Atomistic simulation of the 1-octene polymerization reaction by a (pyridylamido) Hf(IV) catalyst was conducted on the basis of Red Moon (RM) methodology, focusing on the effect of the counteranions (CAs), MeB(C6F5)(3)(-), and B(C6F5)(4)(-), on the catalyst activity and chain termination reaction. We show that RM simulation reasonably reproduces the faster reaction rate with B(C6F5)(4)(-) than with MeB(C6F5)(3)(-). Notably, the initiation of the polymerization reaction with MeB(C6F5)(3)(-) is comparatively slow due to the difficulty of the first insertion. Then, we investigated the free energy map of the ion pair (IP) structures consisting of each CA and the cationic (pyridylamido)Hf(IV) catalyst with the growing polymer chain (HfCat(Pn+)), which determines the polymerization reaction rates, and found that HfCat(Pn+)-MeB(C6F5)(3)(-) can keep forming "inner-sphere" IPs even after the polymer chain becomes sufficiently bulky, while HfCat(Pn+)-B(C6F5)(4)(-) forms mostly "outer-sphere" IPs. Finally, we further tried to elucidate the origin of the broader molecular weight distribution (MWD) of the polymer experimentally produced with B(C6F5)(4)(-) than that with MeB(C6F5)(3)(-). Then, through the trajectory analysis of the RM simulations, it was revealed that the chain termination reaction would be more sensitive to the IP structures than the monomer insertion reaction because the former involves a more constrained structure than the latter, which is likely to be a possible origin of the MWDs dependent on the CAs.