The prediction of loss of position in the offshore industry would allow optimization of dynamic positioning drilling operations, reducing the number and severity of potential accidents. In this paper, the probability of an excursion is determined by developing binary logistic regression models based on a database of 42 incidents which took place between 2011 and 2015. For each case, variables describing the configuration of the dynamic positioning system, weather conditions, and water depth are considered. We demonstrate that loss of position is significantly more likely to occur when there is a higher usage of generators, and the drilling takes place in shallower waters along with adverse weather conditions; this model has very good results when applied to the sample. The same method is then applied for obtaining a binary regression model for incidents not attributable to human error, showing that it is a function of the percentage of generators in use, wind force, and wave height. Applying these results to the risk management of drilling operations may help focus our attention on the factors that most strongly affect loss of position, thereby improving safety during these operations.