Tuesday, July 20, 2010

Is Chris Nolan The Best Director Of All Time?

The short answer is, quite possibly. 

For the longer answer, you'll have to indulge me with a bit of stats. You see, there's this website called imdb, (you may have heard of it), and one interesting fact about it is that it has the largest depository of user-generated ratings in recorded history.

So, after aggregating all of the movies that somebody has directed, it is easy to calculate his average rating on imdb. In order to see whether Chris Nolan really is the best director of all time, I did this for anyone who had seemed to have a reasonable chance of winning.

To be fair, I didn't count early movies that the director probably didn't have much funding for, movies that he wasn't the main director of, and documentaries, because they tend to be lame.

Once I did this, I realized that I had meandered into a dilemma. You see, the best directors had only directed one movie each! At the tops of the list were Florian Henckel von Donnersmarck, who directed The Lives of Others (an 8.5), and Tony Kaye, who directed American History X (an 8.6).

To appropriately punish these slackers for their limited sample sizes, I had an excuse to employ a fancy Bayesian estimator. This sounds much more complicated than it is.

Basically, I calculated the total number of movies each person had directed, inputted the average rating of a movie on imdb (6.9), and set an arbitrary variable, m, to be some value between like 0.001 and 1000. Then, I put each director's average rating and total number of movies through this equation, and viola: it spit out rankings that took into account the fact that von Donnersmarck and Kaye had only directed one movie each.

Now, determining which value to use for the variable m is an open and interesting question. It depends on your values: do you prefer a director that has made a whole lot of good movies, or one who has made just a few great movies? It'd be hard to answer this objectively.

If you prefer quality over quantity, then you should set your m low, so you don't punish low sample sizes as much. If you think that a director has to be somewhat prolific to be even included in the discussion, then you should set your m high. I set m to three different values to be fair to each of these reasonable positions.

When m = 20, the top 5 directors are:

1) Akira Kurosawa, score = 7.40 (weighted), directed 25 movies. Highlights: Seven Samurai, Yojimbo.
2) Stanley Kubrick, score = 7.36, directed 11 movies. Highlights: Paths of Glory, Dr. Strangelove.
3) William Wyler, score = 7.34, directed 26 movies. Highlights: Dodsworth, Ben-Hur.
4) Ingmar Bergmann, score = 7.34, directed 30 movies. Highlights: The Seventh Seal, Wild Strawberries.
5) Luis Buñuel, score = 7.29, directed 32 movies. Highlights: Viridiana, The Discreet Charm of the Bourgeoisie.

When m = 10, the top 5 directors are:

1) Stanley Kubrick, score = 7.58 (weighted).
2) Akira Kurosawa, score = 7.54.
3) Chris Nolan, score = 7.50, directed 7 movies. Highlights: Memento, The Prestige.
4) William Wyler, score = 7.46.
5) Hayao Miyazaki, score = 7.45, directed 9 movies. Highlights: Spirited Away, Princess Mononoke.

When m = 3, the top 5 directors are:

1) Chris Nolan, score = 7.93 (weighted).
2) Stanley Kubrick, score = 7.92.
3) Sergio Leone, score = 7.88, directed 6 movies. Highlights: The Good, The Bad, and The Ugly, Once Upon a Time in America.
4) Quentin Tarantino, score = 7.80, directed 7 movies. Highlights: Pulp Fiction, Inglourious Basterds.
5) Hayao Miyazaki, score = 7.78.

Another sort of difficult thing to choose is how to count Pixar's movies. Most of the movies list different directors, but really, who actually knows what goes on in that forsaken place? If you consider the Pixar movie making team as its own distinct entity, then that entity would end up at 5th, 3rd, and 5th on the above lists.

If you'd like to check my raw data, feel free to peruse this google document at your leisure.

So there you have it. Chris Nolan is the best director of all time... under certain assumptions. Finally, implicit in this post is the recommendation that if you haven't seen Nolan's Inception yet, you need to get your act together.