macmahon scoring applied in football or other team sports

[marc]

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.

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 which teams have a better potential.

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, 1 draws, 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.

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 systems.

Any ideas?

[marc]

I have done some tests and I think I have come up with some interesting approach. A good formula to evaluate a SOS-based ranking in a swiss league is:

points + w * SOS

where w is the % of remaining rounds.

For example in the last round w = 0, and SOS is not considered, which makes sense since in the last round all players SOS is the same. And at half the tournament, w = 0.5.

Post by marc
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.
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 which teams have a better potential.
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, 1 draws, 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.
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 systems.
Any ideas?