There are many studies on the performance of binary fingerprinting codes under a well-known marking assumption. Among many fingerprinting codes, we focus on Tardos codes and Nuida's variants. From the signal processing point of view, the relaxation of the assumption is required for the analysis. In this paper, we consider the averaging attack which has been studied in the spread-spectrum-based fingerprinting schemes, and propose an optimal detector based on a maximum likelihood decoding. From our theoretical analysis about the effect on a pirated codeword caused by the averaging attack, it is revealed that the false-positive probability is strongly dependent on the number of colluders.