The Battle of the Falaise Pocket ended the Battle of Normandy with a decisive German defeat. Hitler's involvement had been damaging from the first day, with his insistence on hopelessly unrealistic counter-offensives, micro-management of generals, and refusal to countenance withdrawal when his armies were threatened with annihilation. More than forty German divisions were destroyed during the Battle of Normandy. No exact figures are available, but historians estimate that the battle cost the German forces , of whom killed or wounded. The Allies had achieved victory at a cost of among the ground forces, including and . The Allied air forces lost killed or missing in connection with Operation Overlord. The final battle of Operation Overlord, the Liberation of Paris, followed on 25 August, and Overlord ended by 30 August, with the retreat of the last German unit across the Seine.