A research-backed thermodynamic model for predicting changes in weight, body fat percentage, and lean body mass.
Protokl uses a weekly time-series simulation to forecast how your body composition will change over 6 to 12 months based on your selected goal (Muscle Gain, Body Recomposition, or Fat Loss), pace (Slow, Moderate, or Aggressive), and training experience level (Beginner, Intermediate, or Advanced).
The model produces two forecast lines on the body composition charts:
The maximum rate of muscle gain is governed by training experience. Protokl uses the Alan Aragon model, which expresses monthly muscle gain potential as a percentage of bodyweight:
| Training Level | Monthly Rate | At 160 lbs |
|---|---|---|
| Beginner (Year 1) | 1.0–1.5% BW | 1.6–2.4 lbs/month |
| Intermediate (Year 2–3) | 0.5–1.0% BW | 0.8–1.6 lbs/month |
| Advanced (Year 3+) | 0.25–0.5% BW | 0.4–0.8 lbs/month |
Instead of discrete step-function tiers, the model uses a continuous negative exponential bounded by the user's genetic ceiling (Fat-Free Mass Index = 25 for natural males, 22 for females):
Where Lmax is calculated from the user's height using the FFMI ceiling, and k is calibrated so the initial growth rate matches the Aragon cap for their training level. As lean mass approaches the genetic ceiling, growth rate smoothly approaches zero with no sudden cliff between training levels.[1][2]
The calorie surplus for muscle gain is derived from the user's actual muscle-building capacity, not a blanket percentage of TDEE. Research shows that larger surpluses primarily increase fat gain rather than augmenting muscle growth.[3]
This means an advanced lifter who can only gain ~0.5 lbs muscle/month gets a surplus of roughly 60–90 cal/day, while a beginner who can gain ~2 lbs/month gets approximately 230–430 cal/day.
The maximum rate at which the body can mobilize energy from fat stores is constrained by the amount of fat currently present. Alpert (2005) established this limit at approximately 22 kcal per pound of fat mass per day (corrected value).[5]
| Current Body Fat % | Fat Mass (at 160 lbs) | Max Safe Deficit | Max Fat Loss/Week |
|---|---|---|---|
| 30% | 48 lbs | ~1,056 cal/day | ~2.1 lbs |
| 20% | 32 lbs | ~704 cal/day | ~1.4 lbs |
| 15% | 24 lbs | ~528 cal/day | ~1.1 lbs |
| 10% | 16 lbs | ~352 cal/day | ~0.7 lbs |
Pace selects what fraction of the Alpert maximum is used: Slow = 50%, Moderate = 70%, Aggressive = 90%. If the deficit exceeds this physiological limit, the body draws the excess energy from lean tissue rather than fat.[5]
The Forbes P-ratio model determines what fraction of weight lost comes from lean mass versus fat mass. The original Forbes equation uses a constant c = 10.4 for untrained individuals, predicting that nearly half of weight lost is lean mass at moderate body fat levels.[6]
Rather than applying a flat reduction multiplier for resistance training (which fails at boundary conditions), Protokl shifts the rate constant c itself based on training status:[7]
| Training Level | Forbes c | Lean Mass Loss % (at 15% BF) |
|---|---|---|
| Untrained | 10.4 | ~49% |
| Beginner | 1.5 | ~12% |
| Intermediate | 1.0 | ~8% |
| Advanced | 0.7 | ~6% |
This is consistent with findings that trained athletes with adequate protein intake preserve 90–95% of lean mass even in aggressive caloric deficits.[3][7]
Body recomposition involves simultaneously gaining muscle and losing fat while keeping total weight approximately stable. The model accounts for asymmetric tissue energy densities: building 1 lb of muscle requires approximately 2,500 kcal, while mobilizing 1 lb of fat yields approximately 3,500 kcal. This means the body must burn roughly 0.71 lbs of fat to fuel the synthesis of 1 lb of muscle at maintenance calories.[8]
The result is a slight net weight increase even at zero energy balance, which is physiologically correct. The rate of recomposition is capped by the Aragon muscle gain rate at 50% of the surplus growth rate, reflecting the reduced anabolic efficiency at maintenance versus surplus calories.
Total Daily Energy Expenditure adapts to changes in body composition and energy balance through three independent mechanisms:
Each pound of lean mass costs approximately 14 kcal/day to maintain. Each pound of fat mass costs approximately 2 kcal/day. As tissue is gained or lost, TDEE shifts proportionally.[9]
The nervous system down-regulates non-exercise activity thermogenesis (NEAT) and basal metabolic rate in response to energy deficit. This is modeled as a logarithmic function of the current deficit size:[10]
Severe deficits trigger disproportionately more NEAT suppression than gradual ones, regardless of total weight lost.
Digesting food costs energy proportional to caloric intake. The model applies a TEF coefficient of approximately 10% for a mixed diet (up to 15% for high-protein diets). A 500 cal surplus adds roughly 50 cal/day to TDEE through TEF alone.[11]
When caloric intake shifts from maintenance, glycogen stores change within days. The body stores approximately 400g of glycogen, and each gram binds approximately 3g of water. This creates acute scale weight swings of 2–5 lbs in the first 1–2 weeks that are not real tissue changes.[12]
The model tracks glycogen and water as a separate compartment. Display weight includes this component (because the scale reflects it), but lean and fat mass calculations exclude it. 70% of the shift occurs in week 1, 30% in week 2.
The forecast includes a 90% confidence interval derived from two independent sources of variance:
On the chart, this appears as a shaded region around the Plan Forecast line, communicating to the user the range of likely outcomes if the plan is followed.
When caloric surplus exceeds what muscle synthesis can use, the remainder is stored as fat. This conversion is not 100% efficient:[4]
For a mixed-macro surplus, the blended efficiency is approximately 85%. The difference is dissipated as heat through the metabolic conversion process.
This methodology is implemented in Protokl's body composition forecasting engine. The model is deterministic given the input parameters and runs entirely on-device with no server-side computation. All projections are estimates based on population-level research and individual results will vary.
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