Unfortunately, I watched Game of Thrones season 8 episode 3.

[SPOILERS WARNING BELOW]

On Game of Thrones fandom, I imagine I fall somewhere in the top quartile. I’ve watched the show and read the books, but beyond that I do not have an encyclopedic knowledge of Westeros.

Maybe it was the bad writing[2] or poor military strategy in a show about war[1] or the dumbing down of smart characters[2] or the fact that it was too dark[3] or the fact that this was supposed to be better than Helms Deep[4].

But all of these reasons are subjective, and when voicing my complaints on my friends they didn’t seem to mind what I viewed as shortcomings. Sweet summer children…

I needed to find something “real.” Something objective to pin against this episode; to ground this in data and be able to prove without a shadow of a doubt* that this episode was bad*.

But what could that “objective” quality be? Then it hit me:

Game of Thrones has always been a show about subverting fantasy tropes. More specifically, it’s been lauded for  killing off important characters in pivotal moments: the good guys don’t always win.

This led me to the hypothesis of this paper: The Deaths that occurred at the Battle of Winterfell were not as impactful to viewers as previous important episodes and were lower than expectations.

I couldn’t analyze the merits of killing a character at the end or beginning of their arch (as Jorah Mormont vs. Missendei) or the way in which a character was killed (aka how a meaningless death ruins a great arch and visa versa) since those are still subjective.

What I could figure out is character importance, since studios obviously would dedicate more screen time to more important characters.

Determining Death Importance

At first, I collected the screentime of all characters in the Game of Thrones show up to season 8[5].

I added a few columns to make my life easier, then scraped all deaths from the wonderful website https://deathtimeline.com/ plus added season 7 deaths to produce:

Character	Minutes	Dead	Episode 8.3
Jon Snow	338	False	True
Tyrion Lannister	337	False	True
Daenerys Targaryen	276	False	True
Sansa Stark	239	False	True
Cersei Lannister	236	False	False
…	…	…	…

The Episode column indicates  if a character appears in that Episode. The above graph is fine, but let’s only look at only dead people, since that’s what we’re exploring. For dead people, I added an “Episode” column for which episode they died in, and MinPerEp, which is how much screentime they had over all the episodes they were in:

Character	Minutes	Dead	Episode 8.3	Death Episode	MinPerEp
Petyr Baelish	119	True	False	67	1.776
Ned Stark	100	True	False	6	16.667
Catelyn Stark	83	True	False	19	4.368
Tywin Lannister*	78	True	False	30	2.600
Margaery Tyrell	78	True	False	60	1.300
…	…	…	…	…	…

At first I charted simply total screentime of all characters killed in an episode:

It’s great to see major plot points + deaths can be captured this way. We can also see how absolutely insane the season 6 finale was– killing off a huge swath of major characters. I was WAY before the scope of other major death episodes, which all hover around 130 – 180.

But there are few things that simply don’t satisfy me about deciding episode quality by screentime of deaths:

1. Ned + Viserys dying in the first season was arguably the most pivotal moment in the series. Here it is less important than the Wildling invasion, which I disagree with
2. Using raw screentime as a metric overvalues deaths that occur late in the show. Even if you are a middling character, if you survive until the end your death can be as significant as Robb Stark at the Red Wedding

So what if we viewed significance not as total absolute screen time, but the amount of screentime per episode? It would stand to reason that an important significant character would have extended screen time across the entire show. A character dying with 100min of total screentime in episode 10 should be much more significant than a character with 100min of total screentime dying in episode 50. Minutes pr Episode could capture this relationship.

That chart looks like this:

This has the opposite effect– early deaths are heavily favored, making a significant later death much harder to achieve. You can almost see the exponential decay line of death value in the above chart.

You can tell this is a comedically unfair representation of Game of Thrones since Ned + Viserys are worth more than everyone who died in seasons 4,5,6 and 7 combined…

Clearly, there is a smarter way to calculate this.

From within my Min/Ep formula, I added a survivorship bonus parameter — essentially maintaining the value of Min/Ep but boosting later series deaths by softening the decay. Every character received 2min screentime bonus per episode survived. While this at first feels hand crafted and less objective, I would argue this can also be viewed as adding weight to deaths as characters progressed through both their own arcs and the stories arcs: even if their screentime does not increase, their extended involvement should naturally increase their significance.

Below is my Survivorship Death Value Formula:

death value = Screentime + (2*Episodes Survived)Total Episodes

Which produces the following chart:

This looks awesome– Ned’s Execution and the Tyrells sit as the most significant deaths of the show’s run, followed by the Red Wedding. It devalues Littlefinger’s Trial, which I would argue is a good thing since a singular semi-decent character’s death is way less of a pivotal moment then the others.

We are getting closer, but aren’t quite there yet:

1. The Red Wedding is undervalued. There is not way it is only as pivotal as the Wilding Invasion, and is dwarfed by Ned’s Execution, which many would argue should be close together
2. The Will Dilemma

To understand the Will Dilemma, take a look at the Dead List, sorted by DeathValue:

Character	Screentime	Death Episode	Death Value
Ned Stark	100	6	16.667
Catelyn Stark	83	19	6.263
Robert Baratheon	31	7	6.143
Will	6	1	6.000
Robb Stark	77	19	5.947
…	…	…	…

First, we have Ned Stark– one of the most unexpected and major deaths in all of cinematic history. It triggered all the events of Game of Thrones, and converted millions* to GoT fans–certainly deserving of the top spot. Next we have Catelyn Stark, the female lead for most of the early season taken at the Red Wedding, and then Robert Baratheon, the brash king whose death started the Game of Thrones.

Then, there’s Will.

He doesn’t even have a last name.

He appeared in the first 6 minutes of 1.1, and then was killed by a white walker.

Despite this tiny role in one scene, he ranks higher Stannis, the Tyrells, and even Robb Stark. Clearly something needs to be fixed.

In short, the Will Dilemma is our model’s tendency to overvalue unpopular characters. Yes, even Game of Thrones is a popularity contest.

But how do you measure popularity? Obviously I can’t go in and rank how important each character is, that wouldn’t be objective.

Instead, we can use the number of links of character’s wiki page has as a yardstick for popularity. The more links and relationships a character has with others, the more popular they are. When we count the links and normalize them (scale them between 0 and 1), we get something like this:

Character	Popularity
Viserys Targaryen	0.605351
Walder Frey	0.896321
Addison Hill	0.267559
Aemma Arryn	0.183946
Sylva Santagar	0.043478
…	…

Anything over 0.34 is considered popular.

So important people like Walder Frey and Viserys Targaryen? Popular. No, names like Sylva Santagar have practically no popularity.

We can now rewrite our Death Value function as:

death value = Screentime + (2 * Episodes Survived)Total Episodes * popularity

Or if you want this to look like a formula to pretend like this is mathematically rigorous:

Using this modified Death Value, we get:

This looks really promising. Ned/Viserys reigns supreme as the most powerful episode, following shortly behind the Tyrell massacre. The Red Wedding, while still being somewhat undervalued, is clearly in a league of its own compared to Stannis and the Wildling Invasion.

Side Note: I used the character pages from the book characters rather than the show to calculate popularity. If you’re worried about this biasing the data, or creating improper value, I would argue that the book wiki captures the true internal popularity of the characters within Westeros rather than the external popularity within HBO. The richness of each character backstory and the sheer number of named characters in the book ensured that important characters were hardly affected by the popularity amplifier, and no ones were heavily punished.

Side Note 2: The above dataset does not include John Snow’s first death, because he didn’t actually die. No fake deaths allowed in my death calculations!

Intangibles in Death

There are several concepts to address that we simply could not account for using our  Death Value:

• The Hodor Effect: A minor character who has a powerful, meaningful death. Hodor, while playing a relatively minor role in the grand scheme of Game of Thrones, had an absolutely stunning death sequence that certainly is worth more than his measly 0.621 score. However ranking how “great” a death sequence was is far too subjective for this analysis.
• The Littlefinger Quandary: A major has a terrible or out-of-character death that ends their narrative arch. This is the opposite of the Hodor Effect, and thus represents a need to reduce a character’s death score.
• The Ygritte Hypothesis: Does a mid-season character deserve the survivorship bonus for episodes they did not appear in? Do we start counting episodes from when they first appear or from the beginning? In the end I decided to go with the simplest answer give them the survivorship bonus from the beginning with no reduction in episodes
• Master of Whispers (Offscreen) Bonus: Raw screen-time isn’t necessarily reflective of story impact. Characters are often times talked about when they aren’t on screen, and their influence over events is also not taken in to account in this value. Perhaps next steps would be to count the length of scenes in which characters are mentioned as well.

Let’s use this to talk about Episode 8.3.

Potential Death Values of The Battle of Winterfell

Below are the Potential Death values of everyone present at the Long Night, with those who actually died in the episode highlighted in red as well as the total Death Value:

Rank	Character	8.3 Death Potential Value
1	Jon Snow	6.829
2	Tyrion Lannister	6.815
3	Daenerys Targaryen	5.944
4	Sansa Stark	5.415
5	Arya Stark	5.201
6	Jaime Lannister	4.844
7	Theon Greyjoy	3.944
8	Samwell Tarly	3.936
9	Davos Seaworth	3.465
10	Bran Stark	3.415
11	Brienne of Tarth	3.401
12	Varys	3.008
13	Jorah Mormont	2.921
14	Sandor Clegane	2.336
15	Melisandre	2.227
16	Gendry	1.121
17	Beric Dondarrion	1.025
18	Gilly	0.801
19	Podrick Payne	0.769
20	Tormund	0.596
21	Missandei	0.502
22	Grey Worm	0.367
23	Eddison Tollett	0.242
24	Lyanna Mormont	0.118

At first glance, it seems that the objective death value of the episode was acceptable. It was not as powerful as the Red Wedding nor the Tyrell Massacre, but still adequately important.

But once you look under the surface, you start to see the cracks.

The characters chosen just weren’t that important. Only one of them — Theon Greyjoy — is in the top half of characters by value, and two of the characters — Lyanna Mormont and Edsison Tollett — were absolutely last by value. In short, the score of >10 came not from critical deaths like in previous important episodes, but from the clearing out of lesser characters.

Also, 21.6% of the death score comes after the battle, when Melisandre decided her pep talk with Arya was her purpose in life before she proceeded to age 100 years and die. It did not add to the drama of the battle itself, but rather artificially inflated the episode.

Side Note: The Night King isn’t included because according to the writers he’s an “elemental” and the embodiment of pure evil[11] and so normal human things don’t apply to him. Like dying. And character development.

You might now be asking yourself: “So what if the value was lower than other important episodes and inflated by minor characters and post-battle deaths? What were people expecting?”

We can figure that out.

First, the obvious question: What if Everyone Died?

Killing everyone — and essentially ending the show early — would have been a cataclysmic event in Westeros, and probably the real world as well. Imagine if the Night King and his horde of undead viciously wiped out all of Dany’s and the Northern forces. All that would be left is Cersei vs. The Night King. Evil vs. Evil. It would have absolutely changed the entire show’s arch, and that is reflected by the insanely high death score above.

To be fair, The Night King vs. Cersei “Wildfire” Lannister would be a Song of Ice and Fire…

Moving to a more realistic expectation, I found an article that listed its predictions for the Long Night:

Grey Worm,Theon Greyjoy','Eddison Tollett','Brienne of Tarth', 'Jorah Mormont','Gendry', 'Podrick Payne'.

And also I asked myself, “prior to the episode, who do I expect to die?” Here are my picks:

'Grey Worm','Beric Dondarrion','Theon Greyjoy','Brienne of Tarth','Jorah Mormont','Gendry'.

 

Amazingly, my predictions and the mass media predictions differed by only 0.02, or 1/4th a Gilly.

Clearly everyone was expecting a death value around 12.75, and got a battle worth 10.48

In conclusion:

The Battle of Winterfell was objectively 17.99% worse than everyone expected

The End Game

Below is the potential death value of all characters still alive for the final two episodes. Since I don’t have access to screen-time during the final season, I simply gave all characters the extra screen-time based on their minutes per episode prior to season 8. Feel free to calculate the death importance for your own imagined episode:

Character	End Game Value
Jon Snow	6.948
Tyrion Lannister	6.934
Daenerys Targaryen	6.036
Sansa Stark	5.491
Cersei Lannister	5.447
Arya Stark	5.270
Jaime Lannister	4.902
Samwell Tarly	3.969
Davos Seaworth	3.484
Bran Stark	3.430
Brienne of Tarth	3.415
Varys	3.020
Sandor Clegane	2.345
Gregor Clegane	1.945
Euron Greyjoy	1.643
Edmure Tully	1.467
Bronn	1.451
Qyburn	1.253
Janos Slynt	1.224
Gendry	1.116
Gilly	0.800
Podrick Payne	0.767
Meera Reed	0.650
Tormund	0.596
Daario Naharis	0.585
Missandei	0.502
Jaqen H’ghar	0.476
Hot Pie	0.403
Salladhor Saan	0.386
Ellaria Sand	0.373
Grey Worm	0.366
Yohn Royce	0.357
Syrio Forel	0.250

Thanks for reading!

*Hyperbole is fun — please don’t yell at me!

Works Cited

2. https://www.theverge.com/2019/4/30/18522060/game-of-thrones-got-season-8-hbo-final-melisandre-tyrion-lannister-long-night-prophecies-tactics
4. https://comicbook.com/tv-shows/2019/03/04/game-of-thrones-final-battle-bigger-than-helms-deep-lord-of-the-rings/
5. https://www.theatlas.com/charts/HJrdxDNKW
6. https://deathtimeline.com/
7. https://en.wikipedia.org/wiki/List_of_Game_of_Thrones_episodes
8. https://data.world/data-society/game-of-thrones
9. https://www.vulture.com/2019/04/game-of-thrones-battle-of-winterfell-who-will-die.html was right?
10. Myself
11. https://mashable.com/article/game-of-thrones-white-walker-night-king-long-night/
12. https://www.wired.com/story/game-of-thrones-plotters-vs-pantsers