In today's Internet, a large part of the traffic is carried using the TCP transport protocol. Characterization of the variations of TCP traffic is thus a major challenge, both for resource provisioning and Quality of Service purposes. However, most existing models are limited to the prediction of the (almost-sure) mean TCP throughput and are unable to characterize deviations from this value. In this paper, we propose a method to describe the deviations of a long TCP flow's throughput from its almost-sure mean value. This method relies on an ergodic large-deviations result, which was recently proved to hold on almost every single realization for a large class of stochastic processes. Applying this result to a Markov chain modeling the congestion window's evolution of a long-lived TCP flow, we show that it is practically possible to quantify and to statistically bound the throughput's variations at different scales of interest for applications. Our Markov-chain model can take into account various network conditions and we demonstrate the accuracy of our method's prediction in different situations using simulations, experiments and real-world Internet traffic. In particular, in the classical case of Bernoulli losses, we demonstrate: i) the consistency of our method with the widely-used square-root formula predicting the almost-sure mean throughput, and ii) its ability to additionally predict finer properties reflecting the traffic variability at different scales.