Game of Thrones Season 5, is the best behind us? [NO SPOILERS]

[This post does NOT contain any spoilers. The reason is very simple, I myself have not yet started the fifth season (OK this might be the only spoiler, there are at least 5 seasons...), so I am only focusing on number of viewers and ratings for each episode aired.]

I'm not even going to present the TV series Game of Thrones. Merchandising for it is perhaps not as overwhelming and invasive as it is for Frozen, I doubt many of view have no idea what this show is about.

As mentioned previously, we are currently midway in the fifth season, and I figured it might be a good time to figure how good of a TV show Game of Thrones is, and how it is performing from a viewership and rating point of view.

Viewership

The following graph displays the evolution of viewership for each episode of each season for the initial airing on HBO on Sundays at 9pm.

Two things clearly stand out: there is a strong steady rise corresponding to the series huge success. But, as is the case with any rise, when does it stop. Well, after reaching an all-time max with the first episode of the current fifth season (8.0 million), viewership has rather dramatically dropped with "only" 6.2 million for the sixth episode. This value is less than each episode of the previous fourth season. Will the decrease continue, or did we just have a few below-expectation episodes. Each season does have a small mid-season dip, somewhat due to the way each season is constructed as a highly-strategic chess game, with the different groups carrying out their tactics. The second half of the season should provide some element of response as to where we are headed.

To really put into perspective the importance of the decline in viewership from the last episodes, I forecasted viewership until the end of the fifth season once using all the available data (including the decrease, in blue), and once ignoring data for the fifth season (in green). The difference in forecasts are quite dramatic:

Metacritic ratings

Let's now turn towards metacritic ratings. According to the site that has made a name for itself by aggregating a wide range of critics into a single value ranging from 0-100, we observe a striking similarity in ratings and viewership:

Again, we observe a steady increase throughout the first four seasons, and the first decrease for the current fifth season.


IMDB ratings

Metacritic also contains user ratings, however I preferred to turn towards IMDB for individual episode ratings. Sample sizes were larger and extraction was easier.

Here is the evolution of the ratings for each episode:

The values for the last few episodes should be taken with a grain of salt. Episode 7 of the fifth season had a rating of 10.0 before it aired, but has now reached a rating more on par with the rest of the series, 9.3.

The trend here is somewhat different from what viewership and metacritic were indicating: it appears that season 5 episodes are rated just as highly as those from previous seasons.





Best series ever?

As indicated previously, I noticed that the last episode of Game of Thrones was briefly rated 10.0 right before airing. This led me to wonder whether episodes had ever been rated a perfect score of 10. It turns out that four of them had, all Dragon Ball Z episodes!


Relaxing to ratings above 9.8, I found 448 episodes (a little under half being Dragon Ball Z!). In the mix, two Breaking Bad (from the fifth and final season) and a Six Feet Under (series finale, also season five). No Game of Thrones, the top-rated episode has 9.7.

Looking at all these series and ratings, one can't help but wonder if there is some sort of agreement on the best show ever. There are naturally many ways and sources to compare them, but everytime, Game of Thrones, Breaking Bad and The Wire seem to top the list:

• best overall IMDB rating (secret IMDB formula): Breaking Bad and Game of Thrones are tied at 9.5, The Wire has 9.4
• average IMDB rating of each individual episode: The Wire has an average episode rating of 8.7, Game of Thrones an average of 8.5 and Breaking Bad an average of 8.3
• metacritic season-by-season rating (critics): The final season of breaking bad got a 99 (5th highest all-time), The Wire seasons 3 and 4 each got 98 (8th/9th highest all-time), the best Game of Thrones season (fourth) had a 95 which is 20th highest all-time
• metacritic season-by-season rating (users): This is where Breaking Bad dominates: all five seasons are in the top 12 all-time (positions 1, 3, 4, 11 and 12), the best Game of Thrones season comes in at position 20 only, while the Wire does rather well with three seasons in the top 10.

So no clear overall winner, but Game of Thrones however is the only one still running. But for how long?

Consequence of Morey's Law: Lucky vs Unlucky teams

In a previous post, I looked at a 1994 paper by Daryl Morey (current Houston Rockets GM) who investigated how a team's winning percentage was related to the number of points they scored and allowed, deriving the "modified Pythagorean theorem":

expected win percentage =
  pts_scored ^ 13.91 / (pts_scored ^ 13.91 + pts_allowed ^ 13.91)

At the end of his paper, Daryl explores teams who had the biggest delta between their actual and predicted wins. In 1993-1994, the Chicago Bulls and Houston Rockets top the list and Daryl refers to them as lucky teams. But why is lucked involved?

The rationale is that if you have two teams A and B with almost identical points scored and points allowed, we would expect them to have very similar win percentages. The only way to create a discrepancy (without changing points scored and points allowed... too much), is by changing the outcome of the very close games. So for all the games team A won by a point, flip the scores so that they lose by 1, and reversely for team B who now wins all the games they previously lost by 1. With this hypothetical construction, we will have two teams still with very similar points scored and allowed but potentially different records. It would make common sense that for very close games the probability of each team winning is around 50%, so winning or losing amounts to "luck", whether a desperation buzzer-beater is made or bounces off the back of the rim. And so it would make sense that teams with high discrepancies between actual and predicted wins were either much better or much worse than 50% in close games. Let's confirm.

Here's the table of teams with discrepancies greater or equal to 6 between their actual and projected records, ranked by year:

Team	Year	Scored	Allowed	Wins (proj)	Wins (actual)	Win %
NJN	2000	98.0	99.0	38	31	37.8
DEN	2001	96.6	99.0	34	40	48.8
NJN	2003	95.4	90.1	56	49	59.8
CHA	2005	94.3	100.2	24	18	22.0
NJN	2005	91.4	92.9	36	42	51.2
IND	2006	93.9	92.0	47	41	50.0
TOR	2006	101.1	104.0	33	27	32.9
UTA	2006	92.4	95.0	33	41	50.0
BOS	2007	95.8	99.2	31	24	29.3
CHI	2007	98.8	93.8	55	49	59.8
DAL	2007	100.0	92.8	61	67	81.7
MIA	2007	94.6	95.5	38	44	53.7
SAS	2007	98.5	90.1	64	58	70.7
NJN	2008	95.8	100.9	27	34	41.5
TOR	2008	100.2	97.3	49	41	50.0
DAL	2010	102.0	99.3	49	55	67.1
GSW	2010	108.8	112.4	32	26	31.7
MIN	2011	101.1	107.7	24	17	20.7
PHI	2012	93.6	89.4	43	35	53.0
BRK	2014	98.5	99.5	38	44	53.7
MIN	2014	106.9	104.3	48	40	48.8

So how did these teams fare in close games? I've labelled a team/year as High if they won 6 or more games than expected (8 teams from the previous list), Low if they lost 6 or more  games than expected (13 teams from the previous list), and Normal otherwise. I then look for each group their win percentage in closely contested games (final scores within 1, 2 and 3 points).

Final scores within 1 point:

Type	# Wins	# Games	Win %
Normal	721	1439	50.1
Low	8	21	38.1
High	2	2	100.0

Final scores within 2 points:

Type	# Wins	# Games	Win %
Normal	1760	3515	50.1
Low	20	52	38.5
High	10	13	76.9

Final scores within 3 points:

Type	# Wins	# Games	Win %
Normal	2820	5617	50.2
Low	24	80	30.0
High	14	19	73.7

Our intuition was correct and so were Daryl's closing comments: teams can indeed be qualified as lucky and unlucky, some winning almost 3 out of 4 close match-ups, others losing 2 out of 3 tight games. This intangible "luck" factor is sufficient to explain why certain teams have much better or worse records than their offense/defense would typically lead to. It doesn't take much for to flip the outcome of an entire game.

As a quick aside, much has been said about the San Antonio Spurs this year and their drop from a potential 2nd seed to 6th seed entering the Playoffs. Most articles focused on their loss on the final day of the regular season which led to that seeding free-fall, but was excessive focus placed on that last game? Had they been particularly lucky/unlucky during the season? It turns out their record is a couple games lower than what the modified Pythagorean theorem would have predicted, and that they weren't particularly lucky or unlucky in their close games, winning 2 of 5 games decided by 1 point, and 6 of 13 decided by 3 points or less.