The proton-boron (p ${}^{11}$ B) reaction is regarded as the holy grail of advanced fusion fuels, where the primary reaction produces 3 energetic $\alpha$ particles. However, due to the high nuclear bounding energy and bremsstrahlung energy losses, energy gain from the p ${}^{11}$ B fusion is hard to achieve in thermal fusion conditions. Owing to advances in intense laser technology, the p${}^{11}$ B fusion has drawn renewed attention by using an intense laser-accelerated proton beam to impact a boron-11 target. As one of the most influential works in this field, Labaune et al. first experimentally found that states of boron (solid or plasma) play an important role in the yield of $\alpha$ particles. This exciting experimental finding rouses an attempt to measure the nuclear fusion cross section in a plasma environment. However, up to now, there is still no quantitative explanation. Based on large-scale, fully kinetic computer simulations, the inner physical mechanism of yield increment is uncovered, and a quantitative explanation is given. Our results indicate the yield increment is attributed to the reduced energy loss of the protons under the synergetic influences of degeneracy effects and collective electromagnetic effects. Our work may serve as a reference for not only analyzing or improving further experiments of the p ${}^{11}$ B fusion but also investigating other beam-plasma systems, such as ion-driven inertial confinement fusions.