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We use simulations to build an analytic probability distribution for theasphericity in the satellite distribution around Local Group (LG) type galaxiesin the Lambda Cold Dark Matter (LCDM) paradigm. We use this distribution toestimate the atypicality of the satellite distributions in the LG even when theunderlying simulations do not have enough systems fully resembling the LG interms of its typical masses, separation and kinematics. We demonstrate themethod using three different simulations (Illustris-1, Illustris-1-Dark andELVIS) and a number of satellites ranging from 11 to 15. Detailed resultsdiffer greatly among the simulations suggesting a strong influence of thetypical DM halo mass, the number of satellites and the simulated baryoniceffects. However, there are three common trends. First, at most $2\%$ of thepairs are expected to have satellite distributions with the same asphericity asthe LG; second, at most $80\%$ of the pairs have a halo with a satellitedistribution as aspherical as in M31; and third, at most $4\%$ of the pairshave a halo with satellite distribution as planar as in the MW. Thesequantitative results place the LG at the level of a $3\sigma$ outlier in theLCDM paradigm. We suggest that understanding the reasons for this atypicalityrequires quantifying the asphericity probability distribution as a function ofhalo mass and large scale environment. The approach presented here canfacilitate that kind of study and other comparisons between different numericalsetups and choices to study satellites around LG pairs in simulations.

We are not the 99 percent: quantifying asphericity in the distribution of Local Group satellites