What was the Number of fighting men on each side in the Saratoga battle?

In the First Battle of Saratoga (Freeman's Farm) on September 19, 777 the British army numbered about 7,200 men; and the America army numbered about 9,000.
The Americans were defeated; and both sides entrenched and awaited reinforcements.

In the second Battle of Satratoga (Bemis Heights) on October 7, 1777 the American Army had been heavily reinforced and the expected British relief had failed to arrive. The British army now numbered about 6,600; and the American army numbered over 12,000.
The British army was defeated.