You make some good points however on Prussia they certainly didn't have any role in almost dominating the world in this period. They did have a very modern army however the British have always been renowned for the training, professionalism, and discipline of it's soldiers. There are accounts form American rebels of how scared they were of the British advance as they would continue to advance outnumbered, soldiers would ignore men dying in their ranks and continue to advance with blank faces. Then you have the Highland regiments and Ghoorkas, some of the most renowned fighters in world. In terms of world domination, the largest powers were the British Empire, France, Spain, Ottoman Empire, Russia(?). Britain being the largest, controlling both the most land and sea.