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When would you use MAPE versus MASE to evaluate a forecast, and what are the failure modes of each?

For Data Scientist ML Engineer Data Analyst

The short answer

MAPE (Mean Absolute Percentage Error) is intuitive and scale-free but breaks when actuals are near zero and penalises under-forecasts more than over-forecasts. MASE (Mean Absolute Scaled Error) solves both issues by scaling errors against a naive seasonal benchmark, making it valid even with zero values and comparable across series with different scales.

How to think about it

Cover the formulas, the asymmetry problem in MAPE, the zero-value problem, and when MASE is preferable. Interviewers at retail/supply-chain companies ask this constantly.

MAE and RMSE — the baseline pair

MAE = mean(|yi - yi_hat|): robust to outliers, in the same units as the series, but not comparable across series with different scales.

RMSE = sqrt(mean((yi - yi_hat)²)): penalises large errors more heavily; useful when big misses are disproportionately costly. Also in the same units as the series.

MAPE — convenient but fragile

MAPE = mean(|yi - yi_hat| / |yi|) × 100

Problems:

Division by zero when yi = 0 (common in intermittent demand, new product launches).
Asymmetry: a 100 % over-forecast (predict 200, actual 100) contributes the same as a 100 % under-forecast. But a 200 % under-forecast (predict 100, actual 300) contributes 67 % — capped at 100 % for over-forecasts, unbounded for under. This causes MAPE-optimised models to systematically bias toward lower forecasts.
Meaningless on negative values (e.g., net revenue, temperatures).

MASE — the better default for business forecasting

MASE = MAE_model / MAE_naive_seasonal

where the naive seasonal baseline predicts Yt = Yt-s (last period’s same season). MASE < 1 means the model beats the naive baseline; MASE > 1 means it doesn’t.

import numpy as np

def mase(actual, forecast, train, period=1):
    """
    actual  : test set actuals (array)
    forecast: model predictions on test set (array)
    train   : training actuals used to compute naive baseline
    period  : seasonal period (1 = non-seasonal naive)
    """
    mae_model = np.mean(np.abs(actual - forecast))
    naive_errors = np.abs(train[period:] - train[:-period])
    mae_naive = np.mean(naive_errors)
    return mae_model / mae_naive

Choosing which metric to report

Situation	Metric
No zeros, single series, stakeholders want %	MAPE
Zeros or near-zeros in actuals	MASE or RMSSE
Comparing across series with different scales	MASE
Penalising large errors more	RMSE
All errors equally important	MAE

Learn it properly Evaluating forecasts (walk-forward)