Quantifying cumulative arm muscle fatigue is a critical factor in understanding, evaluating, and optimizing user experience during prolonged mid-air interaction. A reasonably accurate estimation of fatigue requires an estimate of an individual's strength. However, there is no easy-to-access method to measure individual strength to accommodate inter-individual differences. Furthermore, fatigue is influenced by both psychological and physiological factors, but no current HCI model provides good estimates of cumulative subjective fatigue. We present a new, simple method to estimate the maximum shoulder torque through a mid-air pointing task, which agrees with direct strength measurements. We then introduce a cumulative fatigue model informed by subjective and biomechanical measures. We evaluate the performance of the model in estimating cumulative subjective fatigue in mid-air interaction by performing multiple cross-validations and a comparison with an existing fatigue metric. Finally, we discuss the potential of our approach for real-time evaluation of subjective fatigue as well as future challenges.