3 are the best candidates, but this could certainly change when radial velocities become available. An example of the importance of kinematic information is provided by Ret 2, whose probability drops substantially (from $\sim 0.10$ to $0.01$) when adding its radial velocity to the analysis (assuming first pericenter).

We shall hereafter retain as “Magellanic candidates” systems whose probabilities exceed $50\%$ that obtained for the SMC, without velocity information. The list of candidates is quite short: only $7$ systems of the $20$ new dwarfs make the cut in the case of position-only information: Hor 1, Hor 2, Eri 3, Ret 3, Tuc 5, Tuc 4 and Phx 2.

Second pericenter {#sec:2nd_pericenter}
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The above procedure also allows us to explore the sensitivity of our findings to our assumption that the LMC is on first approach. We do this by performing the same analysis but using the LMCa data at second pericenter ($t_{2p}$), after updating the Galactic coordinate system transformation described in Sec. \[SecLMCaCoord\]. The new probabilities are also listed in Table \[tab:prob\].

Because of the procedure, probabilities are nominally higher, on average, at second pericenter. This is because the LMCa debris spreads out further in phase space at second pericenter, thus 