Combining networks have been suggested to improve the performance of shared memory MIMD computer systems, which can be seriously degraded when many processors access a shared variable at virtually the same time. Although it has been claimed that combining improves performance, the performance improvement has not been fully analyzed because of the complicated nature of combining networks. In this paper we introduce a probabilistic model to evaluate the performance of combining networks quantitatively. Using the probabilistic approach, we show a performance bound of multistage networks that use 2x2 combining switches. The bounds of performance improvement, in terms of network bandwidth and delay gain, are presented. We also discuss the effect of changing the combining queue size on the performance of combining networks.