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Comment by rssoconnor | Hacker News Reader

If the number of students enrolled in my course goes up by 25% one year, and then the next year the number of students enrolled in my course drops by 20%, how many students are now in enrolled in my course compared to the beginning?

What if it were reversed: what if the number of students dropped by 20% one year, and then when up by 25% the following year. How many students are now enrolled in my course compared to the beginning in this scenario?

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In any scenario like that, where a quantity X changes by Y% and then that new quantity changes by Z%, I almost always think about it like (1 + Z) * ((1 + Y) * X).

That is, I compute the new size after adjusting by Y% first, and then take Z% of that. To me, this is still treating values as magnitudes from 0 and the Y% change is totally independent from the Z% change. I guess you can multiply Y and Z first, but that’s not how I think about it.

rssoconner is saying that answering those questions becomes trivial when using the log scale. I find this argument persuasive despite having the same reaction you did to the original graph. The rewritten version is easier to understand immediately and is less confusing, but it's not as usable for answering questions about the data.

If the original author's had included a brief explanation of the unexpected looking axis label and its advantages, the whole problem would have been avoided. And I think the argument that "log scales are standard" is not a valid defense here, as this whole thread demonstrates.

Point is that it seems by the above calculation that a change of increase-by-25% and a change of decrease-by-20% are opposite changes of equivalent magnitude as they perfectly cancel each other out. This is why they are plotted equidistant from 0% on the original chart.

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