  Predicting the outcomes of future events is a challenging problem for which a
variety of solution methods have been explored and attempted. We present an
empirical comparison of a variety of online and offline adaptive algorithms for
aggregating experts' predictions of the outcomes of five years of US National
Football League games (1319 games) using expert probability elicitations
obtained from an Internet contest called ProbabilitySports. We find that it is
difficult to improve over simple averaging of the predictions in terms of
prediction accuracy, but that there is room for improvement in quadratic loss.
Somewhat surprisingly, a Bayesian estimation algorithm which estimates the
variance of each expert's prediction exhibits the most consistent superior
performance over simple averaging among our collection of algorithms.
