Series 8: A Numbery-Wumbery Breakdown

Guest contributor Joshua Yetman presents a statistical breakdown of how Series 8 performed.

It seems like only yesterday since Series 8 started, and now here we are at the other end, twelve weeks of superlative television behind us with only a Christmas special to look forward to before the long wait for Series 9. It’s depressing, but, to a wannabe statistician such as myself, the end of this series bestows a tantalising opportunity to analyse the numbers and figures that underlie Series 8, comment on the results, and, where possible, compare them against other series.

Throughout this series, DWTV has held polls for each individual episode, asking respondents to rate said episode on a score from 1 to 10. A lot of the statistics presented in this article are calculated from the results of said polls. As not every Whovian in the world would have contributed to these polls (only the cool Whovians come to DWTV), they are obviously not representative of the whole population, but are certainly a reliable estimate.

1: The average score of the series (from DWTV poll results)

The average score for this series, as per the DWTV polls, was 8.096/10, a very impressive score indeed. How does this compare against the other series of the revived era? Well, due to limited information, I can only compare this figure to the previous three series of the Moffat era, as they’re the only series with recent and available poll results (from The Best of Matt Smith polls):

1. Series 8: 8.096/10
2. Series 5: 7.962/10
   (Series 7 + 2013 specials: 7.832/10)
3. Series 6: 7.642/10
4. Series 7: 7.637/10

[Note, unless otherwise specified, the average score for each series omits specials.]

So, to the DWTV community (on average), Series 8 is the most highly rated series of the Moffat era to date, comfortably beating Series 5.

2: Most divisive episode (The standard deviation of each episode score)
(from DWTV poll results)

Standard deviation is a measure of the dispersion of a set of data, i.e. how spread out it is from the average. In this context, the dispersion of the poll results tell us how divisive each episode was to the DWTV community. Essentially, all you need to know about standard deviation is that, the higher the figure, the greater the divisiveness of the episode:

1. In the Forest of the Night – 2.465
2. Death in Heaven – 2.346
3. Kill The Moon – 2.326
4. Robot of Sherwood – 2.094
5. Dark Water – 1.775
6. The Caretaker – 1.766
7. Deep Breath – 1.726
8. Into the Dalek – 1.723
9. Listen – 1.636
10. Time Heist – 1.622
11. Flatline – 1.456
12. Mummy on the Orient Express – 1.405

So, In the Forest of the Night was the most divisive episode of the series (which, alongside the fact that it also received the lowest average score, is a testament to how poorly received this episode ultimately was) and Mummy on the Orient Express was the least divisive. In fact, the two least divisive episodes of the series were both penned by Jamie Mathieson, another reason why this exceptional man should definitely return for Series 9!

3: Least Divisive Series (The standard deviation of the series)
(from DWTV results)

The standard deviation of the scores for this series was 0.673 (calculated by taking the standard deviation of all the average scores, not by taking the average of all the standard deviations) here on DWTV. How does this compare against the other series of the revived era? Again, due to limited information, we can only compare this figure to the other three series of the Moffat era:

1. Series 7: 0.581
2. Series 8: 0.673
   (Series 7 + 2013 specials: 0.754)
3. Series 5: 0.928
4. Series 6: 0.990

So, Series 8 is the second least divisive series of the Moffat era to date, after Series 7. So far then, Series 8 is, at a statistical level, proving to be very successful indeed!

Note: some people may be surprised that Series 7 is the least divisive series of the Moffat era, but it’s because almost all the scores for Series 7 were in the 7/10 to 8/10 range, with very few episodes scoring above or below these boundaries. Series 5, Series 6, and Series 8 to an extent have a lot episodes higher than 8/10, but a fair number below 7/10, meaning the results were more spread out for said series, hence why Series 7 is the least divisive Moffat series.

4: Best writer (from DWTV poll results)

This one’s a little bit more difficult due to the number of co-written stories this year, but, for each co-written story, the DWTV average score will be given to both pertaining writers. Hence, the Series 8 leaderboard looks like this:

1. Jamie Mathieson – 8.727/10
2. Steven Moffat – 8.271/10
3. Phil Ford – 8.052/10
4. Stephen Thompson – 7.823/10
5. Peter Harness – 7.808/10
6. Gareth Roberts – 7.795/10
7. Mark Gatiss – 7.512/10
8. Frank Cottrell Boyce – 6.482/10

This marks the first time in Moffat’s era (and probably the whole of the revived era, knowing Moffat’s superb storytelling reputation) where Moffat has not been deemed the best writer (on average) of the series, here losing that title to Jamie Mathieson. However, if you just consider the four episodes Steven Moffat wrote on his own (Deep Breath, Listen, Dark Water and Death in Heaven), his average jumps to 8.556, but Mathieson still retains his victory.

5: 5/10+ proportion results (from DWTV poll results)

The “5/10+ proportion” is a statistic of my own creation. The 5/10+ proportion of an episode is, simply, the percentage of people who gave the episode a 5/10 or higher in the DWTV polls. The ranked 5/10+ proportion results for Series 8 are as such:

1. Mummy on the Orient Express – 98.25%
2. Flatline – 98.06%
3. Listen: 96.65%
4. Dark Water – 95.90%
5. Time Heist – 95.70%
6. Into the Dalek: 95.56%
7. Deep Breath: 95.53%
8. The Caretaker – 94.57%
9. Robot of Sherwood: 90.36%
10. Death in Heaven – 89.66%
11. Kill The Moon – 88.95%
12. In The Forest of the Night – 78.13%

So, for every episode this series, at least three quarters of voters gave the episode half-marks or more, which is a decent result!

6: Average AI scores

The average AI score for Series 8 was 83.3. This is a very respectable score, which is comfortably above the BBC TV AI average of 82.3, though it is to be noted that this is the second lowest AI series average of the revived era, only beating Series 1 (which had an average AI score of 82.8). Regardless, it must be reiterated that Series 8 still performed very well AI-wise, even if it trails behind most of the revived era.

7: AI-DWTV correlation

Correlation is, in certain contexts, a measure of the agreement between two sets of data. How much agreement is there between the AI scores and the DWTV poll results? The Pearson product-moment correlation coefficient between the AI scores and the DWTV poll results is 0.3936, indicating a low level of positive correlation. The fact that the correlation is positive tells us that there is indeed some agreement between the DWTV poll results and the AI scores (which is funny, given how much we complain about the AI scores!).

8: The Series 8 audience figures
Average overnight audience: 5.172 million Average final audience: 7.2625 million.

The final figures in themselves are very impressive, but the L+7 figures, when released, will be only higher! So far, only four L+7 figures have been released and, on average, they add 1.08 million to the final figure. Assuming this average remains constant (which is a fair assumption), we can estimate what the average L+7 audience figure will be:

Projected average L+7 audience: 8.3425 million

If this figure is realised, Series 8 will be the most viewed series of the revival, based on all known data, taking that title from Series 4 (which had an average of 8.047 million, omitting specials). And some people say Moffat is ruining the show!

Conclusion

I hope you’ve enjoyed this statistical breakdown and the interesting inferences we can deduce from it. The vast majority of this analysis goes to show how well received the series was (on average), and, by extension, how overly successful Series 8 incontrovertibly was. It’s definitely been a good year, and Series 9 has a lot to live up to!