Botnets such as Mirai use insecure home devices to conduct distributed denial of service attacks on the Internet infrastructure. Although some of those attacks involve large amounts of traffic, they are generated from a large number of homes, which hampers their early detection. In this paper, our goal is to answer the following question: what is the maximum amount of damage that a DDoS attacker can produce at the network edge without being detected? To that aim, we consider a statistical hypothesis testing approach for attack detection at the network edge. The proposed system assesses the goodness of fit of traffic models based on the ratio of their likelihoods. Under such a model, we show that the amount of traffic that can be generated by a covert attacker scales according to the square root of the number of compromised homes. We evaluate and validate the theoretical results using real data collected from thousands of home-routers connected to a mid-sized ISP.