We study the thermodynamics of the strange baryon system by using an S-matrix formulation of statistical mechanics. For this purpose, we employ an existing coupled-channel study involvinḡ KN , πΛ, and πΣ interactions in the S = −1 sector. A novel method is proposed to extract an effective phase shift due to the interaction, which can subsequently be used to compute various thermal observables via a relativistic virial expansion. Using the phase shift extracted, we compute the correlation of the net baryon number with strangeness (χBS) for an interacting hadron gas. We show that the S-matrix approach, which entails a consistent treatment of resonances and naturally incorporates the additional hyperon states which are not listed by the Particle Data Group, leads to an improved description of the lattice data over the hadron resonance gas model.