Characterizing the abundance of atmospheric hydrogen (H) at Mars is critical for determining the current and, subsequently, the primordial water content on the planet. At present, the atmospheric abundance of Martian H is not directly measured but is simulated using proprietary models that are constrained with observations of H Lyman-a emission brightness, as well as with observations of other atmospheric parameters, such as temperature and solar UV irradiance. To make the data needed to model H abundances and escape rates more accessible to the community, this work utilizes over nine years of observations of H Lyman-a emissions made with the Mars Atmosphere and Volatile Evolution (MAVEN) mission. The H brightness in the upper atmosphere of Mars is analyzed for statistical variability across multiple variables and found to be dependent on solar illumination, solar cycle, and season. The resulting data trends are used to derive empirical fits to build a predictive framework for future observations or an extrapolative tool for primordial estimates. Data that was intentionally not included in the empirical derivations are used to validate the predictions and found to reproduce the H Lyman-a brightness to within 18% accuracy, on average. This first of its kind predictive model for H brightness is presented to the community and can be used with atmospheric models to further derive and interpret the abundances and escape rate of H atoms at Mars.