The Battle of Bunker Hill, although considered a British victory, is a Pyrrhic one as the British actually lose more men (and more officers) than the Americans. Note that the Americans fielded an inexperienced militia army to square with experienced British regular army troops. The British overwhelmed colonial positions in the hills surrounding Boston, but sustained plenty of casualties in doing so, including plenty of their officers. The battle made Americans realize that their under-equipped colonial militia armies can fight against the British.