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  • $\begingroup$ When one's goal is to cover the demand on a service, for a count variable $Y$ representing number of requests for service, a score like a quantile $Q_Y(p)$ at some probability $p$ may be suitable. The evaluation score $$\text{Count}[Y > Q_Y(p)]$$ is intuitively the number of time points the demand was not covered. $\endgroup$ Commented Feb 26 at 15:32
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    $\begingroup$ @Galen: absolutely, yes. But I was not asking about quantile forecasts and quantile/pinball losses in this instance (except in the sense that the MAE is the pinball loss for a 50% quantile forecast). The pinball loss is of course minimized by the true conditional quantile. I just see lots of confusion about forecast error metrics for forecasts of central tendency. (And lots of people estimating conditional expectation forecasts, which are then evaluated using the MAE or MAPE, whether this makes sense or not.) $\endgroup$ Commented Feb 26 at 16:18