# The most important character on Game of Thrones

## According to game theory

Game of Thrones Season 7 is over, and the long wait for the final season is upon us. Now is the time for hot takes, arguments, and predictions. For my own humble entry into the genre of “words on the internet about Game of Thrones”, let’s answer the question of who of the show’s hundreds of characters is the most important.

First, let’s define important. Do we mean important to the story, to the fate of Westeros, or to something else? Let’s say that it means how vital the character is to the success of the show. Which character, over the course of seven seasons, should get the most credit for Game of Thrones becoming the most popular show in the world?

We could argue about who’s the bravest (Jon), the most cunning (Cersei), or the funniest (Tyrion if you ignore season 7), and attempt to prove that these characteristics make our favorite character (RIP Wun Wun) the true MVP.

Or we could use math!

I’m not a mathematician, or a maester, but I know math involves numbers so let’s get some. For some reason, hundreds of thousands of people have rated all 67 episodes on IMDb. Why? Has anyone ever quit watching this show because an upcoming episode scored 8.4 stars instead of a 9.2 stars?

Speaking of heroic acts of knowledge creation, Wikipedia has painstakingly edited summaries of every episode. Note: We could have used the official HBO provided episode descriptions, but they usually just say something hilariously understated like “Robb arrives at a wedding.”

Now we have a numerical score for each episode and a mapping of which characters appeared. It looks like this:

For our analysis, let’s limit ourselves to the seven still-living characters who have appeared in the most episodes.

Now, we could look at the average rating of the episodes each character appears in and say that the character with the highest average wins. But we won’t. We have a Drogon-sized problem.

Game of Thrones, like football or robbing a casino, is a team sport. Two characters, think Cersei and Jamie, might frequently appear in episodes together, so how do you decide which of the two contributed the most? Splitting up credit is even more complicated for an episode like “The Winds of Winter” that features all the main characters.

Guys, it’s time for some game theory. LLoyd Shapely discovered the very coincidentally named Shapely value which lets you fairly assign credit to all the players in a cooperative game. You iterate over all the combinations of players and determine how the score of the game changes when you add or remove players from each combination. In the real world, Shapely values have many applications including marketing attribution.

Here’s an example Game of Thrones calculation:

The average score of episodes with Arya, Daenerys, Sansa, and Tyrion is 9.45 If we remove Arya, the average score of episodes with just Daenerys, Sansa, and Tyrion is 8.7. Subtracting the two, you see that, on average, Arya contributed 0.75 stars.

We just have to repeat this calculation for each possible combination of these seven characters.

And the winner is….

Jon Snow! Perhaps this is not surprising, given his appearances in highly rated episodes like “Hardhome” and “Battle of the Bastards”.

Here’s everyone’s scores:

“That’s preposterous,” you say. “Arya is awesome. How can her score be negative?”

Is Arya really awesome? Is she?

“OK fine,” you say. “Daenerys can’t be last. She has three…um…two dragons. Your math is crazy.”

You are suffering from recency bias. Danny was stuck in Essos pyramids for 20 episodes.

You make one last argument. “Sansa’s score is way too high’.”

I will admit there is one problem with this analysis — not enough data points. For example, there are no episodes that feature just Arya, Daenerys, Jon, and Tyrion. My conclusions, while correct, would be even more correct with 100 additional episodes and ratings. HBO, give the fans, and amateur data scientists, what they want: Game of Thrones season 8 every week for two years.

Interested in poking holes in my methodology or playing with the data yourself? Get the spreadsheet here.

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