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Comment by chacham15 | Hacker News Reader

> It’s just a simple numbers game: there are more obscure books than popular books, so there are more obscure good books than popular good books, so the more books you read the more likely your favorite is an obscure one. In other words, if someone says they love fantasy novels and also their favorite novel is Harry Potter, odds are they don’t actually read that much fantasy.

I hate these kinds of arguments. It assumes that every book has an equally likely chance of being good. Books being popular and books being good generally have a correlation.

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If you have read a lot of fantasy, there's a good chance that your favorite is a book that was popular at some time. My favorite, for example, is John Crowley's Little, Big. It's not obscure! It won critical acclaim and wide readership in 1981.

Most popular books become obscure books, given enough time. (Reading Les Miserables, I had to consult the footnotes repeatedly for Victor Hugo's allusions to then-popular novels and novelists, almost none of which remain popular today.) If you're a serious reader the chances are diminished that your favorite book is something that has just recently been written. But it's also likelier than random chance that your favorite book was once popular, because as you note there's generally a positive correlation between quality and popularity.

> It assumes that every book has an equally likely chance of being good.

No it doesn't, it just has to assume that

P(good|obscure) > - P(popular)/(P(popular)-1)

Or, more practically, when P(good|obscure) is just a hair more than P(popular)

Let's say all popular books are good, so

P(good|popular) = 1.

Then we'll say 1/1000 books are popular.

This means P(popular|good) == P(obscure|good) (i.e this is when the number of good books that are popular equals the number of obscure books that are popular.) when P(good|obscure) = 1/999. This true if we assume that P(good|popular) = 1, which is the highest value it can take. If this number is lower than this constraint is reduced, so we can take this as an upper bound of the relationship.

So knowing nothing about the rate of goodness among popular books, we can assume as that there is a huge number of obscure books, and a book is just reasonably more like to be obscure and good, than it is to be popular, the we can confirm that there are more good obscure books.

This constraint is much less demanding than assuming all books are equally likely of being good.

Both may be true at the same time: “being good may correlate with being popular” and “the more you read the more likely your favorite book is obscure”

The math is the same as hot/crazy/marry plots: draw popularity vs. goodness (random correlated dots: more popular more goodness). Define which books may be favorite e.g., above G line goodness a book has a chance to become favorite, define threshold for obscurity e.g., less than P popularity level. Consider what happens to the number of obscure books the more you read the more of them can become popular.

If you model it with a single threshold then the math is the same as for «the better at programming competitions the worse at “some other metric for coders” among google hires» (imagine you sum two metrics and hire only those who have the sum above a threshold -> you get the positive traits in reverse relationship).

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