In phylogenetic tree construction the neighbor-joining algorithm is the most well known method which constructs a trivalent tree from a pairwise distance data measured by DNA sequences. The core part of the algorithm is its cherry picking criterion based on the tree structure of each quartet. We give a generalized version of the criterion based on the exact box model of quartets, known as the tight span of a metric. We also show by experiment why neighbor-joining and the quartet consistency count method give similar performance.