The cleanliness formula

 You can formalize your idea as a simple multi-variable optimization / balance equation that fits nicely into existing frameworks like utility theory or decision theory.

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Define variables

Let:

 = effort exerted to clean oneself

 = internal (subjective/physiological) feeling of cleanliness

 = actual (objective) cleanliness level

 = perceived cleanliness (social/interpersonal)

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Core idea: maximize “cleanliness utility”

You’re essentially describing a trade-off, so we can express it as a utility function:

U(E) = w_1 I(E) + w_2 A(E) + w_3 P(E) - w_4 E

Where:

 are weights (importance of each factor)

 are all functions of effort 

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Interpretation

Increasing effort generally increases:

: you feel cleaner

: you are cleaner

: others perceive you as cleaner

But with diminishing returns, e.g.:

I'(E), A'(E), P'(E) > 0 \quad \text{and} \quad I''(E), A''(E), P''(E) < 0

And excessive effort has a cost:

time, energy, skin damage, etc.

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Optimal condition

The “correct extent” (your original idea) is when:

\frac{dU}{dE} = w_1 I'(E) + w_2 A'(E) + w_3 P'(E) - w_4 = 0

This means:

> You should clean yourself up to the point where the marginal benefit of cleanliness equals the marginal cost of effort.

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Conceptual translation of your sentence

“To bathe or not to bathe excessively” becomes:

> Choose such that total perceived + actual + internal cleanliness gains are balanced against the effort cost.

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If you want a more philosophical / compact form

\text{Optimal Cleanliness} = \arg\max_E \left[ \text{Internal} + \text{Actual} + \text{Social} - \text{Effort} \right]

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If you want, I can extend this into a named “theory” (like a mock academic framework) or map it to something like behavioral economics or hygiene psychology.