  Using event-by-event hydrodynamic calculations, we find that the fluctuations
of the elliptic flow ($v_2$) in the reaction plane have a negative skew. We
compare the skewness of $v_2$ fluctuations to that of initial eccentricity
fluctuations. We show that skewness is the main effect lifting the degeneracy
between higher-order cumulants, with negative skew corresponding to the
hierarchy $v_2\{4\}>v_2\{6\}$ observed in Pb+Pb collisions at the LHC. We
describe how the skewness can be measured experimentally and show that
hydrodynamics naturally reproduces its magnitude and centrality dependence.
