  A Bayesian inference analysis is performed to quantify the pion excess in the
low transverse momentum ($p_{\rm T}$) regime in heavy-ion collisions. This
quantification is conducted across centrality classes and collision systems at
the LHC and top RHIC energy. The analysis is based on the relativistic fluid
dynamics description of $p_{\rm T}$ spectra of identified charged hadrons. A
$p_{\rm T}$ range scan investigation to determine the optimal range for the
pion $p_{\rm T}$ spectra with respect to a fluid dynamic description is
performed, finding 0.5~$< p_{\rm T} < $~2.0~GeV$/c$. A significant low-$p_{\rm
T}$ pion excess is computed across all centrality classes and collision systems
investigated, indicating that a clear low-$p_{\rm T}$ component arises from
different physics mechanisms, rather than thermal production. Further
comparison with measurements by the PHOBOS Collaboration confirms the
persistence of the pion excess into very low-$p_{\rm T}$, with no enhancement
observed in kaons and protons within the current experimental precision.
