When somebody loses weight, where does the fat go?

You can also piss it out in the form of ketones.

Isn't this the same question as "after you eat, where does the food go?" or "after you put gas in your gas tank, where does the gas go?"

Running at a moderate pace for 45 minutes is an easy 90-110kcal / mile depending on your weight.

Running is a double edged sword on appetite. It tends to shut down your gut for a while, making you less hungry for a period after the workout. But, people tend to misjudge how much they burn on shorter workouts or runs.

Often people only need 2 or 3 habit changes to create a long term deficit. Example: run a few times a week (30 mins, 3 miles each time, -900 kcal). Cut out sugar drinks (2 per day? -1400 kcal / day easy). One per day? (-700kcal) / week). Exercise is likely to simply make you feel better and in my experience causes me to at least think about healthy eating choices. Many people who don't exercise and drink sugary drinks can do just those two and end up with an easy 1600-2500 kcal deficit without thinking much about diet change etc. Even doing that is a huge change, and to sustain that over the course of years is a huge undertaking for anyone.

These are some simple things, yet even then most people will completely fail at a diet. A sobering statistics: http://ajcn.nutrition.org/content/82/1/222S.long -- only approximately 20% of individuals are successful at sustaining weight loss.

Personal anecdote time: I dropped about 45 lbs through calorie counting and a lot of running. Eventually the running allowed me to eat more food than I was eating before I started running. This greatly contributed to satiety and addressing the psychological and mental battles anyone faces undergoing an effort to cut fat. I have maintained the weight loss for 10+ years. It is very hard to separate where the exercise stopped and the nutritional plan started in terms of addressing all of the facets of sustained weight loss. One thing that is clear to me now is that my approach was extreme and probably only a very small fraction of people can or ever will be able to adopt such an approach. I ran at least 20 miles per week, typically 30-40, and at my weight that was for sure 2500-5000 calories per week burned from exercise alone. It put me in a position of actually having to eat more than was comfortable some days just to not push things to a relatively unhealthy range of calorie deficit. My take away is this: you can't out run a diet [^1]. I like to think of myself as "not exceptional"... I am not a fast runner and I have no real gift for it. I just like doing it. (side note: it turned out to have been very effective self medication for ADHD, so it was probably much more rewarding for me than the average person, who would probably not have the same elevated positive feelings surrounding their exercise activity as I probably get).

1: Unless you turn your body into a machine capable of obliterating calories at a rate that outstrips your ability to eat yourself fat.

Also, the whole "ups your metabolism for hours after the activity" that is factored into almost any calorie calculation and the actual burn from that is almost trivial. Its a few calories, but it is mostly your heart rate recovering down to a normal resting range. It doesn't change the basic calculations (100kcal / mile of running, etc.). You nailed that one, but people tout it as an exercise benefit when... it is just calories out and not many at all.

My point about all of this is that many slogans are correct or correct enough to be a reasonable model (calories in, calories out, can't outrun a bad diet, etc.). But the shocking lack of success in sustained weight loss is something you need to look down the barrel of the moment you decide "I will lose some weight" because if you want to keep that weight off what you are really saying is "I will lose some weight; I am going to need to make moderate to significant changes to my lifestyle... forever." It really is that meaty of a decision. Many people don't succeed their first attempt, but learn enough to succeed eventually. Most people never succeed to the degree they desire. It is because completely changing your lifestyle and mentality as an adult is very hard.

So we know all of these true things about weight loss, but I think it is a mistake to narrow it too much down to any one rule aphorism. It must be tackled on all fronts simultaneously (mental, exercise, diet). Most people will try just one and fail. Some people adopt two, but lose the habits because they weren't real change. The mental approach is the hardest to "prescribe" because each individual will have different issues and triggers for their eating. Mileage will vary, but these are some things I have observed.

For me, the slight added friction of tracking what I eat makes it a lot easier to avoid random snacking and excessive eating. It's silly, but "I'll have to put this in the app" is often a bigger disincentive than "I'll get fatter" in the moment.