Ice is a poor conductor of heat. This means that thermal energy of the liquid medium will be exchanged between the ice near the surface of the ice body/bodies.

Ice is a poor conductor of heat. This means that thermal energy of the liquid medium will be exchanged between the ice near the surface of the ice body/bodies. Thus, the rate at which the ice accepts energy from the alcohol is determined by the surface area of the bodies of ice. A single sphere of ice produces the lowest possible surface area. On a graph of drink temperature vs time, crushed ice (highest surface area) would produce a large dip and then level out. The orb would create a broad valley of lower temperature, though never as cold as the crushed ice.