America’s Most Challenging High Schools ranks schools through an index invented by Washington Post education columnist Jay Mathews. The index formula is a simple ratio: The number of Advanced Placement, International Baccalaureate and Advanced International Certificate of Education tests given at a school in 2013, divided by the number of graduates that year. Noted in our national and local tables is the percentage of students eligible for government meal subsidies — a common benchmark for poverty — and each schools’s average SAT score, a common college entrance exam with a national average of 1498 out of 2400. This year, the list also notes whether each school has an 11-person football team as an indicator of changing school cultures, the subject of Mathews’ analysis of the 2014 results. The list includes some private schools — noted with a (P) — for comparison. Certain public schools with highly selective admissions are omitted from the list, but information about them can be found online, along with full local and national lists, at www.washingtonpost.com/highschoolchallenge.