We introduce a new framework for web page ranking -- reinforcement ranking -- that improves the stability and accuracy of Page Rank while eliminating the need for computing the stationary distribution of random walks. Instead of relying on teleportation to ensure a well defined Markov chain, we develop a reverse-time reinforcement learning framework that determines web page authority based on the solution of a reverse Bellman equation. In particular, for a given reward function and surfing policy we recover a well defined authority score from a reverse-time perspective: looking back from a web page, what is the total incoming discounted reward brought by the surfer from the page's predecessors? This results in a novel form of reverse-time dynamic-programming/reinforcement-learning problem that achieves several advantages over Page Rank based methods: First, stochasticity, ergodicity, and irreducibility of the underlying Markov chain is no longer required for well-posedness. Second, the method is less sensitive to graph topology and more stable in the presence of dangling pages. Third, not only does the reverse Bellman iteration yield a more efficient power iteration, it allows for faster updating in the presence of graph changes. Finally, our experiments demonstrate improvements in ranking quality.