The greenhouse gas footprint of oilfield flares comprises carbon dioxide and uncombusted hydrocarbons. It has been broadly assumed that oilfield flares are 98% efficient, and that the unburned fraction is predominantly methane. Recent studies have shown that neither assumption is necessarily true. Gas associated with tight oil production, now the largest source of flared gas in the United States, is a mixture of hydrocarbons in which methane is not necessarily more than half the total. Aerial surveys have found that while many flares function efficiently, a substantial fraction are very inefficient. This work builds on those studies to show how greenhouse gas footprints can be computed when flared gas is a mixture of hydrocarbons, and when flare efficiencies are best represented as statistical distributions. This work finds that the best estimate of GHG footprint of current Bakken oilfield flares is 56,400 tonnes carbon dioxide equivalent per day, compared to an estimate of 31,400 tonnes carbon dioxide equivalent per day under the assumption of 100% methane flares operating at 98% efficiency. Both these estimates considerably exceed the expected GHG footprint for flares based on data from the Environmental Protection Agency Greenhouse Gas Reporting Program.