Expected Value

#core-framework #computational-lens

What It Is

Expected value is the calculation your brain runs to decide whether to allocate effort to a behavior.

The formula:

$EV = \frac{\text{Reward} \times \text{Probability}}{\text{Effort} \times \text{Temporal distance}}$

Motivation isn't a feeling you generate through positive thinking. It's the output of this calculation.

The Mechanism

The brain generates motivational signals when:

1. The task has clear, concrete outcomes with high perceived value
2. The reward is temporally proximate (this week not this year)
3. Progress is visible and measurable (dopamine hits from incremental wins)
4. The effort requirement is manageable relative to current energy state
5. Probability of success feels reasonable

When motivation drops, one of these variables changed. Your brain updated its value estimate based on new data.

This is rational computation, not character failure.

The Four Variables

1. Anticipated Reward

How much value will completing this create?

High reward:

• Shipping product → users + revenue
• Passing exam → degree + career options
• Finishing workout → endorphins + health

Low/unclear reward:

• "Work on project" (vague, unclear what gets created)
• "Be productive" (abstract, no concrete outcome)
• "Improve myself" (unmeasurable)

Engineering lever: Make rewards concrete and salient. Not "build idyllic" but "ship first working skill integration this week."

2. Probability of Success

How likely is it that effort will produce the reward?

High probability:

• Clear path from action to outcome
• Previous success with similar tasks
• Visible progress toward goal

Low probability:

• No clear causal path
• Repeated failures
• No visible progress despite effort

Engineering lever: Make progress visible through tracking. Break large goals into achievable chunks. Front-load small wins.

3. Effort Required

How many willpower units / how much energy does this cost?

Low effort:

• Following existing script: 0.5 units
• Continuing current work: 0.5 units
• Clear next action: 1-2 units

High effort:

• Ambiguous task: 4-6 units
• Cold start after break: 6+ units
• Complex decision-making: 2-3 units each

Engineering lever: Reduce activation energy through bridge scripts, make next action concrete, build automatic triggers.

4. Temporal Distance

How far in the future is the reward?

Near rewards (hours/days) motivate strongly:

• Finish this task → afternoon free
• Complete workout → endorphin hit in 30 minutes
• Write 500 words → visible progress today

Distant rewards (months/years) motivate weakly:

• Build for 6 months → maybe product success
• Study for years → eventual degree
• Work out for months → future fitness

Engineering lever: Break long-term goals into weekly/daily wins. Create immediate rewards for intermediate progress.

Why Trying to "Feel Motivated" Fails

You don't control the output directly. You engineer the inputs.

Trying to feel motivated is like trying to feel the temperature change while the thermostat is set to the same value. The feeling is the readout, not the control.

Change the variables and motivation emerges automatically.

Engineering Motivation

Increase Reward Salience

Before: "Build idyllic" (abstract, distant, unclear value)

After: "Ship first working skill integration this week" (concrete, close, clear value)

The reward becomes real and specific. Your brain can calculate actual expected value.

Make Progress Visible

Implement tracking that shows movement:

• Streak counters
• Metrics dashboards
• Before/after comparisons

Each visible increment triggers dopamine → reinforces behavior loop.

Front-Load Small Wins

Structure work so early tasks are achievable and produce immediate results.

Don't start with the hardest part. Start with the easiest part that produces visible output.

Triggering the reward circuit early makes continuing easier.

Reduce Effort Costs

If task feels too expensive, break it down or build better tools.

"Write documentation" feels impossible (6 units).

"Write 100 words" is manageable (2 units).

Sometimes lack of motivation is your brain correctly computing that the current approach is inefficient.

Use External Commitment Devices

Add external cost to inaction, which changes the EV calculation:

• Public declarations (social cost of not doing it)
• Accountability partners (someone expects updates)
• Financial stakes (money lost if you don't execute)

Now the EV includes: (benefit of action - cost of inaction) / effort

Schedule Explicit Rewards

Complete X → immediate reward Y

Condition your dopamine system by pairing work completion with concrete positive events.

This artificially increases the reward variable and brings it temporally closer.

Courage as Expected Value

Courage is what it looks like when your expected value calculation says "benefit > cost" despite fear signals.

Fear is just one input. Courage isn't absence of fear. It's executing when the math favors action regardless of the fear signal.

Example: Starting Idyllic after Terra collapse

• Staying in crypto: negative EV (sinking ship)
• Starting new thing: positive EV (aligned with skills, market opportunity)
• Fear signal: present but doesn't override calculation
• Result: Execute despite fear

Not heroic bravery. Math.

When Low Motivation Is Informational

If you keep "procrastinating" on a task, maybe the task is actually not worth doing.

Your subconscious may have computed that expected value is negative even though you consciously committed to it.

Low motivation can be a signal:

• Reward isn't actually valuable to you
• Probability of success is genuinely low
• Effort cost exceeds potential reward
• Better opportunities exist

Don't always fight low motivation. Sometimes listen to it and reassess whether the goal is valid.

Expected Value as Causal Leverage

The expected value framework connects directly to agency as the ability to be causal. Under real resource constraints, maximizing agency means maximizing causal leverage—effect per unit cost.

The standard EV formula tells you whether an action is worth taking. The causal leverage reframe tells you which actions to prioritize when you can't do everything:

$\text{Causal Leverage} = \frac{\text{Effect produced}}{\text{Resources consumed}}$

This transforms abstract goal-setting into optimization across three axes:

The deepest move is meta-causality: being causal about the causal architecture itself. Don't be causal everywhere. Be causal once, at the right leverage point, about the thing that will be causal for you forever.

Example - Gym attendance:

Same outcome (30 gym visits). One strategy costs 150+ units and fails eventually. The other costs ~30 total units and persists indefinitely. The second strategy has 5× higher causal leverage because the single architectural intervention produces sustained effect.

This is why Level 4 agency (engineering distributions) beats Level 1-3 (predicting and responding to distributions). You stop forecasting outcomes and start reshaping the generator itself.

Related Concepts

• Motivation - The emergent output of this calculation
• Courage - Expected value > cost despite fear
• Procrastination - Often caused by low EV calculation
• Grit - Maintaining positive EV through setbacks
• Discretization - Breaking work into higher-EV chunks
• Activation Energy - The effort variable in the equation
• Tracking - Making progress (probability) visible

Key Principle

Engineer inputs, not outputs - Manipulate the expected value calculation variables (increase reward salience, make progress visible, reduce effort, bring rewards closer) rather than trying to force authentic enthusiasm.

Motivation isn't a character trait. It's a readout from an expected value calculation. Change the inputs and the output changes automatically.