Motivated by \textit{B. Maurey's} proof [Math. Sci. Res. Inst. Publ. 34, 149--157 (1999; Zbl 0935.46016)] of \textit{W. T.~Gowers} dichotomy theorem [Geom. Funct. Anal. 6, No. 6, 1083--1093 (1996; Zbl 0868.46007)], the authors prove a quantitative version of this theorem. Let \(\mathcal G_\infty (X)\) denote all closed infinite-dimensional subspaces of the Banach space \(X\). For \(U,V \in \mathcal G_\infty (X)\), let \(\phi (U,V) = \sup \{\| u-v\| : u\in U\), \(v\in V\) and \(\| u+v\| =1\}\). For \(Y\in \mathcal G_\infty (X)\), let \(\phi (Y) = \inf \{\phi (U,V): U,V\in\mathcal G_\infty (Y)\}\). If \(\phi (Y) = \phi (X)\) for all \(Y\in\mathcal G_\infty (X)\) and \(\phi (X)