Your Daily Calorie Burn Depends on Which Watch You're Wearing

Energy expenditure breakdown

We can model the total daily energy expenditure as the sum of activity thermogenesis (AT), non-activity thermogenesis (NEAT) and baseline metabolic rate (BMR):

EE = AT + NEAT + BMR
(Energy expenditure = activity thermogenesis + non-exercise activity thermogenesis + baseline metabolic rate)

Activity thermogenesis is the calories we burn while exercising, and is a function of effort. Non exercise activity thermogenesis refers to the calories we burn while moving but not exercising. This could include moving around the office, cooking or fidgeting.

Activity Thermogenesis

When modeling the activity thermogenesis during recorded activity sessions, devices generally use a variant of one of the two expenditure algorithm families, the HR reserve-based (Keytel) or the motion-based, or alternatively a combination of both.

We use a LightGBM model with HR reserve integral and motion features as inputs to decompose each device’s formula. How well these formulas are ‘decoded’ was measured by computing the R^2 value on a test-set. We then plotted the SHAP importances for each input feature. 

Devices A, B, E and F are predominantly driven by the HR reserve formula, device C ranks HR reserve as the second most important feature while device D relies more on motion-derived features.

Non-exercise Activity Thermogenesis

Most devices report per-activity session calories (activity thermogenesis), which we just decomposed, and total daily activity calories. In an ideal data scenario the total activity calories in a day would be defined as:

Total Activity Calories = Σₐ ATₐ + NEAT
(All activity-session calories summed, plus the non-exercise component)

or in other words, all activity session calories summed plus the non-exercise component.

To decode how different devices compute these non-exercise calories we look for days with no activity sessions logged (Total AT = 0) and model total daily activity calories. Similarly to AT calories, we use a LightGBM model and a range of features including steps, distance and average heart rate.

NEAT calories are decomposed with a lower R squared value than activity session calories, which we suspect is a data granularity problem. NEAT calories happen from daily movement that can be captured with accelerometer data but is less reflected on our heart rate or distance. 

This is because small activities like fidgeting or moving while sat down contribute to NEAT but not to total steps.

Most devices agree on the most important features for NEAT, these are distance and steps. Devices E and F were excluded as they do not report the total daily activity calories and/or baseline metabolic rate to isolate NEAT calories.

Baseline metabolic rate

We assume baseline metabolic rate to be constant within a user, and likely derived from BMI, as devices show within user CVs between 0.1 and 12%. There have been multiple formulas developed and refined throughout time with the gold-standard being the Mifflin St-Jeor formula.

BMR (Mifflin-St Jeor) = 10W + 6.25H − 5A + S
(S = 5 for men, S = −161 for women)

We modeled baseline metabolic rate distributions as a 2-component gaussian mixture to account for sex differences and found the biggest disparities across devices in this analysis. Device B consistently scores lower and device D gives the highest estimates.

There are multiple factors that can cause these distribution differences:

• Population bias: different devices attract different profiles
• BMR vs RMR: baseline metabolic rate is the minimum expenditure to sustain the body while the resting metabolic rate absorbs some of the NEAT calories and is higher.
• Noise and different formula coefficients across devices.

For users with two devices we ran direct comparisons for the baseline metabolic rate estimation and found the same disparities which discards the population bias.

We assume device B reports BMR, as it is the lowest. Its NEAT calories are also the only mainly explained by activity minutes which align with the hypothesis that its BMR does not absorb any of the NEAT calories. Devices A and C are likely reporting RMR instead of BMR which is why they score higher, and device D’s high BMR estimates remain unknown.

How much do devices agree?

Apart from baseline metabolic rate which we have found to be very different across devices, most devices agree on the contributors for active calories. These are generally HR reserve and duration for activity session calories, and steps or distance for passive non-exercise calories. However, despite the ranking of features being the same across devices the total numbers can still diverge.

Taking HR-reserve integral as the gold-standard approach for calorie estimation, we plot the mean calories reported for each device at different efforts. We can see a general agreement at low intensities, but differences grow as the integral of HR reserve increases. 

Device B predicts higher calorie expenditure than the gold-standard Keytel rule while device D (motion-feature based) consistently predicts lower.

What does this mean?

If you are one of those users owning multiple brands of wearables and can’t decide which one to follow, probably neither, or all of them! The largest differences in calories come from baseline metabolic rate estimates. 

Some devices include passive activity calories within your baseline, others add it on to the daily activity calories which means you probably should not be comparing activity calories across devices.

If there is one metric you can trust is the activity session calories. Most devices agree that the Keytel formulation for energy expenditure during exercise is the gold standard. This method takes your heart rate over resting heart rate during your activity as a proxy for oxygen consumption and derives calorie burning from it. 

While we don’t have a calorimeter device to compare how truthful this is, this should be consistent on all of your watches.

References

1. Keytel, L. R., Goedecke, J. H., Noakes, T. D., Hiiloskorpi, H., Laukkanen, R., van der Merwe, L., & Lambert, E. V. (2005). Prediction of energy expenditure from heart rate monitoring during submaximal exercise. Journal of sports sciences, 23(3), 289–297. https://doi.org/10.1080/02640410470001730089