What was the outcome the british were looking for from the battle of saratoga?

The British army under General Burgoyne (sp) with its British regulars, Hessians, and Loyalist regiments was cut off by Colonial Continental regiments and militia regiments and after hard fighting was forced to surrender north of Albany. 
An entire British army was taken as prisoners of war. The British attempt to split the American colonies by way of Lake Champlain and the Hudson was utterly defeated. 
Along with Washington's defeat at Germantown, where the French actually thought Washington's army had fought rather well, the complete victory at Saratoga convinced the French government to declare war on England and ally with the Continental Congress and the rebels. This brought the French army, French navy and a whole lot of financial support into the American caus