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\section{Comparison to Toy Models}  In this section we make comparisons of the dynamical SDSS data to simple toy models. We begin by detailing how each toy model is constructed. In the disk and isotropic models, hosts are permitted to have more than two satellites; in these cases, hosts are four times more likely to have n as n+1 satellites.   \begin{enumerate}  1. \item  Disk model - In this model, 2-5 satellites are placed randomly between 0 and 200 kpc from the origin on the xy plane and then randomly given a z coordinate randomly between -10 and 10 kpc. All satellites are assigned a 3D velocity so as to be corotating in circular motion. All satellites are assigned a 3D velocity of 100 km/s. 2. \item  ``Dumbell" model - Here, each host is restricted to exactly two satellites. Once the first satellite is randomly placed on the xy plane, the placing of the second satellite is restricted such that the angle between the position vectors of the two satellites is greater than $170^{\circ}$. From there, each satellite is assigned a z cooridate between -10 and 10 kpc and the model procceeds as in the disk model. 3. \item  M31 model - This model is based on the position and velocities of the 13 M31 satellites belonging to the co-rotating plane identified in \citet{Ibata_2013}. The three dimensional positions of the satellites are taken from \citet{McConnachie_2012} and the line-of-sight velocities are compiled from \citet{McConnachie_2012} and \citet{2013ApJ...768..172C}. Note that we only consider the 13 satellitesthat seem to be  exhibiting coherent rotation; the two satellites aligned with the planar structure but with couter-aligned line-of-sight velocities are(for the purposes of this model)  consideredto be  part of the isotropic background. We estimate assign  proper motions of to  the13  satellites on the assumption that they are to place them  in circular motion orbits around the host. From there the model proceeds as in the "disk model" case.  3. \item  Isotropic model - In this case, each host may again have 2-5 satellites. Each satellite is independently assigned a random position and velocity. \end{enumerate}  In each case, we rotate the hos to a random viewing angle and view the model along the z axis. A statistical sample consists of N $\sim 10^5$ hosts, and most statistical samples will consist of a mixing of the isotropic model with one of the other two models.