  Chiral Magnetic Effect (CME) is a phenomenon in which electric charge is
separated by a strong magnetic field from local domains of chirality imbalance
and parity violation in quantum chromodynamics (QCD). The CME-sensitive
observable, charge-dependent three-point azimuthal correlator $\Delta\gamma$,
is contaminated by a major physics background proportional to the particle's
elliptic anisotropy $v_2$. Event-shape engineering (ESE) binning events in
dynamical fluctuations of $v_2$ and event-shape selection (ESS) binning events
in statistical fluctuations of $v_2$ are two methods to search for the CME by
projecting $\Delta\gamma$ to the $v_2=0$ intercept. We conduct a systematic
study of these two methods using physics models as well as toy model
simulations. It is observed that the ESE method requires significantly more
statistics than the ESS method to achieve the same statistical precision of the
intercept. It is found that the intercept from the ESS method depends on the
details of the event content, such as the mixtures of background contributing
sources, and thus is not a clean measure of the CME.
