  There are several scoring rules that one can choose from in order to score
probabilistic forecasting models or estimate model parameters. Whilst it is
generally agreed that proper scoring rules are preferable, there is no clear
criterion for preferring one proper scoring rule above another. This manuscript
compares and contrasts some commonly used proper scoring rules and provides
guidance on scoring rule selection. In particular, it is shown that the
logarithmic scoring rule prefers erring with more uncertainty, the spherical
scoring rule prefers erring with lower uncertainty, whereas the other scoring
rules are indifferent to either option.
