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In high energy proton-nucleus collisions, the gluon saturation effects fromthe nucleus are fully incorporated into the light-like Wilson lines. The gluonsaturation effects from the proton, which are anticipated to be importanteither in the extreme high energy limit or towards the dense-dense(nucleus-nucleus) collision regimes, have been studied perturbatively withinthe Color Glass Condensate effective theory in previous papers of this series.A configuration-by-configuration expression for the single inclusive semi-hardgluon production including the first saturation correction was obtained. Inthis paper, we perform ensemble averaging in the McLerran-Venugopalan model andthe Dipole Approximation. We find that, in the saturation correction, theeffects of the initial state interactions are negligible while the final stateinteractions play most important role and give a positive-valued contributionto the semi-hard gluon spectrum. Furthermore, we show that the single gluonspectrum scales approximately $1/k_{\perp}^{4}$ at small $k_{\perp}$,suggesting that a resummation of higher order saturation corrections isrequired to regulate the infrared region of the gluon spectrum.

First saturation correction in high energy proton-nucleus collisions: Part III. Ensemble averaging