#request for #help with a #math thing: A function (hopefully excel-friendly) I can use to curve scores according to workload on projects.

I grade student projects by a workload/task document: I break the project down into a couple dozen tasks, and either assign them to individuals on the teams or allow them to choose collectively. Either way, a common thing happens: one or two team members often do very little early on, and conscientious group members pick up their slack. Since I will always try to give credit for work done, this means the workload is unbalanced--that is, imagine there are 100 tasks and a 5-person team. We often end up in this situation for tasks assigned:

Jenny - 35 tasks
Johnny - 30 tasks
Jayda - 20 tasks
Magda - 10 tasks
Melvin - 5 tasks

It's not ideal, of course, but it happens. I'd like to curve (literally) grades so they are proportional to the workload. That is, Jenny should have to work less hard for an A, and Melvin should have to work very hard for an A.

I'd like a function that will turn Jenny's linear 0-100 score into a nonlinear 0-100 score where, e.g., an 80 is turned into a 92, a 90 is turned into a 98, etc. 0 is still 0 and 100 is still 100.

I'd like it to turn Melvin's linear 0-100 score into a nonlinear 0-100 score with curvature going the other way: e.g., a 90 becomes a 60, a 95 becomes an 80, a 99 becomes a 95, etc. 0 is still 0 and 100 is still 100.

I don't actually need this to scale from 0 to 100; I can adjust limits if something ends up going from 23 to 2,428 or something.

Ideas? I've played so far with stacking some inverse, logarithmic, and exponent functions, but I can't get things tweaked to do the above (I have an overly-complex function that will scale Melvin's score but not Jenny's).

Pointers/suggestions are welcome, even if they are not full solutions.

Suggestions that I should not want to do this will be taken for what they are worth; I want to do this, and it makes sense to me as a way to try to shift an unfair situation toward fairness.

I feel silly admitting defeat, but I tell myself it's just that I don't have time to figure this out (after a couple of hours not figuring it out). That is possibly just self-serving cognition.

#professor #highered #grading