values of $M_{halo}$, the maximal self-bound mass of each subhalo; this is included in the database for both Type 0 and Type 1 galaxies. In the following we use the notation $M_{tr,200}$ and $M_{tr,halo}$ to distinguish these two definitions. For either we can calculate the ratio of true mass to Timing Argument estimate, $$A_x = M_{tr,x}/M_{TA},$$ where the suffix $x$ is $200$ or $halo$ depending on the definition adopted for $M_{tr}$. If the Timing Argument is a good estimator of true mass, our samples of LG analogues should produce a narrow distribution of $A$ values. This distribution then allows the TA mass estimate for the real Local Group to be converted into a best estimate of its true mass, together with associated confidence intervals.

Our preferred sets of Local Group analogues contain simulated galaxy pairs which mimic the real system in terms of morphology, isolation, pair separation and pair approach velocity. In addition, they require the halos of the simulated galaxies to have $V_{max}$ values within about $\pm 10\% $ and $\pm
35\%$ of those estimated for M31 and the Galaxy for the tight and loose ranges of $V_{max}$, respectively. In order to understand the influence of these constraints we 