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Using tens of thousands of halos realized in the BAHAMAS and MACSISsimulations produced with a consistent astrophysics treatment that includes AGNfeedback, we validate a multi-property statistical model for the stellar andhot gas mass behavior in halos hosting groups and clusters of galaxies. Thelarge sample size allows us to extract fine-scale mass--property relations(MPRs) by performing local linear regression (LLR) on individual halo stellarmass (${\rm M}_{\rm star}$) and hot gas mass (${\rm M}_{\rm gas}$) as afunction of total halo mass (${\rm M}_{\rm halo}$). We find that: 1) both thelocal slope and variance of the MPRs run with mass (primarily) and redshift(secondarily); 2) the conditional likelihood, $p({\rm M}_{\rm star},\ {\rmM}_{\rm gas} | \ {\rm M}_{\rm halo}, z)$ is accurately described by amultivariate, log-normal distribution, and; 3) the covariance of ${\rm M}_{\rmstar}$ and ${\rm M}_{\rm gas}$ at fixed ${\rm M}_{\rm halo}$ is generallynegative, reflecting a partially closed baryon box model for high mass halos.We validate the analytical population model of Evrard et al. (2014), findingsub-percent accuracy in the log-mean halo mass selected at fixed property,$\langle \ln {\rm M}_{\rm halo} | {\rm M}_{\rm gas} \rangle$ or $\langle \ln{\rm M}_{\rm halo} | {\rm M}_{\rm star} \rangle$, when scale-dependent MPRparameters are employed. This work highlights the potential importance ofallowing for running in the slope and scatter of MPRs when modeling clustercounts for cosmological studies. We tabulate LLR fit parameters as a functionof halo mass at $z=0$, $0.5$ and 1 for two popular mass conventions.

Localized massive halo properties in Bahamas and Macsis simulations: scalings, log-normality, and covariance