The correct principle is to calibrate the thinking budget empirically: start with a moderate budget, measure output quality on representative problem instances, and increase the budget only if there is measurable quality improvement. Thinking budget should not be set to maximum or derived from arbitrary heuristics. The key insight is that thinking tokens incur real cost, and the marginal quality improvement from a larger budget exhibits diminishing returns — there is a sweet spot beyond which additional thinking tokens do not improve output quality. Starting with a moderate budget, measuring quality on representative instances, and scaling up only when there is measurable improvement is the correct engineering approach. The maximum-budget approach is wrong because a maximum thinking budget does not guarantee maximum output quality — for some problems, the model converges on a good answer quickly and additional thinking tokens are wasted. The cost increase is real and can be substantial. The 50-tokens-per-variable heuristic is wrong because there is no principled relationship between the number of problem variables and the optimal thinking budget — this is an unfounded heuristic that may grossly under or over-allocate. The disable-extended-thinking position is wrong because extended thinking is not limited to creative writing; it is effective for complex reasoning across mathematical, analytical, and constraint satisfaction domains.