I love that you are trying to rationalize this concept, or at least to take a step in that direction. Your project touches in some of my favorite areas of thought, so I apologize in advance for this verbose comment.

I don't think you can explore the idea of willpower or pushing yourself without looking at thresholds. Physical exertion is a great model for this. When we deviate incrimentally from what we understand to be our capacity, we slowly change our concept of that capacity just as much (if not more than) we change our actual capacity.

In 2017 I was severely overweight and made the decision (motivated by fear for my health) to join a gym with instruction. Early on, a coach asked me if I could do a pushup. I did not know, having been bullied extensively and avoiding PE altogether in school, I had never tried. My self-concept was that I could not do it at all. I made the attempt and was able to do a few, 5-10. That surprised me and made me want to push myself to my physical extremes to see what I was capable of. Fortunately, I had a good coach who encouraged me to increase those numbers incrimentally. This has proven continuously true for me throughout my fitness journey over the past 6 years.

Sometimes, I must actively recognize that I am not aware of a perceived capacity for work, and intentionally push myself as hard as I can, measure that data, and model future work off of it. I now coach adaptive athletes and individuals with high BMI and use a RPE (Rate of Perceived Effort) model to design their initial programming, founded in the idea that aligning our perceived ability to exert effort with our actual physical limit, paired with metrics, is the most efficient way to improve our actual physical limits.

That's in the gym, though, where we are actively seeking metrics and designing plans which are then tested and used to create more metrics, etc. It's much harder to approach your question when it comes to messier or more esoteric habits. When it comes to my capacity to complete tasks such as writing reports, I would look to past experiences and try to model them against future forecasts.

For many years, I worked as a case worker and routinely developed comprehensive wraparound treatment plans. These were significant time investments with a pretty heavy load for preparation. A seasoned professional like me can write one in 4-5 unbroken hours with a good degree of focus, but to be thorough and minimize stress, they were usually parsed over 2-3 full work days. If necessity demanded, I could bang out several of them in a few days, generally relying upon both external motivation as well as internal factors like self-belief. The important factor that you could operationalize, though, is that the closer I was to a period of rest, the more I could rely on my internal motivation. I think intuitively we understand there is sort of a "regeneration period" for willpower, and the fear of having to continually rely on it in the future makes our present tasks all the more daunting. Over time, I noticed that I was able to sequence together longer periods of relying on that internal motivation, thus requiring fewer "recharge" periods. When I began in my line of work, I couldn't really push myself to work hard for more than a week without the promise of a reward. By the time I left the field after about 10 years, I could push myself to take on relatively herculean workloads with the promise of a 3-day weekend 6 weeks down the road.

Finally, I think our outlook on the future plays an enormous role in how much willpower we are willing to commit to a task. I think of this as an interfering factor against our rational plans for the future. For example, I may know that I have a long weekend coming up in 6 weeks, but if I am worried that a subordinate is going to quit and I'll have to take on extra work, that projected rest becomes worth less and I must rely more on my internal motivation.

In summary, I see willpower as a matter of 3 recursive elements:

1. Remembered experiences of the durability and efficacy of internal and external motivational factors
2. Applying those experiences as forecasts against our planned future events (give or take for our expectations of variability)
3. An emotional impression of the final outcome which is actualized when we reach a period of rest.

Should I push to achieve my goals? Should I instead acknowledge the lack of sleep and rest? Is it reasonable to make a decision here while only considering today, or should the past weeks effort be considered? In essence, how do I know if pushing myself to encourage growth of self-determination is appropriate for any given event? Conversely, how do I know if allowing myself to rest is allowing for healthy recuperation and not just a convincing argument for following the path of least resistance?

This idea is incredibly fun to think about. Without going too far off the beaten path, and trying to consider your central goal of operationalizing all this, I have a few thoughts.

I think that the best or most rational choice cannot be known in any of these instances. Rather, the choices that we make show where we are on the spectrum of valuing internal motivation. Let us say, hypothetically, that there are 100 composite choices within the group of "self-growth vs relaxation." By defining each of these choices, we see a profile of an individual that exists on a spectrum.

For example: John decided to finish his essay, pay his taxes, and hit his eating targets 100%. He made 95/100 of daily self-growth vs. relaxation choices toward self-growth. He now defines himself as a 95% self-growther, and when he sees a single future task that requires anything at or below a 95% level of effort to perform, he will need a standard level of anticipated rest to pursue it 100% of the time. If he perceives something as requiring 99% of effort, though, and he forecasts that he will have to wait double the amount of time he would like before he can rest again, he may underperform at that task and re-adjust his self-perception. He may even decide against pursuing that task.

The next day, he comes to work and sees doughnuts. He knows it's going to be tough to resist, but hey, he's a 95%-er. However, his boss comes in and lets him know half his department has been fired and he's going to have to triple his workload and cancel his vacation next month. Even though his perceived value of self-motivation is very high, he forecasts a long need for expenditure and is going to start rationalizing choices that provide some external motivation to supplement. Because he's now going to have to extend his willpower 3 times more than expected, its perceived value is lowered two a third of its pristine 95%.

He chooses to go into the kitchen and have a doughnut to settle his nerves, but this throws him off his macronutrient plan. He's on his way to lowering his self-perceived willpower value, which was already stretched thin by his circumstances. Not only is John's overall perception of the value of his willpower decreasing, but he may also have specific triggers pertaining to food. In past years, he struggled with overeating and his index of self-perception of willpower as it comes to food in particular is very low (20%, we'll say). Perhaps his self-perceived ability to resist the next doughnut is a factor of the index of his overall willpower value and his food-specific willpower index.

Here's where I think it gets really interesting. Playing with these indices as percentages is fun, but can we say behavior is just random? If I have an overall index score of 50% when it comes to making healthy food choices, is it just a flip of a coin as to whether I go for the extra doughnut? I think this is where goals and goal prioritization come into play.

Let's say I have three major definable goals: making healthy food choices 100% of the time, taking my dogs on a walk once per day, and going to bed by 10:00 p.m. Because the goals are well-defined and achievable, I believe they will contribute significantly to my choices. If I had say, 10 goals, then they would be too diffuse to all be effective. If my goals are poorly-defined, I would also gain less from them. If I have a history of failing at my goals (for any reason) they're not going to mean as much to me in the present (the inverse being true as well).

I'm going to stop there and continue to think about an operationalized model for willpower and choice-making for some time to come. Good luck to you in your quest!