We perform a combined analysis of double Higgs production searching for a hint of new physics in the Effective Field Theory (EFT) framework. We enhance the sensitivity to dimension-6 operators through a shape analysis with m (hh) invariant mass distribution, and combining b b gamma gamma and b b tau tau decay channels. We demonstrate that the b b tau tau process outperforms the b b gamma gamma for the measurement of energy-growing operators, while the precision to the triple Higgs self-coupling is mainly set by the b b gamma gamma. We also propose a novel method for improving the precision to the triple Higgs self-coupling in the relatively overlooked b b W W* channel, by introducing two kinematic functions, Topness and Higgsness. The method delivers a much higher signal significance than existing results do, without employing machine learning (ML) techniques. Our method can be further augmented by the ML, and applicable to different final states such as the b b tau tau and other BSM searches.