How many calories do I need?: An empirical approach

It’s been said many times that weight loss isn’t easy but it is simple. Overall this is a pretty true statement. If you eat a certain number of calories per day, and you want to lose weight, you can reduce this number and, as long as your level of activity stays the same, you will probably lose weight. To get an idea of how many calories are significant, there are a couple of formulas that people tend to use. The first is the number of calories that your body needs, which is stated by many sources as

BMR = 10 * weight(kg) + 6.25 * height(cm) – 5 * age(y) + 5 (man)
BMR = 10 * weight(kg) + 6.25 * height(cm) – 5 * age(y) – 161 (woman)

where BMR is the basal metabolic rate, the number of calories that your body needs to survive. To get your full caloric need, you are then instructed to add a number of calories corresponding to your degree of daily activity

Total needed = BMR + activity.

Now, both of these numbers are highly uncertain for an individual. This is a common problem for health-related sciences, where they have to quantify a huge population of diverse people with an average quantity. For instance, it’s normally assumed that Body Mass Index for a person indicates how fat the person is, but in fact that relationship is highly imperfect:

BMIvsBFDepending on your body type, your BMR might be several hundred calories less than the formula or several hundred more. And estimating your activity level is at least as uncertain, since it will vary based on how much weight you lift, how much cardio you do, and how much walking around you do in your job. All of these things are logical, but they aren’t trivial to quantify.

So I set out to determine what my actual caloric need was, which was kind of a side issue to the fact that I wanted to cut my body fat percentage (call it Justin-Theroux-envy after watching The Leftovers this summer). In my view, what people mostly want to accomplish in a weight loss program is not weight loss per se, but a drop in body fat percentage. For men, this is accompanied by a desire to simultaneously maximize muscle mass, which is somewhat independent from body fat percentage (that is, you can have a very low body fat percentage while still not having very much muscle, like Iggy Pop, and you can also be very muscular but still have a high percentage of body fat, like most NFL linebackers). There is only one scientific fact I use: that a pound of fat is 3500 calories. You might think that this is as unsure as all the other numbers, but in fact I think not—a pound of fat can be put into a bomb calorimeter and the heat released in it measured precisely. So I have every confidence that number is correct.

Here is a method that seems to work pretty well.

Step 1: Measure your body fat percentage.
Step 2: Diet and exercise while collecting weight and caloric intake data every day for a few months.
Step 3: Measure body fat percentage at regular intervals (say, once a month)
Step 4: Determine true fat loss and compare with how many calories you’ve cut
Step 5: Determine the actual number of calories you’ve cut, therefore telling you your true caloric need.

Once these steps are complete, we can calculate our individual body’s caloric need.

Step 1: Measure your body fat percentage

Measuring body fat percentage isn’t all that difficult, and with calipers it’s not that expensive either. A necessary caliper can be bought from Amazon for about $14. Then, follow the directions on this site for where to measure: The formulas given on the page are straightforward to apply, in my Excel file I had, for example

Triceps Pectoral Abdomen Supra-
iliac
Thigh Density % Body fat
7/9/2014 17 14 23 20 12 1.038 25.9
9/1/2014 10 8 17 17 12 1.052 20.1

I took data only after large changes. The measurement itself is a bit cumbersome to do alone, and the idea of pinching my skin every day with those calipers is not appealing. The measurement itself is about +/- 2% when done correctly. Also, be aware that for extremes of body fat this method is not nearly as effective. My presumption is that if I manage to get down to about 10% body fat (unlikely), I will need to visit a bod-pod facility to have my body fat measured professionally. However, in my regime (15-25%), it’s fine.

Step 2: Diet and exercise

It’s really irrelevant how much you decide to cut out of your diet. I estimated based on the BMR and activity that I needed about 2400 calories per day (this turned out to be wrong). I therefore resolved to eat between 1200 and 1400 calories each day, for around a 1000 calorie per day deficit. I also started working out every day, two days lifting and one day cardio. Again, it’s not rocket science. My weight over time looked like this:

weightvstimeObviously the weight you are has a bit of variance from day to day, based on the amount of water in your body and the amount of food still in your stomach and intestines. It’s a good idea to collect the data every day and do a regression fit like this to give a good estimate of your true weight. I also recommend weighing yourself at the same time and under the same circumstances every day. In my case, it was after working out, shoes off, at night.

As for calorie counting, I used the iPhone myfitnesspal app most of the time. Every day I entered my caloric intake into a spreadsheet along with the date and my weight.

Step 3: Determining your actual caloric rate

Since I went from 25% to 20% fat between those two dates, the lean weight gained is

lean weight gained = 0.8 current weight – 0.75 previous weight = 0.7 pounds

Here’s where we make our first correction to caloric need. A deficit of 1000 calories, especially with an increase in my exercise, should have yielded a fat loss of 7000/3500 = 2 pounds a week. Between the two dates that I measured my body fat, my actual body fat percentage dropped 5% and my weight had dropped 9 pounds. That was over 8 weeks exactly, so while I thought I would lose 16 pounds of fat, I actually lost 9.7 pounds of fat. This implies that my caloric deficit was actually 600 calories per day and not 1000. Clearly, the formula predicting 2400 calories was not right for me. And, in fact, my body needs just 2000 calories to maintain weight.

This process should be done iteratively, and I carried out this procedure on a longer time span. Assuming this is right, by now (9/28/2014) I have gained about 1.67 pounds of lean weight and lost 13.2 pounds of total weight, making my total fat loss 14.9 pounds. This predicts a body fat percentage of 16%, whereas a caliper measurement today determines it as 17% (not bad!). Making the assumption that the weight went on evenly, we can plot our weight versus our calorie deficit (divided by 3500) assuming that my “activity” is 369 calories per day:

deficitvsweightlossWith a slope of 1, this now appears to be a correct determination of my metabolic rate (both basal and active). At my present weight I need 1890 calories per day to maintain weight, a far cry from the equation commonly cited, which I thought would predict my rate at 2400 calories. In reality, I was probably overestimating my “activity” by a few hundred calories, and likely my job is too sedentary to fit with the average BMR as well.

But actually it doesn’t matter what the cause is. This process is iterative and totally empirical, and so far as I can tell is a quite accurate way to determine your necessary caloric intake. Now note that even this 1890 calories assumes that my workout plan stays the same. If I start lifting heavier it might go up, and if I slack off it might go down. In particular, I would recommend that any time you see a kink in your weight versus time graph, you start recalculating. That hasn’t happened to me yet.

Here’s the Excel file with all the formulas and with my data. You can use it to enter your own information and determine your own caloric rate.

Shameless plug: My book is on Amazon

Just a quick off-season note: I haven’t been blogging much at all, but I did put all the finishing touches on my book, Thermo for Normals: Everyday Thermodynamics for non-scientists. If you are a regular reader of this site, you have the technical expertise to read and understand it, as it takes a look at thermodynamics from an accessible perspective. Here’s the link: Thermo for Normals

Top 2 projection (updated)

Name Song WNTS MJs VF Not-safe Probability
Caleb Johnson Dream On / Maybe I’m Amazed / As Long As You Love Me 57.667 61.7 32 0.585
Jena Irene Dog Days Are Over / Can’t Help Falling in Love / We Are One 65.333 38.3 68 0.415

Important!

The methodology for the finals model is described here (though some modifications have been made to replace Dialidol with MJsBigBlog’s poll). The model is 87% accurate on ranking within a margin of error of +/- 3%. Probabilities being what they are, somebody with a not-safe probability of just 0.25 will be in the bottom 3 one out of four times. Please do not comment that the numbers are wrong. They are probabilities, not certainties or even claims. Do not gamble based on these numbers.

Name in green is most likely to be safe. Name in red is considered most at risk for being eliminated. The most probable elimination is Caleb. However, no result would be shocking.

The contest is far from a runaway for Jena Irene, but it certainly doesn’t look bad for her.

No matter what happens tomorrow, we will see some Idol history made.

Dialidol (which the IdolAnalytics projection model no longer uses) registered no busy signals for Caleb, but did register some for Jena. If she loses, that will be the first time Dialidol did not project the winner correctly. However, there is no particular reason for us to believe it, since Dialidol has been anti-correlated with being safe this year. It will also be a record for Votefair, which has had the winner up only half the time, but never missed by more than 18.5 percentage points (Jena is currently up by 44 points).

On the other hand, Jena would be the first wild-card to win, and the first to win with a trip to the bottom group when her opponent had never been (this result may not be significant, though).

As such, I’m somewhat comfortable with the assigned odds, which I mentioned before I felt were pretty even. I would not be shocked in the least if Caleb wins. The contest is a bit like a coin flip, though one side of the coin is just a bit heavier than the other.

I’ll update later in the day. Note that I’ve flipped MJs poll since she asked “Who Will Win?” instead of “Who will go home?”

Below are the running stats for the model performance this year. The assigned probabilities have been more accurate than I could have hoped for within one season. Contestants projected with a probability of being not-safe in any category with more than 10 projections were usually right in the middle of the range. In the bin from 50-60%, 8 out of 10 were not-safe, making those possibly a little hesitant, but with such a small sample size it’s impossible to tell. The one dim spot was in the very low end, from 10 to 20%, with only 2 of 26 (8%) being not-safe, lower than 15%, but again it’s still well within the confidence interval (binomial proportion estimate at 95%).

S13ProbsvsResults