Series 10: A Numbery-Wumbery Breakdown (Part 1)

Joshua Yetman presents a statistical breakdown of how Series 10 performed overall.

12 episodes. 33614 seconds of content. 9 writers. 65 million views. 1 final run for the wonderful actor Peter Capaldi, and for the talented writer and showrunner Steven Moffat. These are just a handful of the numbers underlying the extraordinarily interesting run of episodes that was Series 10.

Numbers, however, can be elusive and erratic beasts. Without context or proper elucidation, they can be misleading, intimidating or often just nonsensical. They can be abused, and used to mislead. As someone with a great passion for numbers and statistics, my only wish is to impart and share that passion as much as possible, to make numbers a standard and reliable part of dialogue instead of that fearful, confusing entity that it so often is. Hopefully, these two articles I have prepared will not fall into any of these pitfalls, and will offer a clear, insightful and unbiased look at the statistics, and also provide a small evaluation about their limitations.

For 12 weeks, DWTV ran polls asking you to vote your scores for each episode of Series 10, and each week I analysed the results. With the series now complete, we can consider the results all together to gain a holistic perspective about this series, and, as far as existing data permits, compare this series to others to see just how well Series 10 did!

This first article will focus more on Series 10 and how it stands, whilst the second article will focus more on how the overall revival looks now that is 143 episodes strong.

The full rankings

Repeated in the graph below is the final rankings – from best to worst – of all the episodes in Series 10, along with the 2016 Christmas special The Return of Doctor Mysterio. Also included on the left hand side of the golden bars is the overall position each episode takes in the entire revival:

• With one entry that sits in the top 10 best episodes since 2005, enough 7’s to make Len Goodman’s giddy, and a decent spattering of 8’s peppered throughout, it’s very difficult to call Series 10 a failure. Unambitious perhaps, if you rationalise the abundance of 7’s as evidence of a lack of ‘envelope pushing’, but certainly not a failure. If consistent, solid Doctor Who is what you love best, then Series 10 was a total success.
• Consistent is certainly the key word to describe Series 10, and will probably be used as its primary descriptor in these articles. We’ll explore this in more detail later, but let’s consider something briefly now. Consider the difference between the highest and lowest scores, here 2.078. Sensibly, let’s call this the range. This range of Series 10 is pretty small, and is in fact the smallest range of any series in the revival. We conclude from this that the very best of Series 10 wasn’t too far from its very worst. Of course, this kind of statistic may not be the most insightful in isolation; for instance, Hull isn’t “too far” away from Scunthorpe, but both are frankly a bit rubbish. Fortunately, taken together with the scores, they illuminate a series that kept close to a high bar of quality throughout.

The most divisive episodes

To measure the divisiveness of an episode, we calculate the standard deviation of the votes for that episode. Standard deviation is a useful statistic that measures how far out, on average, votes were from the average, so it’s very informative in this context.

However, whilst an average of 8, or 5, or 3 is immediately interpretable from its value, a standard deviation is perhaps less so, with the only obvious inference being the fact that a higher standard deviation implies the episode was more divisive. There is no pre-established way of classifying standard deviations, but, in this context, I use the rule of thumb that:

• anything over 2 is very divisive;
• something between 1.75 and 2 is moderately divisive;
• something between 1.5 and 1.75 is only mildly divisive;
• and anything less than 1.5 is barely divisive at all!

So, without further ado, the divisiveness rankings of Series 10, from most divisive to least divisive, are given below:

• Thus, the most divisive episode was The Return of Doctor Mysterio, whilst the least divisive was World Enough and Time. This conforms to the natural tendency for the best episodes to be the least divisive, and the worst episodes to be the most divisive.
• The Return of Doctor Mysterio is the 5^th most divisive episode ever, whilst World Enough and Time is the 7^th least divisive episode ever.
• The average standard deviation for Series 10 was 1.865, which means the series was, on balance, moderately divisive. This is comparable to Series 8, which averaged a similar figure of 1.818. However, it is a far cry from the extremely polarising Series 9, which averaged a whopping 2.007 and gave us the two most divisive episodes of all time (Sleep No More and Hell Bent). Although Series 9 remains the highest rated series of the revival, it sure did vex some members of the community. It is definitely refreshing to have a series that succeeded in avoiding such frictional episodes.
• Other than Mysterio, particularly divisive offerings this series included The Lie of the Land (as a conclusion to the Monk Trilogy, it left a lot to be desired), The Eaters of Light (perhaps too uneventful for some, at a guess) and Extremis (the plot twist at the end certainly annoyed some people).

The series average and series comparison

To limit subjectivity, the definition of ‘series’ used in this section is one where Christmas specials are omitted. This is because the series in which some specials reside in is often open to interpretation.

Using this definition, the series average for Series 10 was 7.934, an extremely healthy average which means Series 10 is the second highest rated series of the revival:

• Series 10 primarily owes its high position to a very strongly received finale and a fundamental lack of ‘stinkers’ (anything below 6 in my terminology).
• Series 9 confidently remains the best series. It is still the only series to average above 8 on DWTV, with all the other series nesting somewhere between 7 and 8. It will take a lot to usurp it from this position.
• Four of the top five series are Moffat era series. Of course, as Moffat has 6 series to RTD’s 4, a slight bias is to be expected, but this is certainly more than proportional!

The most consistent series

We have so far considered one measure of consistency, which was range, i.e. the difference between the highest rated and lowest rated episode in a series. Another measure would be to take the standard deviation of all the episodes in a series; the higher this standard deviation, the more spread out episodes are in terms of quality, which would indicate greater inconsistency. If we do this for all series in the revival (again omitting Christmas specials for the same reason as before), the rankings from most inconsistent to most consistent look like this:

• Series 2 is thus the most inconsistent series and by quite a margin, and Series 10 is definitively the most consistent series. Series 7 is the second most consistent series, which may be a bit of a surprising result! However, this is because Series 7 was a consistently average run of episodes – remember, consistency is not always indicative of quality!

Series 10 rated overall

DWTV also held a poll asking you to rate Series 10 as one overall cohesive unit. The results of that poll can now be revealed:

• This implies a holistic average score of 7.824. The modal score (i.e. most common score) was 8/10, and nearly 84% of you thought Series 10 overall deserved a 7 or better.
• Recall that, episodically, the Series 10 average was 7.934. If you throw in the 2016 Christmas special, that episodic average falls to 7.860. Either way, the holistic average is fairly similar to the episodic average, which implies that Series 10 was approximately as good as the sum of its parts.
• The standard deviation implied by the above chart is 1.855, which is very similar to the average episodic standard deviation of 1.865 that we discussed earlier! Thus, Series 10 overall was no more or less contentious than its average episode.

That concludes this first article considering specifically how well Series 10 performed. In the next article, join us as we consider the impact Series 10 has had on the statistics of the overall revival – which showrunner is preferred, which Doctor has had the best era, what are the dream and nightmare series? All will be revealed in part 2!