  We investigate a pattern in the $\alpha'$ expansion of tree-level open
superstring amplitudes which correlates the appearance of higher depth multiple
zeta values with that of simple zeta values in a particular way. We rephrase
this relationship in terms of the coaction on motivic multiple zeta values and
show that the pattern takes a very simple form, which can be simply explained
by relating the amplitudes to the Drinfel'd associator derived from the
Knizhnik-Zamolodchikov equation. Given this correspondence we show that, at
least in the simplest case of the four-point amplitude, the associator can be
used to extract the form of the amplitude.
