Conventional sketching methods on counting stream item frequencies use hash functions for mapping data items to a concise structure, e.g., a two-dimensional array, at the expense of overcounting due to hashing collisions. Despite the popularity, however, the accumulated errors originated in hashing collisions deteriorate the sketching accuracies at the rapid pace of data increasing, which poses a great challenge to sketch big data streams at web scale. In this paper, we propose a novel structure, called XY-sketch, which estimates the frequency of a data item by estimating the probability of this item appearing in the data stream. The framework associated with XY-sketch consists of two phases, namely decomposition and recomposition phases. A data item is split into a set of compactly stored basic elements, which can be stringed up in a probabilistic manner for query evaluation during the recomposition phase. Throughout, we conduct optimization under space constraints and detailed theoretical analysis. Experiments on both real and synthetic datasets are done to show the superior scalability on sketching large-scale streams. Remarkably, XY-sketch is orders of magnitudes more accurate than existing solutions, when the space budget is small.