This medieval fighting force, we'll just call them the Bruiser Army, uses only unarmed combat, but how are they still effective? They have absolutely no range compared to the spears and swords of their enemies, and much less range compared to the bows. Their method of fighting leaves them very vulnerable, certainly not good for winning battles. While I know that many knights did use unarmed combat in their fighting style, they obviously depended on their actual weapons more.
I do want the Bruiser Army to be effective, and consistent at that, but without making other armies simply incompetent or giving this army some kind of magic (I would prefer making magic a non-factor), I don't see a way to do that effectively. The main idea I thought of would be using fear tactics, but seeing as I want this army to go against other competent armies, with actual weapons, I'm questioning the effectiveness of those tactics.
So, is there any way to make them consistently effective against other competent armies despite these disadvantages? I don't expect this army to win every battle, but I don't want them to lose every battle either.
I believe it is important to mention that the Bruisers do have enough resources to be properly armored, gauntlets and all. They don't wield weapons because of strong cultural and religious reasons that stem from the heavy worship of the God of Unarmed Fighting and Savagery, Pugil.
As a last note, the Bruiser Army is willing to disarm their enemies and throw those weapons. However, they will not bring any kind of weapon with them or attempt to even use a weapon, aside from getting rid of it immediately, in order to honor their god.
Edit to answer comments: The Bruisers, which can be "giants" (to the realistic extent), do wear proper armor, and the gauntlets they wear can be heavily modified to increase their combat potential. Shields are acceptable for defensive purposes, but their fists should be the primary method of attack rather than shield bashing. Poisons could also be acceptable, but I'd prefer the idea of a teargas better than the idea of a lethal poison to emphasize unarmed combat.
If there isn't a way to make the Bruiser Army successful by itself (which it might come to that considering many factors addressed in Shadowzee's and other answers), then I could change them to be a subset of an army. Of course, I would try to exhaust all other possibilities before that, such as potentially engineering.