There is almost no way that this can be objectively measured and answered. Generally speaking, the British were very confident at the onset of the war, the British army was well trained, possibly one of the finest professional armies in the world at the time but it was relatively small, in fact less than 50 000 men in all. Britain also had the worlds largest and most modern navy. Added to this, Britain had experienced political leadership and relatively sound finances. Seen from this perspective, all was well for Britain.

However, Britain also had several factors working against them. One was the lack of major allies, distance was another. It could take months for reinforcements, supplies and orders to reach the British troops. This is a major problem, especially for communications as orders could very well be vastly out of date by the time they arrived.

While the British could largely rely on the Navy for supplies, this only functioned while they kept to the coast or major waterways. Moving inland proved a huge logistical challenge. The British also suffered from disciplinary problems, especially as new recruits were brought from England with little training, discipline and motivation (it is worth noting in this context that Britain had a huge recruiting problem, convicts were often pardoned in exchange for military service, drunks and other "dregs of society" frequently made up a sizeable portion of the recruits.

Added to this, the British army was used to fighting a European style of warfare where a victory was often achieved by capturing a major strategic objective (often a major city). Europe was far more centralized than the colonies were at the time. Capture of such a point usually marked the conquest of the entire region. In North America the majority of the population was rural, capture of a major city did not have the same effect on the region as it did in Europe. This, combined with the logistical problems of the British army whenever it attempted to move inland, meant that it could not effectively capture and pacify regions the same way it had done in the past.

The British army had a great deal of experience in dealing with rebellions, however, it had not previously encountered a political situation such as the one in North America. Loyalists and Patriots often came from the same areas, this meant that the British could not use the same harsh suppression of rebellious areas as it had done in the past (for example in Ireland and Scotland) as it would have meant losing Loyalist support.

Generally speaking, there is no consensus on the odds of a British or Patriot victory among historians. Some, such as Ferlig, argue that the Patriot victory was a miracle, others, such as Ellis question whether a British victory was ever realistically possible after the summer of 1776. Personally I tend to agree with Ellis in general terms. The British had one opportunity to crush the rebellion once and for all, this would probably have weakened patriot support and strengthend loyalist support which might have tipped the scales. Still, such speculation tends to end up in the field of "what if"-history.

John E. Ferling - Almost A Miracle: The American Victory in the War of Independence
Joseph J. Ellis - Revolutionary Summer: The Birth of American Independence
Richard W. Stewart, - American Military History Volume 1 The United States Army And The Forging Of A Nation, 1775-1917
Pole and Greene - Companion to the American Revolution
Paul Smith - The American Loyalists: Notes on Their Organization and Numerical Strength
Jeremy Black - War for America: The Fight for Independence, 1775–1783