# Measuring Fat Loss without the scale

**isomorphismes**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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@tdhopper posted his self-measurements of weight loss

a few months back. I recently decided also that I wanted to lose fat-weight—the infamous “I could stand to be a few kilos lighter”—and I think I came up with a more productive way of thinking about my progress: **I’m not going to look at the scale at all.** I’m just going to count calorie estimates from the treadmill estimator or use online calculators for how much is burned by running / swimming — and calories burned is the only thing I will use: no attempts at eating less.

Also, instead of thinking in terms of *weight* I’m going to think in terms of *volume*. Here are some pictures of people holding 5 pounds of fat (2¼ kilos):

As you can see this is a large fraction of a person’s flesh, if their BMI is in the healthy range.

I’m not so fat that I have tens of litres of fat making up my body. Rather if I look at myself and visually “remove 2 litres” that “looks” like it would be very substantial—such a huge volume that, of course it would take weeks of diligent exercise!

But as we know from Mr Hopper’s posts (or I know it from my own experience of weighing myself), the noise is louder than the signal.

The magnitude of daily variation swamps the magnitude of “fundamental” progress.

The goal of counting kcal burned and thinking in terms of volume is to make both the goals and the progress feel more visceral. Everybody knows how to lose weight, the problem is just that one doesn’t do it. Other than simply increasing self-discipline or increasing the mental energy I put towards this goal (neither of which I want to do).

- More accurate measurement of my small-scale progress and
- Choosing meaningful goals in the first place—not a number grabbed out of the air (“five kilos”—why five?), but rather imagine how much volume has left my muffin-top and how much volume is left—whilst still carrying with me the “larger numbers” associated with kcal fat-loss, than the “small numbers” which characterise litres (gallons ~ 8 lbs) of fat loss.

Here’s my mathematical model of why this is hard in the first place:

- I take about 100 measurements at roughly the same time but not exactly
`timepoints <- 1:1e2 + rnorm(1e2,sd=1)`

- the natural variation in weight, in the unit scale of [kcal stored by fat] is on the order of kilos
`daily.variation <- 1e5 * sin( runif(1,min=-pi/2,max=pi/2) + timepoints)`

- even if I subtracted off my daily fluctuation pattern (Mr Hopper does this by weighing himself at the same time every day), there are apparently other noise factors on the order of half a kilo or perhaps .1 kilo
`other.variation <- 1e4 * sin( runif(1,min=-pi/2,max=pi/2) + timepoints)`

- the “underlying phenomenon” I’m trying to measure is perhaps on the order of .01 kilos lost per day. Let’s say I lose 1 kilo in 3 weeks, that would be 8000 kcal if I’m good. (i.e., I actually do my workouts and I don’t eat a compensatory extra 8000± kcal). I could model the underlying fat loss as a step function to be more truthful but I’ll use a linear model, saying I lose 100 kcal per measurement (supposing I measure 3 times a day) rather than 700 kcal every time I work out, which is not once a day (that would be the step function). But the catch is, I’m not sure if I’m compensating by eating more. My statistical task is to estimate
`B`

, in other words to distinguish if I’m losing weight or not, and how fast I’m losing it (in kcal units, leaving the conversion 8000 kcal ~ 1 kilo as an afterthought), from the signal-swamped data.`B<-rnorm(1,mean=100,sd=50); trend<-−B*timepoints`

- Now my job is to estimate
`B`

. Is it even positive? (i.e. am I actually losing weight?) In R I just made the variable so I could print(B) but the point is to model why it’s hard to do this from my real data, which is the sum`data <- daily.variation + other.variation - B*timepoints`

- This is why I like my idea: measurements of kcal burned on the treadmill is 1000 times more precise than measurements of my bodyweight.

So my overall system is to do “chunks” of 7000 kcal = 1 kilo of fat or 3500 kcal =1 pound of fat. I can stand to do 500–700 kcal per cardio session—about an hour. (I also do an extra +1 kcal for every minute it took me to penalise for low speed: exercise crowds out normal metabolism.) Then it becomes a “long count” up to 3500 or up to 7000. That means 5 cardio sessions (of 770 kcal each) to get up to 1 pound of fat-loss, 7 wimped-out cardio sessions (of 550 kcal each) to reach a pound, and so on. It’s easy enough to “count to 5”. This system makes each one of the 5 be significantly large at the order of magnitude appropriate to convert kcal of exercise to litres of body volume.

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**isomorphismes**.

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