A new approach to evaluating changes in Equality of Opportunity is introduced which permits the examination of the degree of dependence of child outcomes on many circumstances. Its advantages over more standard techniques of economic and social mobility analyses are discussed and the approach is exemplified in a study of the grade level attainments of 18 year olds in the face of a list of circumstances (gender, family income, parental education status, family type (intact marriage, divorced-separated and widowed single parent environments)) over the period 1960 - 2000. This was a period during which much school policy (Title 1 - No Child Left Behind) and family law changes (Movement from Maternal Preference to Joint Custody arrangements in settlements) were directed at increasing the mobility of the poorly endowed. Gains were made in all categories throughout the period, more so for boys than girls (though girls were better off in an EO sense to start with), more so for children in single parent circumstances and more so for the poorly endowed.