The Mathematics of Buying Science Fiction Anthologies

by James Wallace Harris, Friday, August 17, 2018

Like the famous vehicle routing problem or the four-color map theorem, I’m proposing the science fiction anthology problem.

We’ve just published The Classics of Science Fiction Short Stories that identified 275 short stories, novelettes, and novellas that are the most remembered in the genre. We gathered stories from 290 retrospective and annual best-of-the-year anthologies, several polls and lists, finalists from three awards (Hugo, Nebula, Sturgeon), three recommended reading lists and put them into a database. We produced what we call The Classics of Science Fiction Short Stories list consisting of the stories that were on at least 5 of those sources. The Stories by Rank (with Citations) report starts with “Bloodchild” by Octavia Butler. She got the most citations – 16. We’ve also created several other interesting reports from the data – see the site menu.

Sense of Wonder - A Century of Science Fiction edited by Leigh Ronald Grossman

Here’s the mathematical challenge that appeals to me. What’s the minimum number of anthologies to buy to get the most of the 275 stories on the list? I’ve already read 63 of these stories in 2018, and it’s been extremely rewarding. I believe anyone who reads a short story or novelette a day and takes two days to read a novella, could finish the list in one year. Sadly, there’s no 5-volume set of the classic science fiction short stories that collect them all.

Even more depressing, most of the anthologies we used are out of print. Anthologies don’t stay in print long. And some of the anthologies we used are textbooks priced far higher than the casual reader is willing to pay. I have spent the past year buying many of the anthologies on our Citation Bibliography list as I could afford, but my collection is far from complete.

My willingness to buy shelves of old SF anthologies to get all these stories isn’t typical. Thus, the mathematical problem I propose of finding the fewest anthologies that give readers the most stories from the 275.

We can’t claim these stories are the very best short works of science fiction. Neither did we pick them. They aren’t our personal favorites. We used math to identify the most remembered stories, which should be more valuable than mere opinion. By promoting the list, we are reinforcing the memory of these stories (maybe at the detriment of better stories). I could easily create “My 100 Favorite Stories Not on the List.” Those stories would be even harder to find. If you look at our Citation Sources Ranked report, you’ll see how many stories each citation source identified.

And let me be perfectly clear, not all these remembered stories are still worth reading today, at least to my taste. Time is cruel to science fiction. Chernobyl, Three Mile Island, and Fukushima has ruined “Nerves” by Lester del Rey. Even though we have a methodology for revealing the most remember science fiction stories, I’m not sure all of them are worth remembering. But I do believe the stories that got the most citations are.

I want to promote the reading of short science fiction. Most fans don’t like short stories or buying anthologies. They need to try short science fiction to see what they are missing. Maybe it will change their minds. So part of this mathematical problem is also recommending the most recommended of the 275 stories, especially the first 100.

I believe the single most useful anthology that’s in print is Sense of Wonder: A Century of Science Fiction edited by Leigh Ronald Grossman. It contains 133 stories, of which 50 are on our 275 Classics of Science Fiction Short Stories list. However, it’s $40 for a Kindle edition. (Granted, it is a huge book that’s probably best read on a Kindle.) And I sure wish it was available on audio because I love listening to short science fiction! If you eyeball our Stories by Rank (With Citations) list, you’ll see that many of the top stories are collected in this anthology. Still, $40 for an ebook book will scare most buyers off. Sense of Wonder is priced as a textbook, so it also contains essays about science fiction putting each story into context. That does add extra value.

The next volumes that are story-list full and in print, are the three volumes of The Science Fiction Hall of Fame. They contain just 48 stories, of which 39 were on our list. This year I listened to all three on Audible. But that’s a commitment of 3 credits to get 39 stories. Buying printed copies of Volume 1, Volume 2A and Volume 2B would be almost $57, so the $40 Grossman book seems less expensive now. I immensely enjoyed hearing these old stories and got them for around $30 by buying credits in bulk. Using full price credits would be $45. But 39 out of 48 stories is a very high hit rate.

Now if you’re willing to buy used, the three anthologies edited by Robert Silverberg and Martin Greenberg give you 188 stories to read, of which 53 were on our list. These books are:

If you’re lucky, you could find these books for a few bucks at a library book sale, or all three on for maybe $15-30.

The Wesleyan Anthology of Science Fiction is in print for $29. It will get you 49 stories to read, but only 34 of which are on our list. You can get it even cheaper used.

The Big Book of Science Fiction edited by Jeff and Ann VanderMeerThe best bargain is The Big Book of Science Fiction edited by Jeff and Ann VanderMeer. For $17.00, you get 107 stories, but only 25 are on our list. It’s also available as an ebook for $18, making it much more convenient to read all those stories. The paperback is like an old-style phonebook. Even though it only has 25 of our stories, I think it’s a fantastic collection.

Between Sense of Wonder and The Big Book of Science Fiction, many of the top stories are collected. Unfortunately, you also get duplicates. That’s another factor in solving the science fiction anthology problem – how to keep duplicate stories to a minimum.

By now, you’re probably sensing the mathematical headaches this problem generates. How to calculate the minimum number of anthologies to buy that cover the most stories. If you factor in costs, it becomes even wormier.

I haven’t figured that out how to solve this problem. It’s very tricky. I’m open to suggestions. Just buying three of any of these volumes I’ve mentioned so far, only gets you just over a 100 of the 275 stories. It might take buying 10 books to get to 200, and 30 to get to 250. I wonder if there’s a mathematical progression involved?

The minimum number of citations to get on the list was 5. But some of the 275 stories might have only come from polls, awards, and recommendation lists. And it’s possible that several stories came from 5 different books that don’t overlap with any other missing story.

I’m not sure if the answer isn’t 290, the total number of anthologies we used.



22 thoughts on “The Mathematics of Buying Science Fiction Anthologies”

  1. And another question: How many of these stories can you get by spending $100, regardless of the number of books?

    I think you’ll go mad trying to collect all 275 stories in the smallest number of books. A more realistic challenge (and one that is more achievable in terms of the mathematical progression) is how to get, say, 100 or 150 of them. After that I’m sure the number of books required grows exponentially greater.

    1. I realized this morning at 5 a.m. that the problem is not as complex as I first thought. There are 190 anthologies, but all but 64 are annual best-of-the-year anthologies which don’t count. Martin Dudley on a Facebook group suggested we create a spreadsheet with the columns being the anthologies and the rows being stories. By checking which stories were in which anthologies we could visually see which subset of anthologies cover the territory best.

      I also started at the bottom of the rank list with citations and quickly saw how many stories were not collected in a retrospective anthology. We need to filter out all those stories. The resultant grid might only be 64 x 200 (or less).

      But like you said, the real goal should be to find the few retrospective anthologies that give the top stories and not all the stories.

  2. Here’s another interesting thought: the quickest solution may involve some books that are NOT on our bibliography! For example, the bibliography doesn’t include any author collections. By design, of course. But then again, maybe not! Author collections always seem to leave out my favorite story.

    1. To me, the virtue of reading anthologies is to experience the diversity of what writers can do with science fiction. Single author collections tend to have a sameness quality. They are fine for reading your favorite author, but I recommend readers new to science fiction short stories try the best retrospective anthology first.

      It’s a shame the textbook anthologies are priced so high. Heather Masri’s Science Fiction: Stories and Contexts is a great introduction to the genre because of its supporting essays. I had to spend $24 for a used copy (including shipping) for the old 1242 page edition. It’s $67 for the new 816-page edition. It has 49 total stories, of which 34 are on the list. Making it almost as successful at spotting classics as the three-volume Science Fiction Hall of Fame.

      It’s a shame that fans can’t get a Kindle copy for $25. The textbook pricing racket really annoys me.

  3. Sounds like a fairly stand Set Covering Problem. In the worst case, this is a hard problem, but many cases encountered in practice are pretty easy. I recommend first setting up a matrix of what stories appear in what anthologies, and then contacting your nearest university that has an Operations Research group.

    1. David, you are the second person to recommend setting up a matrix this morning. The other came from Facebook. I realized the problem will be less complex if we filter out all the best-of-the-year anthologies, and only use the 64 retrospective anthologies. Then the matrix will be around 64 retrospective anthologies x 180-200 stories that are in at least 1 retrospective anthology.

      1. Since I see you have a programming background, I wont be afraid to get technical. If you have access to a linear programming solver, you can set a 0-1 variable x(j) for each anthology j, and then try to minimize the sum of x(j) such that for each story k, the sum of x(j) over the anthologies that contain k is at least 1. If you are lucky, you will get integer answers. If not, you just get a lower bound on the number of anthologies required, and some insight into the true answer. (If you have access to an integer programming solver, you will eventually get the true answer.)

        1. That’s very interesting David. My programming came from a trade school in the early 1970s, and I’m mostly self-taught or learned on the job. I always wanted to get a master’s in computer science. And I thought I might do that after retiring. I even got accepted into grad school CS program, but I had 24 hours of math prerequisites to complete first, including linear programming. I had only finished through the first calculus course in my undergrad B.A. Now I have a linear algebra problem to make me study. Ha-ha.

  4. I would be very interested in your “My 100 Favorite Stories Not on the List.” I’m very impressed with the list of 275 stories. THE CLASSICS OF SCIENCE FICTION SHORT STORIES could someday become a book or an ebook!

  5. Dear James,
    Great work, you are very important.
    There is a small error: The classic Analog all time best poll do not have Dune but Dune World which was the first
    part of the novel serialized in Analog.

    Looking forward to more from you.

    All the best
    Øivind Tvedt.

  6. Hi James

    I appreciate the work you put into creating these types of lists. I love science fiction shorts stories and as I have mentioned before after reading Bud Webster’s essays on the topic I began to collect anthologies compulsively. So this post is one I plan to revisit many times. I am also involved in a reading project with a friend to increase my exposure to stories or authors I have not read andI will be using your list for that. I have already determined that the next two stories I read will be Blood Child and When it Changed.


    1. I reread both “Bloodchild” and “When it Changed” recently and discovered why they have so many citations. I also reread “Day Million.” They came out in 1984, 1972, and 1966, yet they seem modern by today’s standards. Something changed science fiction in the 1960s. Some of it was NASA, some of it was all the social revolutions. Maybe science fiction just grew up. But stories in the last 50 years seem different from stories from the previous 50 years.

    1. I wish I could, but unfortunately, I know nothing about being an anthologist, or how to contact writers or their estates for getting permission to reprint. And even then, the 275 stories would have to be divided into five giant volumes.

      On the other hand, I started a page with links to all the stories that are on the web to read or listen to. It’s surprising how many are online. I don’t know if they are legally online though. I haven’t finished the linking yet, but here’s what I have so far:

      Sadly, I’ve had the page up for a couple days now and it’s gotten zero hits. Which makes me wonder if people aren’t interested in these stories.

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