Raman side scatter, whereby scattered light is resonant while propagating perpendicularly to a density gradient in a plasma, was identified experimentally in planar-target experiments at the National Ignition Facility at intensities orders of magnitudes below the threshold for absolute instability. We have derived a new theoretical description of convective Raman side scatter below the absolute threshold, validated by numerical simulations. We show that inertial confinement fusion experiments at full ignition scale, i.e., with mm-scale spot sizes and density scale lengths, are prone to increased coupling losses from Raman side scatter as the instability can extend from the absolute regime near the quarter-critical density to the convective regime at lower electron densities.