This paper develops a mathematical analysis of the performance of order statistic collusion attacks on Gaussian fingerprinting systems. The attacks considered include the popular memoryless averaging and median attacks as special cases. In this model, the colluders create a noise-free forgery by applying an order statistic mapping to each sample of their individual copies, and next they add a Gaussian noise sequence to form the final forgery. The choice of the mapping may be time-dependent and/or random. The performance of a strategy is evaluated in terms of the resulting probability of error of a correlation focused detector, and in terms of the mean-squared distortion between host and forgery. We prove the surprising fact that all the nonlinear attacks considered result in the same detection performance. Moreover, the linear averaging attack outperforms the other ones in the sense of minimizing mean-squared distortion.