Based on the previous section, one can extract the polariton line widths with respect to different detunings. Experimentally, there are two characteristic phenomena associated with motional narrowing : (1) the subaverage behavior for both the UP and the LP, and (2) the asymmetric linewidths between the UP and the LP. In this section, we explore these effects via both the numerical exact simulations and the analytic linewidth expressions in Eq. 34 (for LP) and Eq. 35 (for UP). 2, 4, 8, respectively. One can see that for all panels, the analytic expressions agree well with the numerical exact simulations for the linewidth of both UP and LP states. And the subaverage behavior is well captured as both linewidths are lower than the silver dashed line in our simulations, but more impressively, for the analytic answer to semi-quantitatively describe them. As N increases, the subaverage behavior for the UP and the LP linewidth become more pronounced. This is because, with a larger N , λ N is smaller (see Eq. 27) so that the exciton contribution to the linewidth becomes smaller (which scales as 1/N in the fast limit considered in the model here) in the polaron decoupling regime. Further, the difference between the UP and the LP linewidth becomes larger, because a larger number of dark states are presented thus more channels for inter-branch transitions. Here, the LP is generally narrower than the UP except for the N = 1 case (when there is no dark state).