High-power impulse magnetron sputtering (HiPIMS) is an ionized physical vapor deposition technique that provides a high flux of ionized target species for thin film growth. Optimization of HiPIMS processes is, however, often difficult, since the influence of external process parameters, such as working gas pressure, magnetic field strength, and pulse configuration, on the deposition process characteristics is not well understood. The reason is that these external parameters are only indirectly connected to the two key flux parameters, the deposition rate and ionized flux fraction, via two internal discharge parameters: the target atom ionization probability alpha (t) and the target ion back-attraction probability beta (t). Until now, it has been difficult to assess alpha (t) and beta (t) without resorting to computational modeling, which has hampered knowledge-based optimization. Here, we present a simple method to deduce alpha (t) and beta (t) based on measured deposition rates of neutrals and ions. The core of the method is a refined analytical model, which is described in detail. This approach is furthermore validated by independent calculations of alpha (t) and beta (t) using the considerably more complex ionization region model, which is a plasma-chemical global discharge model.