What were the results of the Battle of Saratoga?

The British failed to cut off the New England colonies, The French came in on the side of the colonies and Benedict Arnold was set on the path to becoming a traitor.
The British plan to drive a wedge between the New England colonies and the rest of the American Colonies was stopped at the battle of Saratoga. The British were defeated and surrendered their entire army that was driving down the Hudson River. If the British had won the battle of Saratoga the British would have controlled the Hudson River Valley cutting New England off from the rest of the Colonies. This probably would have won the war for England.
The victory of the American armies at Saratoga convinced the French that the Americans had a chance of defeating the British. The French wanted a chance to hurt the British who had defeated the French in the French and Indian wars. The French involvement in the American Revolution was pivotal in the final American victory and independence. Without the battle of Saratoga the French would not have joined the Americans.
Benedict Arnold became very bitter toward the America leadership as a result of the battle of Saratoga. Benedict Arnold actually won the battle but General Gates got the credit for the victory. This insult may have been the beginning of what caused Benedict Arnold to become a traitor.