What makes a household-level short-term load forecast “good”? Individual household load profiles are intermittent, as distinct peaks correspond to specific activities in the household. Using traditional point-wise error metrics to assess household-level forecasts may lead to, for instance, double-digit mean absolute percentage errors. One reason is a double penalty incurred if a peak is forecasted correctly in amplitude, but with a small delay in time. An adjusted forecast error measure based on local permutations was proposed to assess household-level forecasts by optimally aligning the peaks bounded by a displacement limit. This work shows how the choice of this parameter leads to different “best” forecasts in terms of specific applications, namely the optimization objectives of an energy management system. For that, different parameterizations of the Local Permutation Invariant (LPI) distance are compared within k-Nearest Neighbors as a forecasting model for three different optimization objectives. A simulation study on 100 households of the CER dataset shows that the optimal parameterization can decrease the peak load on average by over 22.5% compared to the Euclidean distance. However, for increasing self-sufficiency and minimizing costs, no significant improvements can be achieved. This implies that household-level forecasts should generally be evaluated in terms of their application, as traditional metrics as a proxy may not express its “goodness” adequately.