The magnitudes of the matrix elements for γγ→2π+2π−, γγ→π+π−2π0, γγ→2π+2π−π0, γγ→2π+2π−2π0, γγ→3π+3π−3π+ and γγ→3π+3π−π0are deduced from experimental data as a function of the invariant massW of the system (from 1.0 to 3.0 GeV). It is shown that the data are consistent with a universal energy dependence of the reduced channel amplitudes. A statistical model is shown to describe the peaks in the energy dependence of multipion production in γγ collisions quite well without introducing explicit intermediate resonances.