  We present a powerful formalism, disordered collective dynamics using
truncated equations (d-CUT-E), to simulate the ultrafast quantum dynamics of
molecular polaritons in the collective strong coupling regime, where a
disordered ensemble of $N\gg10^{6}$ molecules couples to a cavity mode.
Notably, we can capture this dynamics with a cavity hosting a single
\textit{effective} molecule with $\sim N_{bins}$ electronic states, where
$N_{bins}\ll N$ is the number of bins discretizing the disorder distribution.
Using d-CUT-E we conclude that strong coupling, as evaluated from linear
optical spectra, can be a poor proxy for polariton chemistry. For highly
disordered ensembles, total reaction yield upon broadband excitation is
identical to that outside of the cavity, while narrowband excitation produces
distinct reaction yields solely due to differences in the initial states
prepared prior to the reaction.
