  In this work, we deal with the problem of rating in sports, where the skills
of the players/teams are inferred from the observed outcomes of the games. Our
focus is on the online rating algorithms which estimate the skills after each
new game by exploiting the probabilistic models of the relationship between the
skills and the game outcome. We propose a Bayesian approach which may be seen
as an approximate Kalman filter and which is generic in the sense that it can
be used with any skills-outcome model and can be applied in the individual --
as well as in the group-sports. We show how the well-know algorithms (such as
the Elo, the Glicko, and the TrueSkill algorithms) may be seen as instances of
the one-fits-all approach we propose. In order to clarify the conditions under
which the gains of the Bayesian approach over the simpler solutions can
actually materialize, we critically compare the known and the new algorithms by
means of numerical examples using the synthetic as well as the empirical data.
