The risk of natural gas hydrate formation in oil and gas flowlines increases when production moves into deep-water regions under high pressure conditions. Unlike hydrate dissociation, which is deterministic, the formation of gas hydrates is a well-known stochastic phenomenon which has not been fully characterized to date. Currently, it is often assumed that gas hydrate will form when the subcooling exceeds 3.6°C (6.5°F); this value is a heuristic based on limited field-tests. To more accurately predict when and where hydrates are likely to form, large experimental datasets are required to quantify probabilistic hydrate formation. Two generations of High Pressure Stirring Automated Lag Time Apparatus (HPS-ALTAs) were developed to repeatedly measure the formation driving force in term of subcooling and induction time. These HPS-ALTAs are capable of generating statistically significant datasets - typically on the order of 100 formation events - that enable the calculation of formation probability as a function of subcooling from hydrate equilibrium. The current results demonstrate that hydrate formation is strongly dependent on shear, with mean subcooling being reduced by 45% when the mixing speed was increased by a factor of seven. Additionally, initial induction time distributions have been measured at two subcooling values, and are described well by an exponential distribution as expected from theory.