Date: Tue, 4 Mar 2003 00:06:34 -0500 (EST)
From: "Keith F. Lynch" <kfl at keithlynch.net>
To: WSFA members <WSFAlist at keithlynch.net>
Subject: [WSFA] Re: Skiffy Book Club Top 50
Reply-To: WSFA members <WSFAlist at keithlynch.net>

Ron Kean wrote:
> What are the chances that the actual sales rank would precisely
> correspond with an alphabetical ordering by title, for 40 titles
> in a row?

For a particular forty, 1 / 40! or about 1 in 8.2E+47.  For any
consecutive 40 out of 50, it would be 50! / (40! * 40! * 10!), or
about 1 in 7.9E+37.

Of course there are many other equally unlikely patterns.  For
instance reverse alphabetic by title, or forward or reverse alphabetic
by author's first or last name, or in order of the author's birthdate.
But there probably aren't more than 79 of them, so I'd give rough odds
of 1.0E-36, or one in a trillion trillion trillion that this pattern
isn't real.

But then you have to apply Bayes' theorem, based on the a priori
probability that the list is not in order of sales (or whatever it's
supposed to be).  If that a priori probability is low enough, i.e. if
you're told this by someone you know to be absolutely trustworthy, who
has personally verified the sales figures, then you could be justified
in dismissing Ted's observation as a remarkable coincidence.  But
that's not very likely.

No doubt Eric will step in to correct me.  But I think I got it right.
--
Keith F. Lynch - kfl at keithlynch.net - http://keithlynch.net/
I always welcome replies to my e-mail, postings, and web pages, but
unsolicited bulk e-mail (spam) is not acceptable.  Please do not send me
HTML, "rich text," or attachments, as all such email is discarded unread.