Although the policy and methodological legacy of "Equality of Educational Opportunity," the so-called Coleman Report published by the US Department of Education in 1966, is widely recognized, the way in which it played a role in shaping theorizing about equality of educational opportunity has been less well-explored. This article reconsiders the Coleman Report in light of how it has contributed to the framing of how we think about the very idea of equality of educational opportunity and its normative capacity to evaluate the education system. The main argument is that the Coleman Report helped to crystallize the concept of equality of educational opportunity as being fundamentally about how education provides ladders of opportunity and enables upward mobility for socially disadvantaged students. This framing has, however, created certain normative blind spots that have seriously impeded its ability to engage certain issues in education. The normative blind spot singled out, in particular, is the competitive structure of the current education system--the school system is structured so that some children win, while some lose. The competitive nature of schools has often been challenged, from a wide range of perspectives, but rarely utilizing an equality of opportunity framework. Given this normative blind spot, the more constructive dimension of the article is to advance an alternative theory of equality of educational opportunity that is better able to function as a regulative ideal for competition in the education system, one that identifies standards or principles of fairness to guide policy on how to deal fairly with winners and losers.