Multi-injector burner systems offer a high spatial-temporal mixture homogeneity due to their small size and thus have a high NOx emission reduction potential at increasing flame temperatures. This potential is reduced due to the sensitivity of the mixing quality to inflow distortions caused by the flow path in the burner head. A deep understanding of the link between the inflow conditions and the mixture quality helps to optimize the flow field upstream of the injectors within the spatial and pressure loss constraints of gas turbine combustors to obtain minimal NOx emissions. This paper presents a new model approach for determining the mixture quality in multi-injector burners with output-based Proper Orthogonal Decomposition (O-POD). The sensitivity to the inflow distortion is considered with the so-called observable vector, which describes the injector inflow conditions and is given as model input. The target quantity is the Probability Mass Function (PMF) of the equivalence ratio at the injector outlet. This model allows a fast estimation of the mixing PMF for arbitrary inflow conditions, which is otherwise only accessible with complex time-resolved experimental or numerical approaches. The performance of the model was demonstrated with 21 reference datasets, for which a good agreement between the experimental results and the model output was obtained.