Summary: We investigate the preduals of \(JBW^*\)-triples from the point of view of Banach space theory. We show that the algebraic structure of a \(JBW^*\)-triple \(M\) naturally yields a decomposition of its predual \(M_*\), by showing that \(M_*\) is a \(1\)-Plichko space (that is, it admits a countably \(1\)-norming Markushevich basis). In case \(M\) is \(\sigma\)-finite, its predual \(M_*\) is even weakly compactly generated. These results are a common roof for previous results on \(L^1\)-spaces, preduals of von Neumann algebras, and preduals of \(JBW^*\)-algebras.