Radiation quality for determining biological effects is commonly linked to the microdosimetric quantity lineal energy ( ) and to the dose-mean lineal energy ( ). Calculations of are typically performed by specialised Monte Carlo track-structure (MCTS) codes, which can be time-intensive. Thus, microdosimetry-based analytic models are potentially useful for practical calculations. Analytic model calculations of proton and radiation protection quality factor ( ) values in sub-micron liquid water spheres (diameter 10-1000 nm) over a broad energy range (1 MeV-1 GeV) are compared against MCTS simulations by PHITS, RITRACKS, and Geant4-DNA. Additionally, an improved analytic microdosimetry model is proposed. The original analytic model of Xapsos is refined and model parameters are updated based on Geant4-DNA physics model. Direct proton energy deposition is described by an alternative energy-loss straggling distribution and the contribution of secondary electrons is calculated using the dielectric formulation of the relativistic Born approximation. MCTS simulations of proton values using the latest versions of the PHITS, RITRACKS, and Geant4-DNA are reported along with the Monte Carlo Damage Simulation (MCDS) algorithm. The datasets are then used within the Theory of Dual Radiation Action (TDRA) to illustrate variations in with proton energy. By a careful selection of parameters, overall differences at the ~ 10% level between the proposed analytic model and the MCTS codes can be attained, significantly improving upon existing models. MCDS estimates of are generally much lower than estimates from MCTS simulations. The differences of among the examined methods are somewhat smaller than those of . Still, estimates of proton values by the present model are in better agreement with MCTS-based estimates than the existing analytic models. An improved microdosimetry-based analytic model is presented for calculating proton values over a broad range of proton energies (1 MeV-1 GeV) and target sizes (10-1000 nm) in very good agreement with state-of-the-art MCTS simulations. It is envisioned that the proposed model might be used as an alternative to CPU-intensive MCTS simulations and advance practical microdosimetry and quality factor calculations in medical, accelerator, and space radiation applications.