The World Trade Organization (WTO) features prominently in studies of international institutions, although it is often over-simplified either as a tool of rich world domination over the global South or as the only stop-gap preventing a breakdown in the international system. This article analyzes how the WTO has sought legitimacy for itself and for the underlying institution of free trade in the midst of questions regarding its organizational mandate and the management of international trade negotiations. Initially, legitimacy appeared to derive from an expanding membership and the lowering of tariffs in progressively more categories of goods and services. More recently, legitimacy comes from institutional deepening by means of dispute resolution procedures and rulings by the dispute settlement body. This shift, it is argued, raises foundational questions of expertise, the relationship of models to real-world outcomes, and methods for bounding disputes over scientific and economic facts. Based on a case study of Brazil's interaction with the WTO - especially in a decade-long claim against U.S. cotton subsidies - and a trend analysis of over 400 total WTO disputes, I argue that the WTO dispute process is helping to legitimize the institution of free trade through its public display of rational authority and neutral expertise. At the same time, dispute panels have begun to pass judgment on issues of scientific and econometric uncertainty. As a result, the basis for dispute judgment and the broader legitimacy of the WTO is shifting from questions of representation that have long drawn the attention of critics and WTO leaders to epistemological issues, especially concerning the basis of expertise and the design of econometric models. This article provides insights on the resolution of disputes in global trade while contributing to our understanding of the evolving role of scientific and econometric modeling at internation