Before revision:  For labeled order types, this number has average 4- \frac{8 and variance at most 3. - The (labeled) order types read off a set of n points sampled independently from the uniform measure on a convex planar domain, smooth or polygonal, or from a Gaussian distribution are concentrated, i.e. such sampling typically encounters only a vanishingly small fraction of all order types of the given size.
After revision:  For labeled order types, this number has average 4- \frac{8 and variance at most 3. - The (labeled) order types read off a set of n points sampled independently from the uniform measure on a convex planar domain, smooth or polygonal, or from a Gaussian distribution are concentrated, i.e. such sampling typically encounters only a vanishingly small fraction of all order types of the given size.