In Washington's Crossing, what made the Battle of Trenton a bloody but decisive American victory?
The key to Washington's success at the Battle of Trenton in December of 1776 was surprise. No one could have expected Washington's beaten, shrinking and demoralized army to be able to successfully cross the river--onto the same side as the massive 20,000 strong force under General Howe--and march on a force of experienced, tough mercenaries such as the Hessians guarding the city.
It was Christmas morning, and many of the Hessians were hung over. This was their day off, they had celebrated the night before, and they were supremely overconfident. This was garrison duty after all, and they were only expected to watch the colonials across the river so that they did not escape while Howe waited for the river to freeze.
This is what makes Washington's attack so brilliant. He had no alternative, he went against every rule of military training he had received and took the Hessians completely by surprise. What made it bloody was that much of the fighting was hand to hand combat, house to house, where bayonets and pikes were used in place of rain-soaked gunpowder.
For the record, the Continental Army's victory over Hessian mercenaries at the Battle of Trenton was anything but 'bloody,' especially for the Americans. Washington's troops suffered fewer than 10 casualties, while German killed and wounded numbered less than 100. Considering that 4,000 soldiers went at each other the battle hardly qualifies as a blood bath.
As for the decisiveness of Trenton, the battle's truth worth to the American cause was that it proved a significant morale booster to a seriously demoralised army. It also encouraged a surge in enlistments, which gave Washington's tired little army new life and new hope for the future of the war.