How the Math Works

Each day, Muscle Diary decides how much muscle you build from the balance between "stimulus to your muscles" and "recovery from fatigue," and any calories not used to build muscle go to body fat. This page explains the formulas used in the game and what they're based on.

The game works in metric units internally (kilograms and centimeters) and shows pounds and feet/inches on screen. 1 lb = 0.4536 kg and 1 in = 2.54 cm.

1. Estimating your one-rep max (1RM)

Your one-rep max (1RM) is the most weight you can lift for a single rep. The game estimates it from the weight and reps you enter on the first screen, using the Epley formula.

Example: you can bench 135 lb for 5 reps
135 × (1 + 5 ÷ 30) = about 158 lb

If you enter 1 rep, that weight is your 1RM. The more reps, the less accurate the estimate, so the game goes up to 12 reps.

If you don't know your lifts, the estimate is your body weight times the ratio below (the squat is 1.3 times that, and the deadlift 1.55 times).

2. How muscle grows

Muscle is tracked as lean mass (your weight minus body fat). The muscle you build each day is calculated like this:

Monthly limit for your experience

About how much muscle you could build in a month with ideal training and nutrition. It's based on experience-level guidelines commonly used in strength coaching.

Stimulus

The total stimulus for the muscle groups you trained that day. It's set so that training each of the three groups (chest, legs, back) twice a week at Normal intensity averages out to exactly 1 per day. This follows research showing that training each muscle at least twice a week builds more muscle than once a week.

• On full-body days, each of the three groups gets 0.6 times the stimulus and fatigue.
• Training a muscle that's still fatigued multiplies its stimulus by "1 − fatigue ÷ 100" (half at fatigue 50).
• Keep the same plan for 4 weeks and you hit a plateau: stimulus is multiplied by 0.8. Change your plan and it goes back to normal.
• On days when the gym is packed, stimulus is multiplied by 0.7.

Protein, sleep, and food

Research suggests that, for building muscle with strength training, more protein helps up to about 1.6 g per kg of body weight (about 0.73 g per lb) per day, and eating more than that makes little difference. In the game, adding a shake to reach 1 g/lb still gives a factor of 1.0; it only adds 120 kcal a day.

The food factor is based on the calorie difference set by how much you eat (plus 1,200 kcal on days with a night out), blending smoothly between −500 kcal and +300 kcal. It doesn't include the extra calories burned only on training days.

Room to grow

The closer you get to your natural limit, the harder it is to build muscle. The game uses the fat-free mass index (FFMI) as a guide to that limit.

The limit is 25 for men and 21 for women, and the reference (the upper end for people who don't train) is 20 for men and 16.5 for women. The male limit of 25 is based on a study that found the FFMI of people not using drugs topped out at about 25. There's less research on women, so the female values are estimates based on the gap with men.

When you don't train

If you don't train at all for a week, you lose 0.005 kg (about 0.01 lb) of muscle a day. And for any muscle group you haven't trained in more than 10 days, its 1RM drops by 0.05% a day.

3. How your 1RM goes up

Your 1RM goes up by the sum of the muscle you built in that group and neural adaptation.

• Muscle: it rises in proportion to the share of that day's new muscle that went to that group (each group is counted as one third of your lean mass).
• Neural adaptation: when you first start lifting, your body gets better at producing force before your muscles actually grow, so your lifts go up first. Each experience level has a pool for this (20% for brand new, 8% for under 6 months, 3% for 1 year or more), and every time you train that group, you use up 15% of what's left. Lifts jump in the first 4–6 weeks and then level off.

Lifts map to muscle groups like this: bench press = chest, squat = legs, deadlift = back.

4. Fatigue, injury, and motivation

• Fatigue: each muscle group has a value from 0 to 100 that recovers with sleep each night. Recovery is 18 for 5 hours, 30 for 7 hours, and 36 for 9 hours. With 7 hours of sleep, fatigue from a Normal session wears off in about 2 days.
• Injury: if you train "To failure" and that group's fatigue goes over 80 afterward, there's an 8% chance of injury. An injured group can't be trained for 7 days.
• Motivation: a value from 0 to 100 that drifts toward 60 if nothing happens. Rest days and personal records raise it; training to failure, short sleep, cutting, and injuries lower it. Below 60 there's a 5% chance of skipping a workout, and below 30 a 40% chance (each +10% on weekends and rainy days).

5. Calorie balance and body fat

Calories burned are calculated the same way as in Diet Diary. Resting metabolism (BMR) uses the Mifflin-St Jeor equation.

Calories eaten start from "maintenance calories" (BMR × activity factor plus your average daily calories from lifting across the week), then add the amount set by how much you eat (Cut −500 kcal, Maintain ±0, Bulk +300 kcal). A protein shake adds 120 kcal, and a night out adds 1,200 kcal.

From each day's balance, the calories used to build muscle (about 2,500 kcal per kg, or about 1,130 kcal per lb) are subtracted, and what's left changes your body fat.

Body fat tissue is about 80% fat, and 1 g of fat holds about 9 kcal, so 1 kg of body fat is equivalent to about 7,200 kcal (1,000 g × 0.8 × 9 kcal), or about 3,300 kcal per lb. You may have heard the common "3,500 calories per pound" rule; that's a little higher than the value used in this game. Your weight is the sum of your lean mass and body fat.

Sources

• Epley B. Poundage Chart. Boyd Epley Workout. Lincoln, NE: Body Enterprises, 1985.
• Morton RW, Murphy KT, McKellar SR, et al. "A systematic review, meta-analysis and meta-regression of the effect of protein supplementation on resistance training-induced gains in muscle mass and strength in healthy adults." British Journal of Sports Medicine, 2018; 52(6): 376–384.
• Schoenfeld BJ, Ogborn D, Krieger JW. "Effects of resistance training frequency on measures of muscle hypertrophy: a systematic review and meta-analysis." Sports Medicine, 2016; 46(11): 1689–1697.
• Kouri EM, Pope HG Jr, Katz DL, Oliva P. "Fat-free mass index in users and nonusers of anabolic-androgenic steroids." Clinical Journal of Sport Medicine, 1995; 5(4): 223–228.
• Mifflin MD, St Jeor ST, et al. "A new predictive equation for resting energy expenditure in healthy individuals." The American Journal of Clinical Nutrition, 1990; 51(2): 241–247.
• Ainsworth BE, et al. "2011 Compendium of Physical Activities: a second update of codes and MET values." Medicine & Science in Sports & Exercise, 2011; 43(8): 1575–1581.

The calculations in the game are simplified from the sources above and widely used guidelines so the game is easy to play. The odds and effects of fatigue, injuries, motivation, and events are tuned for gameplay. Real results vary from person to person. Talk to a doctor, certified trainer, or other professional about real training and nutrition.