How did the number of british groups troops compare with the number of american troops

British troops were always fewer in number but they were very fierce soldiers. Many historians give accounts of how the british soldiers fought very bravely in the face of extremely unfavourable odds and sometimes also succeeded, mostly due to their bravery. However, in terms of sheer size, the British army was much smaller than the American one because Britain was a naval power more or less throughout its whole history and for that reason didn't really need a big and strong standing army. 

The dethroned emperor!