Context: Non-determinism in deep learning algorithm design and implementation leads to performance variation, meaning model performance is not a single value, but rather a distribution. These model performance distributions are underexplored despite their impact on robustness. Objective: We investigate the robustness of deep learning performance to sources of non-determinism, specifically focusing on how performance distributions differ across various architectures and tasks. Method: We conducted 186 experiments on image classification and time series forecasting architectures. Each experiment was run 100 times with different random seeds to generate performance distributions, resulting in 18,600 runs. Robustness was quantified using metrics for spread, symmetry, and tail risk. Results: Performance distributions are frequently non-Gaussian, particularly in time series forecasting. Model size does not systematically affect robustness -- larger image classification models show fewer outliers but not lower spread, while smaller time series models show lower spread but more extreme underperformers. Training duration does not scale linearly; early stopping effectively balances performance and robustness. Mean performance does not predict robustness - time series forecasting shows moderate correlation while image classification shows none. Time series models produce nearly three times more underperforming outliers than image classification models, indicating substantially higher tail risk. Conclusions: Tail risk poses serious concerns for Trustworthy AI in high-stakes applications. Models performing well on average may exhibit long tails and extreme outliers revealed only through distributional analysis. Mean performance alone should not guide model selection; assessment of spread, symmetry, and tail risk is essential for reliable model assessment where consistent performance is critical.

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