The Monte Carlo results of Michels and Wiegel (1982. Phys. Lett. A 90: 381 and Windwer (1990 J. Chem. Phys. 93: 765) who studied numerically the probabilities of knot formation for ring polymers are explained analytically in terms of the modern knot theory. A very good agreement between the theory and the available numerical experiment data is reached. Some applications of knot theory to polymer dynamics are also briefly discussed.