Statewide assessments in reading and math are required every year under the Every Student Succeeds Act (ESSA) of 2015, at an annual expense of billions of taxpayer dollars. Analyzing 10 years of school-level results from public schools in two states-- Nebraska and Texas--we found that year-to-year correlations of schools' test scores were exceptionally high, with reading and math correlations regularly above r = 0.9, indicating that little new information is derived from annual testing. Furthermore, while schools experiencing the largest demographic changes had significantly lower year-to-year correlations--highlighting the sensitivity of these scores to changes in underlying student demographics--even these lower correlations remained strong. We argue that the frequency of these tests may therefore be reduced, yielding substantial savings of time and money and no loss of useful information.