With better statistics and precision, eccentricity could prove to be a useful tool for understanding the origin and environment of binary black holes. Hierarchical triples in particular, which might be abundant in globular clusters and galactic nuclei, could generate observably large eccentricity at LIGO and future gravitational wave detectors. Measuring the eccentricity distribution accurately could help us probe the background and the formation of the mergers. In this paper we continue our previous investigation and improve our semianalytical description of the eccentricity distribution of mergers of hierarchical triple systems. Our result, which further reduces the reliance on numerical simulations, could be useful for statistically distinguishing different formation channels of observed binary mergers.
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