Physics-based battery models can be very complex and require careful experimental validation, but yield greater insights into the internal processes and their interactions than other cell modelling approaches. The complexity is associated with the large number of input parameters that (a) have varying degrees of identifiability, (b) can be constant or varying, and (c) appear in complex combinations with the model variables and each other. The current work studies this complexity by proposing a unique stepwise approach and purposefully addresses the computational cost associated with estimating these parameters. An initial set of 50 input parameters is reduced to only 8 highly influential parameters that can be subjected to parameter optimization. Elementary effects analysis using the Morris method is applied and demonstrates that the electrode kinetic parameters dominate the cell’s voltage response as simulated by the model. These influential parameters are subjected to variance-based sensitivity analysis using Monte Carlo experiments and Jansen’s formulae for variance decomposition. The first-order and total sensitivities during various modes of operation indicate that the charge transfer coefficients and effective exchange current densities have the most influence on the model error and should be subjected to further optimization. The model error’s sensitivity also reveals high parameter identifiability within subsets of the experimental data and indicates that some parameter values might be valid for longer timescales rather than shorter timescales. The proposed stepwise approach can be applied to any complex physics-based cell model regardless of the cell’s chemistry, format or form factor.