Relation between molecular mass and retention of a gas on a planet
I didn't really understand where did this &quot;one-sixth of the escape velocity&quot; figure come up from.

The &quot;one-sixth of the escape velocity&quot; a ballpark number. As a general rule, three sigma events (events that are three standard deviations from the mean) happen all the time, while twelve sigma events are so very, very rare that they can essentially be ruled out. Six sigma events are rare but do happen. In a logarithmic sense, six is halfway between three and twelve.
A bit less hand-waving, it can be shown that the Jean's escape flux (which is what your text is addressing) is proportional to $v_s \, (1+\left(v_e/v_s\right)^2)\,\exp\left({-\,\left(v_e/v_s\right)^2}\right)$ , where $v_s$ is the expected value of the magnitude of the three-dimensional velocity of the gas at the top of the exobase and $v_e$ is the escape velocity at the top of the exobase. That factor of $\exp\left({-\,\left(v_e/v_s\right)^2}\right)$ means that Jean's escape is extremely sensitive to changes in $v_s$.