We develop and successfully verify a reliable method that matches the fieldwide oil and gas production from all horizontal hydrofractured wells in the Eagle Ford Shale and calculate the play-wide Estimated Ultimate Recovery (EUR). Unlike purely empirical industry-standard forecasting methods, our approach relies on the physics of hydrocarbon flow in a hydrofractured shale geometry and captures the probabilistic uncertainty of shale geology and well productivity. For this study, the Eagle Ford play is divided into 24 spatiotemporal well cohorts based on shale geology, fluid composition, and completion date. For each well cohort, we fit the distribution of annual production via Generalized Extreme Value statistics. Expected values are then used to construct historical well prototypes. Next, we extrapolate these well prototypes for up to two more decades, using a physical scaling method that accounts for variations in fluid composition across the Eagle Ford Shale. The resulting well prototypes provide robust history matches and predictions of total field production. Finally, to estimate the play-wide EUR, we calculate the well infill potentials for each subregion of Eagle Ford, then we assign the well prototype to each of the potential wells. Based on fluid composition and shale geology, we first mapped all Eagle Ford wells into eight spatial cohorts. To capture the advancement of completion technologies over time, we further divided the well cohorts into three completion date intervals. The total 25,707 existing wells in the Eagle Ford will ultimately yield 2.53 Gbbl of crude oil, 2.79 Gbbl of natural gas liquid (NGL), and 25.67 Tscf of natural gas by 2035. We found that there are 50,115 potential wells that can be drilled across 18,665 sq. mi of Eagle Ford play. With future drilling programs, there will be additional 8.60 Gbbl of crude oil, 2.42 Gbbl of NGL, and 63.7 Tscf of natural gas by 2065. To our knowledge, this project is the first successful attempt to evaluate the play-wide ultimate recovery of the Eagle Ford shale combining physical scaling, generalized extreme value statistics, play geology, and realistic future drilling programs. We also develop a new reserve-assessment method in shales that considers not only the geology of the shale play geology, but also the production dynamics with uncertainty quantifications. In our opinion, this hybrid, data-driven, and physics-based approach is the future of production forecasting and reserves estimation in all shale plays which also provides an objective way of avoiding estimates that are unrealistically low or high.