Gamma-ray pulsars constitute a class of high and very high energy emitters for which the known population is steadily increasing thanks to the Fermi/Large Area Telescope. More than a hundred such pulsars have been detected, offering a reasonable sample on to which to apply statistical techniques in order to outline relevant trends in the averaged properties of this (maybe not so) special class of pulsars. In this paper, their gamma-ray luminosity and spectral features are explained in the framework of synchrotron radiation from particles located in the stripe of the pulsar wind. Apart from radiative losses, particles are also subject to a constant re-acceleration and reheating for instance by a magnetic-reconnection-induced electric field. The high-energy luminosity scales as Lγ ≈ 2 × 1026 W (Lsd/1028 W)1/2 (P/1 s)−1/2, where Lsd is the pulsar spin-down luminosity and P its period. From this relation, we derive important parameters of pulsar magnetosphere and wind theories. Indeed, we find the bulk Lorentz factor of the wind scaling as , pair multiplicity κ related to the magnetization parameter σ by and efficiency η of spin-down luminosity conversion into particle kinetic energy according to the relation η σ ≈ 1. A good guess for the associated reconnection rate is then τrec ≈ 0.5 (Lsd/1028 W)−5/12. Finally, pulses in gamma-rays are visible only if Lsd/P ≳ 1027 W s−1. This model differs from other high-energy emission mechanisms because it makes allowance not only for rotational kinetic energy release but also for an additional reservoir of energy anchored to the magnetic field of the stripe and released for instance by some magnetic reconnection processes.