Measuring Consensus in Binary Forecasts: NFL Game Predictions

Previous research on defining and measuring consensus (agreement) among forecasters has been concerned with evaluation of forecasts of continuous variables. This previous work is not relevant when the forecasts involve binary decisions: up-down or win-lose. In this paper we use Cohen’s kappa coefficient, a measure of inter-rater agreement involving binary choices, to evaluate forecasts of National Football League games. This statistic is applied to the forecasts of 74 experts and 31 statistical systems that predicted the outcomes of games during two NFL seasons. We conclude that the forecasters, particularly the systems, displayed significant levels of agreement and that levels of agreement in picking game winners were higher than in picking against the betting line. There is greater agreement among statistical systems in picking game winners or picking winners against the line as the season progresses, but no change in levels of agreement among experts. High levels of consensus among forecasters are associated with greater accuracy in picking game winners, but not in picking against the line.