The risk, or probability of error, of the classifier produced by the AdaBoost algorithm is investigated. In particular, we consider the stopping strategy to be used in AdaBoost to achieve universal consistency. We show that provided AdaBoost is stopped after $n^{1-\varepsilon}$ iterations---for sample size $n$ and $\varepsilon \in (0,1)$---the sequence of risks of the classifiers it produces approaches the Bayes risk.