Using Monte Carlo simulations we study the association of flexible oligomers terminated by a donor and an acceptor group capable of orientationally specific reversible bonding. On the basis of simulation results, we have obtained equilibrium constants for chain growth and ring closure. These constants were employed in an analytical model, which reproduces the large-scale simulation results very well. We also propose an analytical approach which can be used to analyze experimental data or make predictions of molecular weight, chain/ring distributions, etc., which are hard to obtain experimentally. Our simulation and analytical results show that an increase of orientational specificity of reversible bonding decreases the degree of association and molecular weight and leads to the suppression of small rings. As a result the ring-chain crossover concentration (i.e., the concentration at which the number of reversible bonds in chains and rings coincide) decreases and exhibits a maximum as a function of oligomer length N. With a decrease in the energy of reversible association or increase in temperature the ring-chain crossover shifts to lower concentrations and molecular weight either systematically decreases if the system is in the chain-dominated regime (high concentrations) or increases and exhibit a maximum if the system is in ring-dominated regime (low concentrations). Higher orientational specificity of association in combination with a short spacer length ensures a larger value of the molecular weight at its maximum which is reached at lower temperatures and higher oligomer concentrations. These results are supported by recent experimental observations and can be explained based on the oligomer redistribution between chains and rings near the ring-chain crossover.