Since the hash is derived purely from the password, it demonstrably does not have any more entropy than the password. Before you mention the salt - the salt is

Since the hash is derived purely from the password, it demonstrably does not have any more entropy than the password. Before you mention the salt - the salt is only useful if it if available. The client needs to know the salt in order to perform the calculation, therefore your attacker will also know the salt, so that doesn't count as entropy in the hash, either.