Teaching Notes

Choose the Question Before the Score

A small error or an improved average answers only its own question. Event timing and worst-group reliability need their own checks.

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A score becomes useful when its connection to the intended question is clear. Before choosing one, ask: which output must this comparison support?

A final state is not an arrival time

In When a Traffic Solver Invents a Jam, one numerical solution has an exceptionally small final global error because the shock aligns with a cell boundary at the final time. Earlier, its smeared front crosses the fixed sensor threshold late.

Both measurements are valid. The final norm compares cell averages at one time; the event measure checks when a sensor trajectory crosses a declared threshold. Neither substitutes for the other. If arrival time matters, the evaluation needs an arrival-time check, together with its threshold and interpolation rule. This is a dimensionless synthetic benchmark, not evidence about real-road delays or a universal ranking of traffic solvers.

An improved average can leave a difficult group behind

When Solar Power Changes Fast separates relative improvement from an absolute reliability requirement. Descriptor CQR improves the compared worst-group endpoint at every confirmation station and improves aggregate proper interval scores. Yet no deployable candidate clears the study’s all-station absolute criterion.

Wider intervals can improve coverage while imposing an efficiency cost elsewhere. Reporting width, coverage, proper score and eligible-group support keeps those trade-offs visible. It does not establish the value of a dispatch decision, which the study did not evaluate.

These examples use different models and data. Their lesson is about evaluation design, not pooling their scores: name the target output, specify the comparison and eligible population, declare the relevant criteria, and retain failures alongside improvements. A successful aggregate score can be part of the answer without becoming permission to stop asking about the quantity that motivated the study.

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