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How Long is "The Blacklist's" Blacklist?

I'm almost always late to the game on pop culture*. I didn't know about Firefly until it was off the air for many years, and am much more likely to wait for shows to hit Netflix than I am to see them when they first run.

Such is the case with The Blacklist with James Spader (note: the show is not for young viewers -- I'm not sure if I'm even old enough to watch some parts of it -- but this post is more than safe). I watched the pilot earlier today and found it interesting. But you probably want to know what it has to do with statistics.

Image from netflixlife.com

It's the list itself. The so-called Blacklist that Spader's character references in the pilot. A list of all the baddies in the world. Each baddie has a number, and each episode of the show focuses on one baddie. However, these numbers aren't presented sequentially, which begs the question:

How long is The Blacklist's Blacklist?



Here are the titles of the first two episodes (after the pilot):
  • The Freelancer (No. 145)
  • Wujing (No. 84)
Any guesses as to how many baddies are on the list? Obviously, at least 145, right? But can we make a more intelligent guess? Maybe 290 (2 x 145)? Or maybe 229 (145 + 84)? Is there a principled way we can do this?

It turns out, statisticians have already looked at this problem, but with a little bit more serious application: based on observed serial numbers, how many tanks did the Germans have in WWII?

Hence, we're really looking at the "German tank problem."



The Wikipedia page for the German tank problem outlines things nicely, but here's the upshot. If you're the USA during WWII, and you happen to notice that the Nazi tank parts all have serial numbers (bless that German precision), from the chassis to the wheels to the gearboxes. Instead of relying on rumors, why not figure out a statistical model to make a more educated guess? At least if you know what you're up against, you can plan better.

That's exactly what they did. And their estimates were constantly better than ones from the intelligence community (doesn't that make statisticians the "more intelligent community"? -- I digress).



The math for this one is a little more challenging than I'd like to go into this time. So I'll just provide the result, and hope you'll trust me (or go look up the German tank problem on your own).

The best estimate for the number of tanks (or number of baddies on the Blacklist) is:


where m is the maximum value we've seen, and n is the number of episodes we've watched.


So, based on the first estimate alone, our guess would be 289 baddies.

Adding the second episode, our guess is 216.5

The third episode, "The Stewmaker (No. 161)," though the highest number so far, still brings it down ever slightly to 213.667

Plotting this out for the first 3 seasons yields the following:
Technically, I'm going by number of baddies, not episodes, as one episode has 4 in a row and others split one baddie between two episodes. C'est la vie.
So, at the end of season 1, the guess is 167.318. By the end of season 2, it's 163.744. At the end of season 3, it's 162.639.

I find this rather fascinating, because that means the third episode (after the pilot) had potentially one of the last baddies on the list.

Anyway, with approximately 20 baddies per season (22 episodes, some cliffhanger episodes where two episodes have the same baddie), this gives The Blacklist just over 8 seasons of baddies total.

So heads up, James Spader, you've only got 5 more seasons of this gig before you need to find your next psychopathic villain role.


* There are some exceptions to this, including Studio 60 on the Sunset Strip and The Good Guys. I found them before anyone liked them. And yes, I'm still waiting on other people to like them. (seriously, Studio 60 is probably my favorite show, and yes, I've seen Breaking Bad, Parks & Rec, The Office, The West Wing, Unbreakable Kimmy Schmidt, Battlestar Galactica (the new ones), New Girl, and so many other phenomenal shows. go watch it)

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