Two running teams take part in competitions on the same course, but their competitions differ because of the number of teams entered in each competition.
Results are based solely on position - times are not taken.
Competition 1 has 7 teams of 8 runners Each team enters 2 of its runners in each of 4 races Points are awarded on the basis of 1 for first place down to 14 for fourteenth place The points for all 4 races are added together. The winning team had a total of 40 points.
Competition 2 has 5 teams of 8 runners Each team enters 3 of its runners in each of two races (15 competitors in each) and a further 2 runners in a third race (10 competitors in this one). Points are awarded in each race on a similar basis to competition 1 (2 races award from 1 to 15 and the other, 1 to 10). The winning team has a total of 46 points
Statistically, which is the better team?
I'm not a statistician, but my logic lead me initially to compare each team's performance with what I would (probably incorrectly) call the mean number of points in each competition (average of the most and least number of points the team could score). However this would seem disadvantage the team in competition 2, because their best possible points score is 15 versus 12 for team 1. And the "mean" numbers are in any case similar. I did think about comparing each team's performance against the best case and worst case scenarios in their respective competitions and averaging those scores? The other thought is that I should somehow compare each runner's performance against the best & worst case?
In reality, I'm a bit stuck. Help please!