  Plastic events in sheared glasses are considered an example of so-called
avalanches, whose sizes obey a power-law probability distribution with the
avalanche critical exponent $\tau$. Although mean-field theory predicts a
universal value of this exponent, $\tau_{\rm MF}=1.5$, numerical simulations
have reported different values depending on the literature. Moreover, in the
elastic regime, it has been noted that the critical exponent can be different
from that in the steady state, and even criticality itself is a matter of
debate. Because these confusingly varying results were reported under different
setups, our knowledge of avalanche criticality in sheared glasses is greatly
limited. To gain a unified understanding, in this work, we conduct a
comprehensive numerical investigation of avalanches in Lennard-Jones glasses
under athermal quasistatic shear. In particular, by excluding the ambiguity and
arbitrariness that has crept into the conventional measurement schemes, we
achieve high-precision measurement and demonstrate that the exponent $\tau$ in
the steady state follows the mean-field prediction of $\tau_{\rm MF}=1.5$. Our
results also suggest that there are two qualitatively different avalanche
events. This binariness leads to the non-universal behavior of the avalanche
size distribution and is likely to be the cause of the varying values of $\tau$
reported thus far. To investigate the dependence of criticality and
universality on applied shear, we further study the statistics of avalanches in
the elastic regime and the ensemble of the first avalanche event in different
samples, which provide information about the unperturbed system. We show that
while the unperturbed system is indeed off-critical, criticality gradually
develops as shear is applied. Moreover, the critical exponent obeys the
mean-field prediction $\tau_{\rm MF}$ universally, once the system becomes
critical.
