I have a question that those who understand a bit about the MacMahon scoring system and its associated tiebreaker SOS and SOSOS may want to answer.which teams have a better potential.
Let's take a sports league, say the premier league or any amateur league in football or whatever sport. The league will be a complete round robin, most likely with 2 games per team (home and away). But so far we are in say round 5, and we want to know
Regular sports leagues rate their participants according to the number of points, and as tiebreakers there is usually the goal average. In our example, if after round 5 team A has 6 points (2 wins, 0 draws, 3 losses) and team B has 7 points (2 wins, 1draws, 2 losses), the standings will display team B above team A.
But let's assume that team A has played (and lost) against 3 of the stronger teams, which so far have won all of their games, and that team B has played and lost against 3 teams on the lower side of the board.systems.
It is quite logic to say (and if you want, bet) that team A will finish the league above team B because it has had a more difficult league so far than team B, i.e. team A has a much higher SOS than team B.
My question is: what is a good way to combine points, SOS and SOSOS (and perhaps other macmahon tiebreakers) to get a good rating for the standings?
I have tried using points + SOS/2 as the score with some real data and it gives quite a good result. It seems to give a better result than points + SOS. But I have no mathematical backing for that. Perhaps for other datasets there are better scoring
Any ideas?
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