Word-Hoard Or Word Problem?

(I get the vague impression that I've articulated this somewhere before, but I find no evidence of it. Either that or it's so obviously a blog post I can't believe I haven't yet.)

Among my various half-tended patches of language is Old English. I'm not sure if it's a matter of being interested in Old English per se, but since I am interested in comparative translation, historical linguistics, an English speaker...Beowulf sort of keeps coming up.

A housemate finally gave me another copy of Seamus Heaney's bilingual translation of the poem (I either gave mine away or left in in Vermont) and this has brought me back to another book I picked up a while ago, Barney's Word-Hoard: An Introduction to Old English vocabulary. (1985)

This story is going to veer into mathematical territory here, as unlikely as that may seem from my largely linguistics-based interest in the work, but there's an interesting series of numbers thrown out in the introduction that have always struck me. (That, and the nickname "Old Anguish," which I hadn't heard before I found the book.)

"The total vocabulary of [preserved] Old English poetry...is something over eight thousand words, of which about sixty percent are compound words. But a student need learn only a quarter of this number of words to know the meaning of over ninety percent of the running words he will meet in reading Beowulf." (vii.)

I remember the first time I read this a couple of years ago going "wait, what?" It struck me as a very indirect way of expressing these quantities, so of course I got cracking. For the following, I assume the phrase "this number of words" refers to the total vocabulary, and not the subset of that comprised of compound words.

compound words in preserved OE lexicon: "something over 8000"*"about sixty percent"=~5000 compound words.

"a quarter of (this number of words)"="over ninety percent of the running words he will meet in reading Beowulf."
.25 * ~8000 = ~.9 * B

B = ~2000/~.9 = ~2200-2250.

Well, now we know how many "running words" there are in Beowulf. The running words vs. hapax legomena post will have to wait for another day.

This wasn't a math problem, you say? Could have fooled me.