I am creating a rubric to measure how good my focus was during a study session. I find a simple 10/10 rating system is too inconsistent and can very from person to person. Right now I am modeling how physical and mental distractions would effect the sessions focus rating. Lets focus on mental distractions for now. I want to be able to take the number of times I get distracted and also weight the distractions based on how bad it was. I wish to use this to measure my ability to stay focused. for instance during a study session, I can have 2 distractions with a rating of 5/5 meaning they were really bad distractions and 3 distractions with a rating of 2/5 meaning they were somewhat bad distractions.
I dont want the number of distractions to linearly scale the rating. For instance 12 distractions should not be twice as bad as 6 distractions. It should be significantly worse. I was thinking of an exponential scale. Similarly how bad the distraction is should also not linearly scale the rating. For instance, a 5/5 should be much worse than a 1/5.
Does anyone have a good model to form these ratings? I would like the final output to be out of 10.
One I idea I had was $R = 10 \cdot e^{-k \cdot \sum_{i} \left(Weight_i)^p \cdot Distraction_i^q\right)} $, where R is the rating out of 10, k is the factor by which to scale how bad the distractions were. to measure how bad the distractions were, I have a weighted sum where the weights are between 0 and 1 where 1 is the absolute worst the distraction could be, and distraction is the number of times you got distracted by by a distraction with the weight i. The only issue is I'm not sure how good of a model this is and I'm not sure how to find the parameters.
I was also thinking of removing the exponential q.
This equation is meant to improve upon my original rubric and equation
any ideas recommendations or better ways to model and measure depth of focus would be greatly appreciated.