The Ram-Yip formula gives a combinatorial expression for the nonsymmetric Macdonald polynomials in terms of alcove walks; in type A, the Ram-Yip formula is related though not identical to the combinatorial formula of Haglund, Haiman, and Loehr. In joint work with Mark Shimozono, we extend the Ram-Yip formula to arbitrary (not necessarily reduced) affine root systems. By specialization we obtain a formula for the nonsymmetric Macdonald polynomials at t equal to infinity. The terms that survive this specialization are captured by a condition involving the quantum Bruhat graph. As a consequence we obtain the q-positivity of the coefficients of nonsymmetric Macdonald polynomials at t=infinity. In this talk I will discuss these results as well as a conjecture giving a representation-theoretic interpretation of this q-positivity.