"I learned that it is really hard to accurately measure calories consumed, even if you are trying. "
I'd just like to highlight this, because it is profoundly true. There are probably very few people who have the patience to log everything they eat, diet or no diet, unless they have some kind of payoff close at hand! Even if you do log everything you eat, it's still not easy. Here are just a few reasons why:
1. The best foods to eat on a diet don't come in prepackaged portions with the calorie count labelled on the back.
2. Packaged food often does not have anywhere near the same calories as the label claims. Food manufacturers often aren't very precise and they have an incentive to underestimate.
3. The ideal way to measure the absorbable caloric content of food would be to feed it (and nothing else) to human test-subjects (other animals can metabolize foods quite differently; e.g. grass and cows) for an extended period of time while strictly regulating the test-subjects' physical activity. Measure the weight change, and there you have it. Yeah... This experiment is never going to happen. That's why we stick food in a calorimeter, burn it, and consider the heat it provides to be a measure of its caloric content. This crude method provides decent estimates on average, but can occasionally be misleading.
For these reasons, I'm actually a bit surprised that the author's data matches the theory so closely. This indicates the author scrupulously measured his portion sizes, found accurate estimates for the caloric content of the foods he ate, and logged everything. This is seriously impressive. If the author had failed to log something as insignificant as the sugar and cream he puts in his coffee it would have thrown his numbers way off over a period of 75 days. Similarly, he must have scrupulously recorded his physical activities. The fit is so perfect I actually suspect he... ah... played with his data slightly after the fact. A "fortuitous" choice for alpha is obviously helpful too.
One other thing worth pointing out is that weighing yourself daily and plotting it on a graph like this is a fantastic way to observe progress and stay motivated to stick to your new routine. First, if you don't regularly observe your weight then you have no feedback. If you fail to accurately measure your caloric intake/expenditure the results might not be as desired. Feedback is necessary. However, daily feedback can be wildly misleading if you don't place it in context. If you look at the author's data, there are plenty of ups and downs around the trend. For example, on day 7 he observed a large gain and on day 8 a large loss. If the author only kept the previous day's weight in his head he might conclude that he did poorly on day 6 and made up for it on day 7. In reality, he might have consumed very healthy, fiber-rich food (e.g. a lot of beans) on day 6 and a bunch of sugar-rich processed garbage on day 7. The author might have stored away some fat on day 7 but wound up weighing less on day 8 purely because of passing the fiber from his meal on day 6. Pure sugar doesn't leave much behind to be passed!
I do question the worth of calculating your caloric deficit. It's simply too hard to get an accurate measure of consumption. However, measuring your weight regularly and plotting it so you can observe the larger trend is invaluable. About five years ago I dropped 60 pounds (it's still off, and I've gained lean muscle mass). I didn't count calories. I simply measured my weight regularly and plotted it on a graph similar to the author. I looked at the larger trend and made small adjustments gradually to keep it going in the right direction. If you don't weigh yourself regularly you can undo months worth of progress with one new bad habit. If you don't place your weight in context you'll have difficulty identifying habits that are a problem. Finally, watching that line steadily come down is a fantastic way to stay motivated.