# Ranking teams playing solo games?

I am looking for a quantitative way of ranking teams that do not play each other, but all play the same set of challenges.

1. There are N teams.
2. Each team plays the same set of k different solo challenges.
3. Each challenge is given a score between zero and unity, thus the $j$ team's score on the $i$th challenge would be $s_{ij} \in [0,1]$.

The total score for the team $T_j = \sum_i^k s_{ij}$ is a reasonable metric at ranking the teams, but does not differentiate between two teams with the exact same total score.

A better metric would take into consideration how hard the challenge was, like say $T^*_j = \sum_i^k (s_{ij} - \left <s_{i,m} \right >_m )^2$. I'm only guessing here, but I'm supposing that this is a solved problem.

What is a good ordinal rank for the same set of solo games?

• Hello, I'm afraid I don't have an answer, I'm just curious. Why would taking how hard a challenge was be a better metric? Assume that two teams have the same total score. If one did better than the other on the difficult problems, then that would mean that it did worse on the easy problems. To me, all this says is that one team is less typical than the other. Certainly, we may be looking for atypical teams, but I don't see how being atypical is necessarily better, if that's truly what we're looking for. – John Madden Nov 25 '15 at 0:01
• @JohnMadden would know, he's a hall of fame coach! – user95564 Nov 25 '15 at 0:12