Gamblers in particular and others generally are not as interested in a
'right'/'wrong' prediction as they are in a probabilistic prediction of an
outcome. Are the bookies' pay-out odds being offered on an event reasonable
given our perceived probability (e.g., 52\% or 97\%), or what are the risks
of some medical procedure? A logarithmic scoring function for probabilistic
predictions used by Wallace and Patrick (1993, Machine Learnng 11, 7-22) and
Dowe and Krusel dates back to I. J. Good in the 1950s, is equivalent to
fully-invested gambling (Cover and Thomas, 1991, Elementary Information
Theory, Wiley) and can also be thought of as a Kullback-Leibler distance
minimisation problem. A probabilistic football tipping competition using
these ideas was initiated at Monash University in 1995 and a Gaussian
competition based on Kullback-Leibler distance was also developed by the
first author in 1996 (Dowe, Farr, Hurst and Lentin, 1996, Mathematical and
Computational Sport). We describe the performance of a tipping method
developed in 1997 and used in The Australian newspaper in 1998 which
combines an Elo system used for rating teams modified to include home-ground
advantage with bookies' odds, and the general benefits of Bayesian
integration and other ways of combining predictors.