I would have thought more than a footnote would have been helpful. To avoid lazy other-optimizing, I've written some content below which you may use/adapt/modify as you see fit.

The odds form of Bayes' theorem is this:

P(a|b)/P(~a|b) = P(a)/P(~a) x P(b|a)/P(b|~a)

In English, the ratio of the posterior probabilities (the posterior odds of a) equals the product of the ratio of the prior probabilities and the likelihood ratio.

What we are interested in is the likelihood ratio p(e|is-real)/p(e|is-not-real), where e is all external and internal evidence we have about the DN script.

e is equivalent to the conjunction of each of the 13 individual pieces of evidence, which I'll refer to as e1 through e13:

e = e1 & e2 & ... & e13

So the likelihood ratio we're after can be written like this:

p(e|is-real)/p(e|is-not-real) = p(e1&e2&...&e13|is-real)/p(e1&e2&...&e13|is-not-real)

I abbreviate p(b|is-real)/p(b|is-not-real) as LR(b), and p(b|is-real&c)/p(b|is-not-real&c) as LR(b|c).

Now, it follows from probability theory that the above is equivalent to

LR(e) = LR(e1) LR(e2|e1) LR(e3|e1&e2) LR(e4|e1&e2&e3) ... * LR(e13|e1&e2&...&e12)

(The ordering is arbitrary.)

Now comes the point where the assumption of conditional independence simplifies things greatly. The assumption is that the "impact" of each evidence (i.e. the likelihood ratio associated with it) does not vary based on what other evidence we already have. That is, for any evidence ei its likelihood ratio is the same no matter what other evidence you add to the right-hand side:

LR(ei|c) = LR(ei) for any conjunction c of other pieces of evidence

Assuming conditional independence simplifies the expression for LR(e) greatly:

LR(e) = LR(e1) LR(e2) LR(e3) ... LR(e13)

On the other hand, the conditional independence assumption is likely to have a substantial impact on what value LR(e) takes. This is because most pieces of evidence are expected to correlate positively with one another instead of being independent. For example, if you know that the script is a 20,000 word long Hollywood plot and that the stylometric analysis seems to check out, then if you are dealing with a fake script (is-not-real) it is an extremely elaborate fake, and (e.g.) the PDF metadata are almost certain to "check out" and so provide much weaker evidence for is-real than the calculation assuming conditional independence suggests. On the other hand, the evidence of legal takedowns seems unaffected by this concern, as even a competent faker would hardly be expected to create the evidence of takedowns.

[The suggested back-of-the-envelope calculation could go along the lines of the last paragraph, or as I said in the grandparent you might get rid of most of the problematic correlations by considering 2-3 hypotheses about the faker's level of skill and motivation (via a likelihood vector instead of ratio). My own guess is that stylometrics pretty much screens off all other internal evidence as well as dating and (most of) credit, but leaves takedown unaffected.]

Note to self: consider testing the obvious conspiracy theory here.

But you don't add the different probabilities for where the first item can be. No matter where the first item in the pair occurs, there is a 1/29 chance the second item will be next to it.

Another way of thinking about it. For any given item, there are 29 other items. Only one of these can be paired with the first, and all these events are equally likely. The probabilty has to be 1/29 and not 1/15, because 29 copies of 1/15 don't add up to 1.

Actually, the probability is slightly lower, because some items are not leaves at all. If we take the tree in the article as representative, then we expect roughly 10 pairs among the 30 items, which gives a probability of 2/87: with probability 2/3, the first item ends up as half of a pair, and with probability 1/29, the second item ends up as the other half of that same pair.

In the movie subtree, we have 12 items, so the probability of being paired is 2/33 rather than 1/6.

Edit: Laplace-adjusting the "is a random item in a pair" probability, we get 11/32 as an estimate instead, and 1/16 for the final answer. Note that because of the reasonably large sample size, this doesn't make a huge difference.

Ah, sorry about that. Should have read the footnotes.

You may have made the same mistake in the Plot section when adding up (rather than multiplying) a bunch of likelihood ratios.

Look, this is certainly a interesting post, and I enjoyed reading it. But that is not a sufficient criterion for a post being in Main. Compare this to the other recent posts in Main, and you will see a big stylistic difference. A worked out example of using Bayes is very interesting and insightful, but it is not anything "new". To use an analogy, if the other posts in Main are the content of a textbook, this is one of the worked-out sample exercises to show you how the exercises in the book are actually done. That is no less valuable, but it is simply not the same class, and a distinction is necessary.