Between January 2017 and March 2020 a coalition of oil producers led by OPEC and Russia (known as OPEC+) cut oil production in an attempt to raise the price of crude oil. In March 2020 the corona virus shock led to a collapse of this coalition, as members did not agree on keeping the oil market tight in the face of a large negative demand shock. Yet, was OPEC+ actually effective in sustaining the price of oil? Between 2017 and early 2020 when the OPEC+ strategy was in place, oil inventories fell substantially and the price of oil reached a peak of around 80 USD per barrel, from a minimum of 30 USD in 2016. This suggests that the OPEC+ strategy had a significant impact on the global oil market. Yet, to what extent did crude prices actually reflect OPEC+ production cuts rather than other factors, like swings in demand for oil? How would the price of oil have evolved had OPEC+ not cut supply? This paper provides an answer to these questions through a counterfactual analysis based on two structural models of the global oil market. We find the impact of OPEC+ on the market was overall quite limited, owing to significant deviations from the assigned quotas. On average, without the OPEC+ cuts, the price of oil would have been 6 percent (4 USD) lower.