## The Calorie Project – Update 3: How Calorie Intake & Energy Expenditure Affect Body Weight, Body Fat %, Strength and Appearance

When I first started The Calorie Project, my ultimate goal was to gather enough data in order to analyze the relationship between calorie intake, energy expenditure, weight and body fat. Fully understanding these relationships would allow me to gain, lose or maintain weight more precisely without having to guess the appropriate calorie intake. In this update, I’ll go over some of the tweaks I’ve made to this project, showcase new graphs and discuss my future goals.

**History**

Update 1 – 15 Sep 13: 152.6 pounds – 6.0% body fat

Update 2 – 03 Nov 13: 152.2 pounds – 5.7% body fat

**Progress Since the Last Update**

- Body Weight (daily average 19-25 Jan): 145.49lbs
- down from 152.2lbs in the last update

- Body Fat Percentage (daily average 19-25 Jan): 4.49%
- down from 5.7% in the last update

**Progress Picture: 20 Jan 14 – 144.0 pounds – 3.9% body fat – full size**

**What is The Calorie Project?**

In the beginning, this project was simply about tracking how calorie intake affected body weight. I weighed myself once per week and counted my calorie intake everyday (with the help of MyFitnessPal). I compared my average weekly calorie intake to my once a week weigh-in.

Over time, I started making new relationships and tracking more data such as strength, energy expenditure, body fat and physical appearance. Exercise and diet play a very important role in life and this is my way of showing everyone how. For a more in depth description of The Calorie Project, read through update 1 and update 2.

**Tweaks**

**Daily Weigh-Ins.** Until a few weeks ago, I was tracking weight and body fat once per week and comparing those numbers to my average calorie intake and energy expenditure for the entire week. I only recently realized this approach doesn’t make much sense.

This project is about correlating specific levels of calorie intake & energy expenditure to changes in weight and body fat. There are many factors affecting weight, some of them permanent and others, only temporary. This project is concerned with the permanent changes in weight caused by increases and decreases in body fat and muscle.

Temporary weight changes aren’t caused by calorie intake, but instead, water weight and/or meal size. A once per week weigh-in isn’t the most accurate way of tracking weight. If I ate more or less than I normally do or drank too much/too little water the day before, my weight would not reflect my calorie intake or exercise level for that entire week.

Instead of a once per week weigh-in, I’ve started daily weigh-ins and body fat tracking. At the end of each week, I calculate my average weight and body fat for the past seven days. I now compare my average weekly weight/body fat to my average weekly calorie intake/energy expenditure. This should smooth out daily weight fluctuations caused by meal size and water weight.

Image: Daily Weight, Calorie, Body Fat Tracking

**Nike FuelBand.** I’ve also been gathering more data on my Nike FuelBand. In addition to motivation, the FuelBand gives you valuable data on how many calories you burn each day. Calorie intake is only part of the weight balance equation. A full understanding of calorie intake in addition to energy expenditure makes weight balance much easier. If accurate, this energy expenditure data has the potential to be very useful.

**The Calorie Project’s Main Goal**

The main goal of The Calorie Project has always been to better understand the relationship between calorie intake, energy expenditure, weight and body fat. Weight control advice goes something like this:

- Step 1: Estimate out how many calories you burn with a calorie calculator.
- Step 2: To gain weight, eat 500 calories more than you burn. To lose weight, eat 500 calories less than you burn. To maintain weight, eat and burn the same amount.
- Step 3: Weigh yourself weekly. Make adjustments to calorie intake based on long term changes in weight.

This is pretty good advice, it’s what I tell people who are looking for weight guidance. Since this advice is based on the calorie calculator‘s estimate of how much energy you burn each day, it might take weeks of trial and error before figuring out the proper calorie intake for a specific weight goal.

I’m looking for more control. Once I know what a certain calorie intake and exercise level does to my bodyweight, I can reach my weight goals with a lot less guesswork. The Calorie Project gives me the information I need to reach my weight goal easily without weeks of calorie trial and error.

**Scatter Plots and Correlations**

All graphs are current as of 25 Jan 2014.

The following scatter plots are the heart of this project. They plot calorie intake & energy expenditure to weekly changes in body weight. With the help of some simple algebra (and Excel), I can find the best fitting line, giving me insight on the appropriate calorie intake and energy expenditure levels for certain weight goals.

**Scatter Plot # 1: Calorie Intake vs. Changes in Body Weight**

This graph plots my average weekly calorie intake (X-axis) against my week to week change in weight (Y-axis). Excel calculated the equation of the best fitting line (y = 0.0023x – 7.2285).

According to MathIsFun, the best fitting line is defined as, “A line on a graph showing the general direction that a group of points seem to be heading.” The individual points on this scatter plot are generally moving up and to the right: a positive correlation between the two variables. This positive correlation means a larger calorie intake is generally associated with an increase in weight. The best fitting line simply shows the general direction of all the points.

The R^{2} value of the scatter plot describes how well the two variables correlate to each other. An R^{2} value of 1.0 is a perfect correlation while a lower R^{2} value shows a weaker correlation. The R^{2} value of this graph is 0.1737 which is a somewhat weak correlation.

**Math Alert!**

The equation of the best fitting line is important because it provides suggestions on how much to eat. My weekly change in weight is plotted on the Y-axis. If I wanted to mathematically figure out which calorie intake is best associated with no weight change, I could plug zero into the equation for Y. This would give me the X value when Y equals zero; in other words, this would give me the calorie intake level (X) that’s best associated with no weekly change in body weight. Here’s the math:

- Step 1 – the equation: y = 0.0023x – 7.2285
- Step 2 – plug zero in for Y: 0 = .0023x – 7.2285
- Step 3 – solve for X: -.0023x = -7.2285
- x = -7.2285 / -.0023
- x = 3,143 calories

This tells me that historically, 3,143 calories is associated with no change in body weight. If I wanted to keep my body weight constant, I should eat approximately 3,143 calories per day. Unfortunately, with an R^{2} value of 0.17, this calculation isn’t anywhere near perfect. Hopefully, as I gather more data (especially the average weekly weight rather than the once per week weigh-in), the grouping of the points will tighten up giving me more accurate calorie suggestions.

**Scatter Plot #2: Energy Expenditure vs. Changes in Body Weight**

This graph plots my average weekly energy expenditure (as calculated on my Nike FuelBand – X-axis) against the week to week change in my body weight (Y-axis).

Unfortunately, the Nike FuelBand data doesn’t seem to be as accurate as I hoped. The R^{2} value of this graph is 0.0046 which means there is no correlation. I starting using the FuelBand in August and have much less energy expenditure data than I do calorie intake data. Though unlikely, I’m hopeful that over time, this data will somehow become more accurate.

Though the data seems inaccurate, the ability to track movement on a device such as the FuelBand is extremely motivating and pushes me to keep increasing my physical activity level. In my opinion, the FuelBand is a great tool to help you move more, and ultimately, improve your fitness standing and overall health.

**Scatter Plot #3: Calorie Surplus/Deficit vs. Changes in Body Weight**

Alone, calorie intake and energy expenditure are only half of the equation. The difference between calories consumed and calories burned causes weight change. This graph is a combination of the first two. When you subtract energy expenditure from calorie intake, you either get a calorie surplus (positive number) or a calorie deficit (negative number).

- calorie intake – energy expenditure =
- positive number = calorie surplus
- calorie surplus: consuming more than you burn; leads to weight gain

- negative number = calorie deficit
- calorie deficit: burning more than you consume; leads to weight loss

- positive number = calorie surplus

Since this graph is based on the above graphs (the ones with low R^{2} values), the correlation here is also going to be weak. The R^{2} value of this graph is 0.05, a very weak correlation. Generally, the best fitting line is going in the expected direction. As the difference between calories consumed and burned increases (a more positive value means consumption is increasing relative to energy expenditure), so does weight gain.

I want to know what level of calorie surplus or deficit keeps my weight stable. Technically, this number should be zero (weight is unchanged when calorie consumption equals energy burned – neither a surplus or deficit) but since none the variables are 100% accurate (calorie counting, FuelBand data, or body weight measurements), the weight balance spot (neither gaining or losing weight) won’t be zero calories.

The point on the graph where weight is unchanged is where Y equals zero. Looking at the graph, Y=0 at around 350 calories. We can verify this mathematically like we did in the first graph:

- Step 1 – the equation: y = 0.0014x – 0.5229
- Step 2 – plug zero in for Y: 0 = 0.0014x – 0.5229
- Step 3 – solve for X: -0.0014x = -0.5229
- x = -0.5229 / -0.0014
- x = 373.5 calories

When (calorie intake)-(Nike FuelBand energy expenditure) = 373.5 calories, my body weight stays the same. I know this might seem confusing because weight is supposed to stay the same only when calorie intake **EQUALS** energy expenditure. Unfortunately, that only happens in a perfect world when all the variables are 100% accurate.

If I had a way to [100%] accurately measure my body weight and [100%] accurately measure my calorie intake and [100%] accurately measure my energy expenditure, then yes, weight would be unchanged only when calorie intake and energy expenditure were equal. Unfortunately, it’s very difficult to [100%] accurately measure all of these variables, especially energy expenditure and to a lesser degree, permanent changes (body fat and muscle) in body weight. According to the data I’ve gathered so far, when my calorie intake is 373.5 calories above my energy expenditure (according to the Nike FuelBand), my weight remains the same.

**The Classic Graphs**

Here are the graphs I used in the previous updates.

**Graph #1: Body Weight vs Calorie Intake & Energy Expenditure**

This graph illustrates the basic weight control equation: body weight (blue) vs. calorie intake (red) and energy expenditure (green). As we found out earlier, the FuelBand energy expenditure numbers don’t seem to be accurate. The general trend here is when my intake is below 3300 calories, I lose weight.

**Graph #2: Body Weight vs Calorie Intake & Energy Expenditure**

This graph is similar to graph #1 but it combines calorie intake with energy expenditure into one line. A positive red line indicates a calorie surplus while a negative red line indicates a deficit. Again, since the energy expenditure data is inaccurate, this graph is somewhat useless other than reminding me how inaccurate the data is.

Graph #1 and #2 illustrate the most basic weight balance rule: the combination of calorie intake and energy expenditure is the only way to control weight.

**Graph #3: Body Fat Percentage vs. Calorie Intake**

This graph illustrates body fat percentage (blue) and calorie intake (red). Many people think it’s possible to burn fat without cutting calories. When you cut calories and create a calorie deficit, the body is forced to make up the shortfall of energy with stored fat leading to weight loss and a reduction in body fat. As with body weight, my body fat decreased only when my intake fell below 3300 calories.

**Graph #5: Body Fat Percentage vs. Body Weight**

This graph illustrates body fat percentage (red) and body weight (blue). The point of this graph is to show that burning fat causes a decrease in body weight. Many people are obsessed with gaining weight and refuse to believe that burning fat requires weight loss. There is no way to burn body fat without losing weight. Weight loss and fat burning are different ways of describing the same process.

**Strength Numbers**

In update 2, I began tracking the effects of decreasing body weight on my strength numbers at the gym. Typically, strength decreases with weight loss because during periods of calorie deficiency, the body burns fat and muscle for energy.

There are two ways to measure strength: relative and absolute. Update 2 contains a complete description of the differences.

As of update 2, both my absolute and relative strength numbers were increasing even though my body weight was decreasing. I said, “I am not sure why I seem to be getting stronger as I lose more weight but I doubt I can keep this pace up for much longer if I continue my weight loss.”

I was unfortunately right and my strength numbers recently began to plummet as I continued to lose more weight. Luckily, I’ve reached my weight loss goal of 145 pounds. Once I began increasing my calorie intake, my strength numbers began to level off.

**Graph # 6: Absolute Strength vs. Body Weight**

This graph illustrates absolute strength (sum of all three lifts: squat + deadlift + bench press – red) and body weight (blue). Between July and November, my absolute strength was increasing slightly despite a decreasing body weight. In November, I had my first big strength collapse followed by another one in December/January. The slight uptick at the very end of the graph is what I hope to be a leveling off as I increase calorie intake.

**Graph # 6a: Squat, Deadlift, Bench Press 1-Repetition Max vs. Body Weight**

This graph also illustrates absolute strength and body weight (blue) but separates the three lifts into separate lines.

**Graph #7: Relative Strength vs. Body Weight**

This graph illustrates relative strength (red) and body weight (blue). Relative strength is a ratio:

- relative strength = (amount lifted) / (body weight)
- if you lift 300 pounds and weigh 160 pounds, relative strength = 300 / 160 = 1.875, in other words, you lift 1.875 times your body weight

This graph shows the sum of all the ratios: squat ratio + deadlift ratio + bench press ratio.

**Graph #7a: Relative Strength of Squat, Deadlift and Bench Press vs. Body Weight**

This graph also illustrates relative strength and body weight (blue) but separates the three lifts into separate lines.

**My Future Goals**

Now that I’ve reached my weight loss goal, it’s time to start the next phase of my body transformation. If you’ve been following my War on Bulking series, you know my philosophy on gaining muscle. Too many people (including my younger self) are obsessed with gaining weight rather than muscle.

Muscle growth is a very slow process limited to about 10-15 pounds per year. The 10-15 pounds is strictly muscle; body fat gains are essentially limitless. Because 10-15 pounds per year is painfully slow, many bulkers simply eat more to speed up weight gain with the mistaken belief that more calories and protein lead to faster muscle growth. The amount of calories (and even protein) we eat is not the limiting factor in muscle growth; the body simply lacks the ability to grow muscle at a faster pace.

Stored body fat is extra energy. If you gain 10 pounds of muscle and 40 pounds of fat in an year, the 40 pounds of fat represents the excessive part of your calorie surplus. It’s energy beyond what the body needs to build muscle.

**Fat-Free Muscle Gain**

My goal over the next year is to gain 10 pounds of muscle with minimal fat gain. Though it pounds doesn’t sound like a lot, 10 pounds of 100% muscle is quite a bit of weight to put on.

Ten pounds divided by 52 weeks per year equals 0.19 pounds per week or roughly one pound every 5-6 weeks. I was hoping my calorie scatter plots would’ve given me more accurate data which would’ve allowed me to mathematically pick the appropriate calorie intake and energy expenditure level. Unfortunately, the data turned out to be inaccurate, especially the energy expenditure part.

To achieve my 0.19 pound per week weight gain goal, I plan to slowly increase my calorie intake and track changes to weight. Based on my average weight change, I’ll make adjustments to my calorie intake as needed.

Yes, this seems like a lot of work to gain what seems like such a small amount of weight but there’s no point in gaining 50 pounds of body weight if only 10 of those pounds are muscle. The route of gaining excessive body fat followed by a lengthy period of cutting is wasteful and time consuming. What’s the point of gaining all the fat (which is defined as unneeded and excessive energy) if you plan on burning it when beach season starts? Gaining fat does not lead to faster muscle growth.

**My Plan**

One pound of body weight is equal to approximately 3500 calories. If you want to gain a pound, create a surplus of 3500 calories over a given period (for example a week or month). Gaining muscle without fat doesn’t require too much extra energy. For my goal of 0.19 pounds per week, I’ll need an energy surplus of (3500 calories X 0.19lb) 665 calories per week or only 95 calories per day.

The amount of fat gained is defined as extra energy the body did not use. Food is stored as fat when you consume more energy than the body needs. If the body needs 3000 calories to build muscle at the fastest pace it’s capable of, any amount of food above 3000 calories is stored as fat. More food does not necessarily lead to faster muscle growth. Small increases in calorie intake should allow me to gain muscle with very little added body fat.