What are the true numbers for the battle of the somme ?

it is held that german casualties at the somme were ranging from 468000 to 680000, while the allied casualties are 623000, many including winston churchill said that german losse were below 300000, again the british media still claims that they were 680000, how can the germans suffer so many casualties in a battle were they enjoyed great defensive stance and also minimized there casualties by applying the defence in depth theory and were the enemy's entire offensive plan was flawed and a third of vritish shells were duds and most fired shrapnels, what r the real german casualties ???