Excess electrons in liquid water, commonly known as hydrated electrons, have been of great theoretical and experimental interest. Despite this, there is still no definitive understanding of how the surrounding water molecules are arranged and fluctuate around the hydrated electron. Experiments have shown that the hydrated electron has a large positive solvation entropy, which is quite anomalous among small ions in water, which usually have negative entropies of solvation. In this work, we use alchemical simulation, machine learning, and a reference potential methodology to calculate the solvation entropy of several simulation models of the hydrated electron, including ab initio molecular dynamics based on density functional theory (DFT). We find that cavity-forming one-electron models with relatively soft cavity structures correctly predict the sign of the hydrated electron’s entropy but underestimate its magnitude. Both a non-cavity one-electron model and hard cavity-forming DFT simulations yield a solvation entropy with the incorrect sign, indicating that the hydration structures predicted by these methods must be qualitatively incorrect. We rationalize the calculated solvation entropies of the different hydrated electron models by examining the structure and dynamic behavior of the first-shell waters.