How to isolate individual contributions to group against another group? Is there a way to compare individual team member contributions when pitted against another team multiple times?  This is in a sport like rowing where you take N number of individuals from a set A and M number of individuals against set B.
Is there a way to make estimations on-going with incomplete sets (not all unique combinations of N vs M exist) or with some interdependence where some in N or M are never changed out?
In a similar vein to this question How to extract an individual's (normalized) contribution from a group? I am interested if there are some recommended approaches or literature on this subject.  The difference in my question is this limited to two groups with known team vs team data.
Just to make it clear, I'm trying to compare relative times between teams and then try to see individual performance.  So for example here is some fake data between Team A and Team B with 9 members to choose 5 from with the teams results for that Event (note the times are the same for members because they are racing in the same boats).
TEAM A      Event1     Event2   Event3
N1          55.5       53.3     51.2
N2          ----       53.3     ----
N3          55.5       53.3     ----
N4          55.5       -----    51.2
N5          55.5       ----     51.2
N6          ----       53.3     51.2
N7          ----       53.3     ----
N8          55.5       ----     ----
N9          ----       ----     51.2

Vs TEAM B
TEAM B      EVENT1     Event2   Event3
M1          55.0       52.9     53.2
M2          ----       52.9     ----
M3          55.0       52.9     ----
M4          55.0       ----     53.2
M5          55.0       ----     53.2
M6          ----       52.9     53.2
M7          ----       52.9     ----
M8          55.0       ----     ----
M9          ----       ----     53.2

Each event occurs in different conditions so only the same events can be directly compared of Team A vs B.  So for example Team A group at Event1 clocked 55.5 and Team B group won at 55.0.
What I've Tried
I've computed their relative time difference per event.  Then I've taken each individuals average time difference and compare them.  This works ok, but I don't think this is an accurate comparison and I don't know how to estimate cases where the data is limited or how to know what data still should be gathered.
 A: I would use a fixed effects regression, with a fixed effect for each team member, and the team time as a dependent variable. Formally, this is identical to an OLS regression with a dummy variable for each team member.  
Let your dependent variable be $Outcome_{ts}$ for team $s$ at time $t$ - the outcome could be the time by team $s$ on day $t$ in the race. Let $Mi_{ts}$ be a dummy variable denoting team member $i$ on team $s$ at time $t$, i.e., $Mi_{ts}=1$ if $i$ was on team $s$ at time $t$, and $Mi_{ts}=0$ otherwise. The simplest fixed effects regression is then:
$$Outcome_{ts}=a_1 Constant+a_2M2_{ts}+\ldots+a_nMn_{ts}+\varepsilon_{ts}.$$
Note we are omitting variable $M1$ and instead include a Constant in the regression; thus, member 1 is the "reference category" in the regression and all other team member estimates are relative to member 1. 
The estimate $a_1$ for the constant then represents the average contribution of member 1; the remaining estimates $a_2,\ldots,a_n$ give you the average contributions of the other team members relative to member 1. Negative estimates mean that member is on average worse than member 1, positive estimates mean that member is on average better than member 1. To obtain the absolute average contribution of members $i=2,\ldots,n$, just compute $a_1+a_i$.
You can use additional variables in the regression if you have more data; for example, you could control for things like whether which might differ by $t$. In that case, the regression would be
$$Outcome_{ts}=a_1 Constant+a_2M2_{ts}+\ldots+a_nMn_{ts}+\beta\cdot  X_{ts}+\varepsilon_{ts},$$
where $X$ is a vector of these control variables and $\beta$ is a vector of their contributions to the team outcome.
This fixed effects approach has been used in labor economics before, where the effect of supervisors on team output was determined (supervisors were randomly allocated to teams at the beginning of each day) - I believe this was a study where Edward Lazear was one of the authors.
I think the important thing for you is to think about how each individual's performance maps into the team output. Does the average contribution matter, or the minimum contribution ("weakest link in the chain")? Depending on the answer, different estimation techniques might be suitable. The above FE approach would be suitable if the average contribution matters. You can see that in the above regressions, where the team outcome is modeled as a (weighted) sum of the individual team members' contributions.
