Mild traumatic brain injury (mTBI), more colloquially known as concussion, is common in contact sports such as American football, leading to increased scrutiny of head protective gear. Standardized laboratory impact testing, such as the yearly NFL helmet test, is used to rank the protective performance of football helmets, motivating new technologies to improve the safety of helmets relative to existing equipment. In this work, we hypothesized that a helmet which transmits a nearly constant minimum force will result in a reduced risk of mTBI. To evaluate the plausibility of this hypothesis, we first show that the optimal force transmitted to the head, in a reduced order model of the brain, is in fact a constant force profile. To simulate the effects of a constant force within a helmet, we conceptualize a fluid-based shock absorber system for use within a football helmet. We integrate this system within a computational helmet model and simulate its performance on the standard NFL helmet test impact conditions. The simulated helmet is compared with other helmet designs with different technologies. Computer simulations of head impacts with liquid shock absorption predict that, at the highest impact speed (9.3 m/s), the average brain tissue strain is reduced by 27.6% ± 9.3 compared to existing helmet padding when tested on the NFL helmet protocol. This simulation-based study puts forth a target benchmark for the future design of physical manifestations of this technology.