Annual vegetation aboveground net primary productivity (ANPP) exhibits a non-linear dependence on annual precipitation. A common pattern of non-linearity, called asymmetry, arises when productivity responses in wet years are larger than declines in dry years. To date, ANPP asymmetry has been attributed primarily to vegetation water stress, an internal ecosystem response to precipitation and soil water availability. However, when quantified via the asymmetry index (AI) estimated from productivity measurements, the asymmetry can be a sampling artefact that arises from a positively skewed annual precipitation distribution. In this paper, we aimed to separate the sampling effect (from external precipitation variability) from the non-linear response of the system (the internal ecosystem dynamics). We constructed a probabilistic model that integrates the precipitation distribution with the precipitation-productivity response curve (PPT-ANPP curve), derived using empirical formulae and a process-based soil water balance model. The model was used to derive the probability density function of AI and to attribute its shape to the PPT distribution and the PPT-ANPP response curve. The models were compared to data from 47 grasslands. Results demonstrated that positively skewed precipitation produces a positive AI as a statistical artefact. The non-linear ecosystem PPT-ANPP dependence can further enhance or dampen this statistical artefact. In all sites, the precipitation skew highly affected the probability of correctly identifying asymmetry using AI. Observed negative asymmetry arises from a larger soil water holding capacity and positive asymmetry from plant water stress. More robust statistical indicators of non-linear ecological responses to climate variability are needed to improve ecosystem forecasts.