  The martensitic transformation in Ni$_{2}$Mn$_{1+x}$Sn$_{1-x}$ alloys has
been investigated within ab-initio density functional theory. The experimental
trend of a martensitic transition happening beyond $x$ = 0.36 is captured
within these calculations. The microscopic considerations leading to this are
traced to increased Ni-Mn hybridization which results from the Ni atom
experiencing a resultant force along a lattice parameter and moving towards the
Mn atoms above a critical concentration. The presence of the lone pair
electrons on Sn forces the movement of Ni atoms away from Sn. While band Jahn
Teller effects have been associated with this transition, we show
quantitatively that atleast in this class of compounds they have a minor role.
