Determine individual score or ranking from group scores Preliminary note: I have a specific problem that arose during evaluation of some experimental data, but since I am not very well versed in statistics (I am primarily an engineer), I cannot find the proper terms to google for; so instead I stripped down my problem to an analogous one, which is as follows.
Assume we have $N$ (say, 300) individuals that can partake in a task that requires $n$ (say, 16) people, and which has a measurable score after completion. The goal is to determine some kind of measure of how good each individual is at this group task (if that even makes sense). If we could measure the performance of all possible $\binom{N}{n}$ groups, and calculate the total score achieved by each individual across all groups they were part of, that could provide us with the sought measure. (Or at least so is my intuition.)
However, in the special case this question is about, we do not have the possibility to score all possible groups due to time constraints. What is available is that we create random groups in such a way that each individual performs the task $k$ (say, 64) times. This results in $M=\frac{N \cdot k}{n}$ (with the above data, $=1200$), completions of the group task, with scores for each. (This condition can be relaxed if there is another evaluation method that has at most $\approx M$ instances of completing the task.)
In this scenario, how can we -- or, can we even -- make at least an assumption of some "score", "measure of ability" or -- if not --, ranking of the individuals themselves based on these $M$ group scores and the participants of the groups?
(I think that this question only makes sense if there is no negative effect on the score between a group of individuals, only a nonnegative or positive effect. In my case this is unknown and the relationship is certainly nonlinear, but maybe this nonnegativity can be assumed, if it is needed for the question to make sense.)

This sounds like an analysis of variance is needed first. Very first preliminary is to analyze the scores for individuals and scores for groups just to check that there are meaningful differences. If there's not much different between individuals and between groups, then no need to proceed trying to model the nonexistent differences.
Assuming there are differences, and assuming all groups are the same number of individuals, an initial approach to model might be to fit scores to a model using each of individuals as dummy variables, e.g., Individual001=1 if Individual001 was in the group, 0 otherwise. If the model fits, then higher coefficients mean that individual is contributing more to group scores, lower means less of a contribution, maybe even some negative coefficients if there are individuals that drag down group scores.
