# Littlefinger was probably a Statistician

##### This post does NOT contain spoilers for Game of Thrones Season 7

Game of Thrones Season 7 has just concluded and what a finale! In hopes of not ruining anything for those readers who are not yet up to date, I shall be talking about a character whose influence cannot be overstated enough. Among Thrones’ vast number of characters, Petyr ‘Littlefinger’ Baelish can be thought to be one of the most sly, charming and cunning. In the most recent season, we get a slight glimpse into the methodology behind the way this character functions:

Sometimes when I try to understand a person’s motives, I play a little game.
I assume the worst.
What’s the worst reason they could possibly have for saying what they say, doing what they do?
Then I ask myself, how well does that reason explain what they say and what they do?

When I heard him say this for the first time, my interest was immediately peaked. This was exactly the process by which statisticians do statistics! Let’s see what he’s saying exactly:

1. Littlefinger proposes that you should always start with the worst possible reason for a person’s motives.
2. Using this, he then weighs that assumption by the person’s respective actions
3. He then sees how best that explains their actions.

Assuming the worst possible motives for a person might not be the most optimistic of assumptions to take, but it makes sense for the context. In a world filled with deceit, murder and betrayal, assuming that the other player wants to get you out of the picture seems like a reasonable stance to take. In other words, it’s more of a “Guilty until proven innocent” type ordeal.

The mechanism of assuming a hypothesis and observing the likelihood of that hypothesis’ ability to explain its physical manifestations through data is a standard practice within the field of Statistics.

Consider the following fictional example for context. Jack claims to have the ability  to correctly predict the result of a coin flip. Obviously, you are naturally dubious of this fact and would like to test this claim. You carry out several trials whereby you carry out a number of coin flips and let Jack make his predictions. Based on the results, you may observe whether it is more likely that Jack has this ability, or not (whereby he is then just randomly guessing).

This is not a simple case of seeing whether he gets everything right. Neither is it a question of seeing of which he gets more of. The world is a messy place filled with errors, especially when it involves human interaction. Statistics does a good job at rigorously quantifying these types of errors and as a result, is very good at identifying when and how much of it is mostly at play.

We propose 2 types of hypotheses for our experiment with Jack:

$H_0 : \text{Jack has no ability}$

$H_1 : \text{Jack has an ability}$

We always assume the null hypothesis ($H_0$) and see how well it explains the data. If there is a reasonable low probability that the data could come out as it does, given that $H_0$ is true, then we reject it in favor of the alternative hypothesis ($H_1$).
This doesn’t mean that $H_0$ isn’t true. All that we are saying is that based on the information available, there is more reason to believe that Jack has an ability, rather than otherwise.

Let’s translate this to Littlefinger’s case. The following null and alternative hypotheses would be kept in mind:

$H_0 : \text{Individual has worst intentions}$

$H_1 : \text{Individual doesn't have worst intentions}$

We assume the worst intention for that individual ($H_0$) and observe their actions and words (data) assuming that this hypothesis is true. If there is a reasonable low probability, we reject our null hypothesis for our alternative. Otherwise, there is not enough evidence to reject $H_0$ and we have to conclude that the person is more likely to have the worst possible intention in mind.

There you have it. If Petyr Baelish lived in modern times he would most probably be an excellent statistician. Along with a spy, poker pro, con-artist and businessman to boot. Although I can’t help but feel that the medieval setting is just perfect for such an interesting character.

Cheers to you Lord Baelish!

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