What Focus Horizon Calculates
Quality = 100 × e^(−0.01 × min). Half-life ~69 minutes. The tail is where the bugs live.
Focus Horizon answers one question: how long until your work quality drops below usable?
Focus is not steady — it decays exponentially from the moment you start. Quality = 100 × e^(−0.01 × min), floor at 0. Half-life ~69 minutes. After that every additional unit of time delivers half the output. The tail is where the typos and bugs live.
Quick answer
Focus Horizon answers one question: how long until your work quality drops below usable?
Key points
- ▸ Formula: quality = 100 × e^(−0.01 × min). Capped at 0 because below ~3% is operationally dead.
- ▸ Above 70% = peak focus. This is where the hard problems actually get solved.
- ▸ 15-40% = decaying. Still productive on routine work but do not start anything new and hard.
- ▸ Below 3% = focus collapse. You are making bugs, not progress.
- ▸ Horizon shows minutes until quality drops below 15% — take the break at that marker, not after.
Examples
- 45 min into sessionQuality 63.8% → sustained focus. ~145 min left before collapse. Window for hard work is now.
- 180 min unbrokenQuality 16.5% → decaying. Grinding on fumes. 20-min break recovers more than pushing.
- 300 min unbrokenQuality 5% → collapse. Whatever you ship in the next hour will need rewriting tomorrow.
When to use which tool
- CYAN · STABLE — Quality above 70% — peak focus; spend it on the hardest problem.
- GOLD · GUARDED — Quality 15-70% — decaying; stick to routine work, break at the marker.
- MAGENTA · CRITICAL — Quality under 15% — collapse; what you ship now gets rewritten tomorrow.
Related
- Deep Work Capacity · Focus HorizonExponential decay model of focus quality. e^(−0.01×min) half-life ≈ 69 minutes — the horizon shows how long until quality drops below usable.
- When to Set a Focus HorizonFive situations where marking the decay curve changes what you ship.
- Five Focus-Horizon MistakesThe errors that spend peak focus on the wrong things.
- What Task Switching Tax CalculatesRetention = 0.80^(n-1). Every context after the first costs 20% of remaining capacity.
Frequently asked questions
› Does everyone decay at the same rate?
No. λ (the decay constant) varies by person, sleep, task difficulty, and interest. 0.01/min is a rough baseline. Adjust mentally if you know yours is flatter (professional deep-workers) or steeper (sleep-deprived or new to the task).
› Why cap at 0? Troubleshooting
Exponential decay never reaches 0 mathematically, but focus quality below ~3% is operationally dead. The cap prevents misleading "2% focus" readouts that suggest you are still working.
› Does a break fully reset the horizon?
A 20-minute break with no screens recovers most of the decay. A 5-minute Slack break does not. Recovery quality matters as much as recovery time.
› How should I use a decision framework in real life? How-to
Use a decision framework to expose the tradeoff, not to outsource the decision. Write down the inputs, compare the output with your constraints, then ask what would change the answer. The strongest use is scenario testing: base case, conservative case, and failure case.
› Is this financial, legal, or tax advice? Trust & accuracy
No, this is not legal, financial, tax, medical, or professional advice unless the page explicitly says that use case is supported. It organizes assumptions so you can inspect them. Verify high-stakes choices with qualified people who can review facts, contracts, regulations, and downside risk.