Earth System Models project a decline of dissolved oxygen in the oceans under warming climate. Observational studies suggest that the ratio of O₂ inventory to ocean heat content (O₂-OHC) is several fold larger than can be explained by solubility alone, but the ratio remains poorly understood. In this work, models of different complexity are used to understand the factors controlling the O₂-OHC ratio during deep convection, with a focus on the Labrador Sea, a site of deep water formation in the North Atlantic Ocean. A simple one-dimensional convective adjustment model suggests two limit case scenarios. When the near-surface oxygen level is dominated by the entrainment of subsurface water, surface buoyancy forcing, air-sea gas exchange coefficient and vertical structure of sea water together affect the O₂-OHC ratio. In contrast, vertical gradients of temperature and oxygen become important when the surface oxygen flux dominates. The former describes the O₂-OHC ratio of individual convective event in agreement with model simulations of deep convection. The latter captures the O₂-OHC ratio of interannual variability, where the pre-conditioning of interior ocean gradients dominates. The relative vertical gradients of temperature and oxygen, which in turn depend on the lateral transport and regional biological productivity, control the year-to-year variations of O₂-OHC ratio. These theoretical predictions are tested against the output of a three-dimensional regional circulation and biogeochemistry model which captures the observed large-scale distribution of the O₂-OHC ratio, and agrees broadly with the prediction by the simpler model.