An improved adaptive authentication technique involves defining a window array which stores the number of distinct fact values per time unit over a predetermined number of time units. Each element of the window array has a value set to the number of distinct fact values over a time unit. The window array is stored in a database. Under the improved technique, upon a user initiating an authorization request, the risk engine extracts the request and the window array from the database into a cache on the authorization server. The risk engine uses the request which contains a value of the fact to adjust values of the elements of the window array and, once the adjusting is completed, computing the fact velocity which is used in the determination of a risk score for the request.