I used the accuracy calculation equation to make this simple form that works out how well a prediction must perform to be better than a weighted guess. For example if the incidence of what we are trying to predict is 40% (gender=female, for example) then the model prediction must have an accuracy greater than 52% for it to be better than randomly assigning 40% of cases to gender is female and assigning the other 60% to gender isn't female. As this weighted-guess will have an accuracy of 52% over a large sample.
