Unlike the matching strategy of minimizing dissimilarity measure between descriptors, Lowe, while introducing the SIFT-method, suggested a more effective matching strategy using the ratio between the nearest and the second nearest neighbor. It leads to excellent matching accuracy. Unlike all these strategies that rely on deterministic formalism, some researchers have recently opted for statistical analysis of the matching process. The cornerstone of this formalism exploits the Markov inequality and the ratio criterion has been interpreted as an upper bound on the probability that a match do not belong to the background distribution. In this paper, we first examine some of the assumptions and methods used in these works and demonstrate their inconsistencies. And then, we propose improvements by refining the bound, by providing a tighter bound on that probability. The fact that the ratio criterion is an upper bound indicates that refining the bound reduces the probability that the established matches come from the background. Experiments on the well-known Oxford-5k and Paris-6k datasets show performance improvement for the image retrieval application.