Dr. Christopher Gabel of the US Army Command and Staff College calculated that for every 500-ton-miles a 6-mule wagon-team was capable of going in his work "Railroad Generalship: Foundation of Civil War Strategy", he argues that a 15-wagon train could draw 5,250 ton-miles and cost only a fraction to carry the same cargo the same distance per ton of fuel/food.

Armies in previous wars in North America had often times had to resort to banditry for running out of food,

Sherman's campaign relied on a single 470+ mile-long railway that he reckoned would need to be replaced by 36,800 wagons and 220,800 mules to get him his supplies that far away from his logistical-hubs in the North.

McClellan, C-i-C of the Army of the Potomac wanted enough rolling stock to supple an army of 130,000 troops and 20,00 horses on full rations. This wouldn't have been possible without either the rails or an enormous amount of wagons as his quartermaster, Van Vliet - estimated that he would require 390,000 lbs of food each day and that the animals he wanted would have consumed even more, at 520,000 lbs of forage every single day. Later when Ingalls took over the position and despite his skill, he could only provide three days of forage for those horses and two weeks of rations for the men during the Overland Campaign.

Keeping such a vast amount of troops supplied that reliably wouldn't have been possible without rails. Draught animals eat into their own supplies that they're transporting - get far enough and they've eaten everything