Quantum Chromodynamics, the theory of the forces binding quarks, provides a fundamental description of hadron physics. Establishing an explicit relation between the long distance physics of confinement and the dynamical interactions of quarks and gluons at short distances has been a long-sought goal. Using holographic QCD, we derive a direct analytic connection between hadronic masses and the scale \Lambda_{s} that controls the predictions of perturbative QCD at very short distances. The resulting prediction, \Lambda_{s} Show Partial Abstract