I am using ‘corps’ here in one of its British senses, such as the Royal Army Service Corps or the Royal Army Medical Corps.
The arms (infantry, artillery, armour) are the obvious candidates for contributing most as they do all the fighting.
But if men aren’t fit to fight then they’re useless, so the medical services become important, from avoiding or reducing disease by field hygiene to providing medical services. In New Guinea in WWII the ratio of disease to battle casualties exceeded 30:1 at times, which was reduced by medical corps instituted measures as simple as rolling down sleeves before dusk to minimise bites by malarial mosquitoes.
But if the medical services and the men in the arms don’t receive supplies then often they can’t peform their functions effectively.
Then there are the field engineers who clear obstacles for the arms and the mechanical engineers who keep the machines moving and various other corps which all contribute to the needs and operation of an army.
Frankly, I don’t think that one can identify any one corps as contributing the most to an army’s effectiveness as they are all necessary parts of the whole army. But I think that far too little attention is paid in much amateur military history to the people behind the battlefield scenes whose efforts were crucial to battlefield actions.
Nowadays they become even more remote in functions maybe even a couple of continents away from the action in running electronic monitoring or control systems which inform or aid battlefield commanders and leaders even down to platoon level.
And the reality is that even during WWII the vast bulk of troops, or at least Allied troops, never got anywhere near a battle because most troops were engaged in rear area activities supporting the front line troops.
While it’s fun for people to disparage them as REMFs, it might be the case that, for example, an Allied transport driver who kept up his effort from mid-1944 to Germany’s surrender made a measurable and vastly greater contribution to Germany’s defeat than some poor bastard who got shot dead or wounded and taken out of the war on a Normandy beach on D Day.
So, do we measure effectiveness and contribution solely by the intensity of front line conflict and the viciousness of that conflict or by other factors which, on a more dispassionate assessment, evaluate all the factors and corps which contributed to achievement of the aim?
Do we make the mistake of equating military effectiveness or military importance with the scale or intensity of battle, which is always attractive and interesting to most amateur military historians, rather than evaluating the wider issue of overall effectiveness judged by the cohesion of all corps, most of which are not engaged in battle, in achieving the aim?
They usually are far stronger, in different places, and have much higher morale than we think. Just ask the “poor bloody infantry!”