This paper studies the robustness of data valuation to noisy model performance scores. Particularly, we find that the inherent randomness of the widely used stochastic gradient descent can cause existing data value notions (e.g., the Shapley value and the Leave-one-out error) to produce inconsistent data value rankings across different runs. To address this challenge, we first pose a formal framework within which one can measure the robustness of a data value notion. We show that the Banzhaf value, a value notion originated from cooperative game theory literature, achieves the maximal robustness among all semivalues -- a class of value notions that satisfy crucial properties entailed by ML applications. We propose an algorithm to efficiently estimate the Banzhaf value based on the Maximum Sample Reuse (MSR) principle. We derive the lower bound sample complexity for Banzhaf value estimation, and we show that our MSR algorithm's sample complexity is close to the lower bound. Our evaluation demonstrates that the Banzhaf value outperforms the existing semivalue-based data value notions on several downstream ML tasks such as learning with weighted samples and noisy label detection. Overall, our study suggests that when the underlying ML algorithm is stochastic, the Banzhaf value is a promising alternative to the semivalue-based data value schemes given its computational advantage and ability to robustly differentiate data quality.