This isn't really an answer to the question you're asking, but I got a pretty strong impression from the fluff in MToF that the devils are losing--almost to a point that the Blood War is a story of desperation for them:
(from MToF)
Avernus—"Zariel rules over the ruin that Avernus has become. Once it was a bustling realm filled with cities, trade outposts, and other features, but recent activity in the Blood War has reduced it to a blasted wasteland."
Minauros—"The layer of Minauros teeters on the edge of ruin. The realm is a great swamp, interspersed with cities and fortresses that are in constant need of repair, upkeep, and replacement. Time and again, structures built on this layer are left untended and are eventually drawn into the bottomless muck of the swamp. Mammon refuses to spend any more coin than necessary to keep the soul marketplace in the Sinking City functioning."
Maladomini—"Maladomini was wracked with fighting as the other Lords of the Nine took to the field against the conspirator. The resulting devastation left much of the layer in ruins"
Stygia—"Stygia has become a war-wracked realm. Any devils bound to either of the archdevils that aren't needed for service in the Blood War engage in constant skirmishes across the ice, Every other layer of the Nine Hells has a function related to warfare, industry, administration, or commerce, but Stygia is an expanse of untamed, unimproved territory."
Cania—"Mephistopheles and his devotees prefer to conduct their studies in a wasteland where they can unleash gouts of arcane energy without destroying anything important. Experiments involving new spells, new magic items, and other innovations for the infernal arsenal regularly cause localized cataclysms in this place."
Nessus—"By design, the place is devoid of activity"
That's six out of nine layers which have been destroyed by armed conflict or neglect, or are basically empty of productive enterprise, with a clear implication that things in Baator used to be better but that the plane's hopeless leadership shows no sign of turning things around.
I don't see them winning.