Phylogenetic trees are frequently used in biology to study the relationships between a number of species or organisms. The shape of a phylogenetic tree contains useful information about patterns of speciation and extinction, so powerful tools are needed to investigate the shape of a phylogenetic tree. Tree shape statistics are a common approach to quantifying the shape of a phylogenetic tree by encoding it with a single number. In this article, we propose a new resolution function to evaluate the power of different tree shape statistics to distinguish between dissimilar trees. We show that the new resolution function requires less time and space in comparison with the previously proposed resolution function for tree shape statistics. We also introduce a new class of tree shape statistics, which are linear combinations of two existing statistics that are optimal with respect to a resolution function, and show evidence that the statistics in this class converge to a limiting linear combination as the size of the tree increases. Our implementation is freely available at https://github.com/WGS-TB/TreeShapeStats.