  Qualifications for several world championships in sports are organised such
that distinct sets of teams play in their own tournament for a predetermined
number of slots. Inspired by a recent work studying the problem with the tools
from the literature on fair allocation, this paper provides an alternative
approach based on historical matches between these sets of teams. We focus on
the FIFA World Cup due to the existence of an official rating system and its
recent expansion to 48 teams, as well as to allow for a comparison with the
already suggested allocations. Our proposal extends the methodology of the FIFA
World Ranking to compare the strengths of five confederations. Various
allocations are presented depending on the length of the sample, the set of
teams considered, as well as the frequency of rating updates. The results show
that more European and South American teams should play in the FIFA World Cup.
The ranking of continents by the number of deserved slots is different from the
ranking implied by FIFA policy. We recommend allocating at least some slots
transparently, based on historical performances, similar to the access list of
the UEFA Champions League.
