Off the bat, I can think of three areas of efficiency to measure: provisioning, troop retention, and combat ability.

Provisioning

One of the things that's hardest to imagine about the past is scarcity. The industrialized world is, for the most part, a post-scarcity society when it comes to material goods. This was not the case during the Revolution. Feeding and dressing an army was a complex task that involving dozens (if not hundreds) of contracts, even when well-executed and well-funded, could deplete a region's resources in a matter of months.

The Continental Army suffered from a lack of funding throughout the war, and few (if any) Americans had experience in running logistical operations on the scale of an army. As such, provisioning was often terrible in the early days of the war. Joseph Plumb Martin, who wrote the most famous memoir of a Revolutionary soldier, often complained about going days without food. Hungry men with guns will often find a way to get food, of course, and thus plundering was endemic around the army, particularly when it stopped maneuvering and settled into winter camps. The constant threat of theft did nothing to endear the army, or the Revolution, to the civilian population.

The biggest obstacle to the army's efforts to feed and clothe itself was the fact that many American farmers and merchants would only except hard currency (gold and silver coins). The economy of colonial America ran largely on credit; with few having big cash reserves, trading favors and IOUs was the preferred method of doing business. That the Congressional treasury was largely empty meant that the Continental Army would hang on the brink of starvation while surrounded by some of the most productive farms in the country.

The horrors of the winter at Valley Forge prompted the army to make a major overhaul to its supply system. While the army would not live off plunder, as the armies of the French Revolution would do a few decades later, the army formalized a system of confiscated compensation. Essentially, they would tell farmers that they could either seize grain and livestock outright, or pay them with IOUs or paper money. Nearly everyone accepted the IOUs, and Congress did a good enough job paying a few people back that others remained patient with the system. After 1778, French gifts and loans pumped enough money into the American cause that the army was able to feed itself through more conventional means.

In terms of weaponry, the Continentals first armed themselves with whatever muskets they could collect, and cannons taken out of British arms caches (Fort Ticonderoga in particular). While the states commissioned some American-made copies of the British Brown Bess, French weapons were far more common. American merchants teamed with Pierre-Augustin Caron de Beaumarchais (author of the play The Marriage of Figaro, amongst others!) to smuggle weapons and ammo to America starting in 1776. This was replaced with open aid from France in 1778. By the end of the war, American soldiers were carrying French weapons, dressed in French wool, and paid with French money.

Troop Retention

The American Revolution, ideologically, sprang from the Enlightenment. The political thinking of this movement generally held that standing armies can only lead to tyranny, and that a virtuous people need only to commit to the idea of a defensive militia to keep themselves safe. It's a lovely idea, but it turns out that the virtue and commitment of a militia tends to evaporate when the weather turns cold and they start losing battles.

Trying to keep the Continental Army as militia-like as possible, the states first offered army enlistments of a few months, or a year at maximum. Uncertainty about when the men would be released from service, and troops developing a short-timer mentality (to use a Vietnam-era phrase) and not wanting to risk death when they only had a few days/weeks left to serve, hamstrung the American invasion of Quebec at the end of 1775, and almost led to the main army dissolving completely after fleeing New Jersey in the last days of 1776. Only Washington's desperate pleading with his men, and a stinging victory at Trenton on Christmas Day 1776, kept the army together.

These two near-disasters helped convince Congress that they needed a more serious, regular force if they ever hoped to beat the British. They eventually settled on two different enlistment terms: three years, or for the duration of the war. By the end of the war, more than half of the army had enlisted for the duration. These longer hitches gave Washington and the other American commanders a stable manpower pool and allowed soldiers to stay in long enough to develop proficiency in drill, arms, marching, and making camp. Considering that much of the latter half of the war in the North consisted of the Americans staying in garrison for long stretches of time, leaving only to block British foraging expeditions or trying to draw them into a trap, the improved ability of the army to sustainably exist was more important than it might appear.

Combat Ability

The Continental Army lost more battles than it won. Still, across the eight years of its existence, it did see a rapid growth in military competence. The biggest change, famously, came at the Valley Forge encampment of 1777-1778, when Washington appointed Prussian officer Baron von Steuben as Inspector General of the Army. Von Steuben developed both a simplified drill and a method for teaching it, which became standard for the entire army. Von Steuben's leadership, coupled with the camaraderie of longer service and the pride of overcoming shared hardship, helped instill in the Continentals the espirt de corps necessary for regimental formations to hold together in the face of musket volleys, artillery barrages, and bayonet charges.

The Continentals first got to put their post-Valley Forge skills on display at Monmouth, where they fought the rear guard of the British army to a draw (whether the Continentals ever had a real shot at winning the battle is a matter of some debate). During the battle, the British Grenadier Battalion attacked a line of American troops in the manner to which they had become accustomed: marching in relatively close, firing a single volley, and charging with the bayonet. In previous battles, this had never failed to scatter an American line. At Monmouth, the Continentals held, and the Grenadiers suffered heavy casualties, including the loss of their colonel.

Between Monmouth and Yorktown, Northern body of the Continental army only embarked on one major offensive operation: the invasion and devastation of Iroquois country in Western New York. The Continentals won the only pitched battle of this campaign, but were more generally effective in their ability to destroy every physical trace of Iroquois habitation across much of their territory. They drove the Iroquois entirely into the hands of the British, clustered outside Fort Niagara or camps in Canada.

The Southern Department of the Continental Army, bolstered by frequent reinforcement from the North, fought Cornwallis' army from their initial conquest of Savannah to the surrender at Yorktown. In these campaigns, the army developed a way of war that minimized the cost and impact of defeat while making their victories count. The army maintained cohesion as it led the British on a chase across North Carolina and Virginia, while scoring a stinging victory at Cowpens and inflicting a Phyrric victory on the British in the woods around Guilford Courthouse.

Washington's march to Virginia was a masterstroke. In the summer of 1781, Washington rendezvoused with French army in the lower Hudson Valley. After a failed attempt to draw the British out of their defenses into a general engagement on the day of the rendezvous (sneaky sneaky), Washington was able to quietly sneak most of his army into New Jersey before the British caught on. By that time, the allied army had enough of a head start that the British commander-in-chief, Sir Henry Clinton, considered the Americans' lead insurmountable. The main British army sat bottled in New York as the allies laid siege to Yorktown.

Yorktown was the one formal large-scale siege the Continentals ever got to do, but they did successfully construct siege trenches around the British. This paved the way for a bombardment that British officers described as unusually accurate. Once their trenches got close enough, the Continentals launched a bayonet attack against one of the British outer works. This is all pretty technical stuff, and would have lain far outside the capacities of the early-war army.

Sources

Wayne Bodle, The Valley Forge Winter

James Kirby Marin an Mark Edward Lender, A Respectable Army

Matthew Spring, With Zeal and with Bayonets Only