How the MaxDex Energy Index Is Calculated

What is the MaxDex Energy Index?

The Energy Index is a 0-100 estimate of how much capacity you have at a given moment. It sums seven weighted physiological drivers into a single arousal value, then maps that value through a sigmoid onto a 0-100 scale.

It is not a weighted average of step count and sleep hours. It is an arousal model: each subsystem contributes a signed push toward or away from alertness, those pushes are summed, and the sum is squashed into a bounded score. That structure matters, because it means two moderate negatives can combine into a genuinely bad afternoon rather than averaging out to "fine".

The whole model runs on your device as pure functions. No energy computation happens on a server, and the inputs never need to leave the phone to produce a score.

What is the actual formula?

arousal = Σ (weighted drivers) + asleep floor, then E(t) = clamp(sigmoid(1.25 × arousal) × 106 − 3, 0, 100). The seven drivers are circadian, homeostatic, metabolic, fitness-fatigue, cognitive, movement and sleep inertia.

The gain of 1.25 widens the dynamic range so a genuinely excellent day can reach 100 and a genuinely terrible one can reach 0. The ×106 − 3 end-expansion exists for the same reason: a plain sigmoid never quite touches its bounds, and a score that can only ever read 8-92 hides the extremes that matter most.

While you are estimated to be asleep, a floor of −2.4 is added to arousal, which pins the curve low rather than letting a well-rested sleeper read as "high energy" at 3am.

Why weight sleep pressure highest?

Homeostatic pressure carries a weight of 1.5 against 1.0 for everything else because sleep loss has the largest and most reliable effect on next-day functioning of any input we can measure from a phone.

Van Dongen and colleagues showed that chronic restriction to six hours a night produced cognitive deficits comparable to two nights of total sleep deprivation — and, critically, that subjective sleepiness ratings barely moved while objective performance kept degrading. People systematically underestimate their own impairment. A model that weights self-report equally with sleep history would inherit that blind spot.

That is also the argument for the whole product: if you cannot feel the deficit, you need something outside your head to plan around it. See what the model will not tell you for where that reasoning stops.

How far ahead does it forecast?

The past 24 hours are reconstructed hour by hour from real logged events at their real timestamps. The next 48 hours are projected forward through a scheduled sleep window, with a confidence band that widens from ±3 to ±30 points.

The widening band is deliberate and visible. A forecast for two hours from now rests on known sleep, known meals and a known circadian phase. A forecast for tomorrow evening rests on assumptions about a night that has not happened yet. Presenting both with the same apparent precision would be dishonest, so the band grows with the uncertainty.

The projection steps sleep pressure forward with the same accumulation and dissipation functions used for the past, rather than switching to a cruder model for the future half of the curve.

How does it personalise to me?

A decaying exponential moving average nudges two parameters toward you as days accumulate: your chronotype phase and your personal sleep need. The learning rate is 1 ÷ (samples + 3), clamped to between 0.05 and 0.34.

Early days move the estimate quickly; later days refine it. Sleep need is clamped to a 5-10 hour range and only drifts on well-rested days — days with under three hours of accumulated debt — so a run of short nights cannot quietly redefine your baseline downward as "normal for you".

This is an EMA, not a Kalman filter or a learned model. It is documented that way in the source because overstating the sophistication of a smoothing rule would be exactly the kind of claim this page exists to avoid.

What stops it inventing a number?

Four guards. Days with no real data return a neutral 50 flagged as "no data" rather than a fabricated reading; future sleep cannot leak backwards into reconstructed past hours; low-confidence nights regress toward your baseline; and driver contributions are computed as true sigmoid deltas.

The last one is subtle but matters. To say "sleep cost you 12 points today", you cannot multiply the sleep driver by a fixed per-unit factor — that is only accurate near the middle of the sigmoid. The engine instead recomputes the entire stack with that one driver zeroed and reports the difference, so the attribution stays correct at the extremes where it is most likely to be quoted back at you.

The "no data" guard is the one users notice. If the app has nothing logged for a date, the curve is a bare circadian default, and the interface is gated so it cannot be presented as a genuine reading or forecast.

Frequently asked questions