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09 May 2013 @ 11:18 pm
Warning: maaaaaaajor geekery ahead! A closer look at Doctor Who ratings  

OK so I like math. Although I'm not a statistician, I am pretty good with math (which is lucky for anyone in the USA haha bc in a few short months I will be using said math to prepare intravenous drug compounds for hospitalized patients... tl;dr if I sucked at this, it would suck WAAAY worse to be you bwahahah XD)

ANYWAY! It should not have escaped anyone's attention that Doctor Who ratings appear to be teetering a bit. Some people think "eh, it's not a big deal" while some think that this is dangerous. I'm one of the latter group. And because I have a huge-ass assignment due tomorrow that I don't feel like doing right now, I thought I'd explain why. (For simplicity's sake, there are no Xmas specials or 2009 specials included in this data - just final BARB ratings from 2005-present).

OK first off, if you compare the OVERALL numbers from s1-s7, although s7 (in red) looks like it's a bit low, there doesn't seem to be much difference ... right? Right???? And, truth be told, the only ~statistically significant~ differences (eg, where s7 really comparatively sucks balls) are when it's directly compared to s1. But ... this chart is a colorful mess. A colorful MEANINGLESS mess, because all I'm showing you is a bunch of lines without analysis. Six would probably proudly wear this chart as a coat it's so fugly. Anyway, this is usually the data people are looking at when they glance at the ratings and shrug it off as being "not all that different." This is not accurate.


So let's clean it up a bit!!! To simplify things, I'm gonna compare apples to apples. All RTD-era episodes are accounted for by the blue line ("You said BLUE!!" ... "I said NOT blue!!!"), the beginning of the Moffat era (s5-6) is the green line, and s7 is the red line. NOW things start to look interesting!!

OK this is not a calculus class but I hope this shows why math is kind of cool if you're a total fandom nerd and you want to prove other fandom nerds wrong XD. Look at the pretty lines and numbers!!! Here's what they mean: see the dotted lines with the equations? Those are ~trendlines~ for the graph. Basically what that means is it tells you, on average, where the hell your data is going. See the equations? Those tell you how fast viewers are flocking to your show (or, alternatively, turning it off bc it sucks and going to read fanfic or something lol idk). And see the (sorrysorry tiny font I knowww) "R^2" value? That tells you if you can trust your trends or not (lol @ those evil, untrustworthy trend bitches). The closer to "1" the better, and these are all pretty freaking close to one which means the trends are pretty strong. (So anyone who tries to respond and say it's meaningless - look at the R^2 value and hush lol).

So what does this mean? Again this isn't a calculus class so I'll skip the lecture on how to calculate derivatives and try not to make this too boring (BUT CALCULUS IS SUPER COOL AND YOU SHOULD LOVE IT GUYZ), but essentially the first number (x^2) is saying "this is how fast viewers are coming/going".

And this is where the RTD era is strong, s5-6 are a bit weaker, and s7 is in trouble. For the RTD era, the first number shows that yeah viewers were coming and going - but that there was a general trend back up. For s5-6, there are fewer people coming and going. And for s7, the number is negative --- that means there is a trend of people leaving. How reliable is this? Well back to the R-squared thingy I was telling you about - it's pretty freaking close to 1, so the trend is pretty tight.


One of the big weaknesses here is that premieres and season finales tend to have more viewers, so in this next graph, I simply removed the premieres and finales (which meant I had to remove mainly s6-7 episodes from the data pool bc of the split season). Taking away those premiere/finale bumps in viewership looks even worse for s7 - the number of viewers leaving is even MORE negative now!!!! And s5-6 has a much flatter line too ... viewers were pretty stagnant. Again, the RTD era had some swings, but at the end of the day, viewers were coming home. That's not happening for the past few years, especially this year.


So what can we make out of all of this? Tl;dr, the numbers aren't good. And they're getting not-gooder by the season.


(Deleted comment)
kilodaltonkilodalton on May 10th, 2013 08:29 pm (UTC)
Why thank you!! =D ... and yeah, it does seem to be missing something =(
Arabian: I ♥ RTDarabian on May 10th, 2013 03:55 am (UTC)
As someone who's been waiting for the rest of the DW-watching public to pick up on how shallow Moffat's DW is, this is heartening to read. (And I totally wish you could do this for another show I watch, just so I could compare the ratings throughout the season, LOL!)

BTW: I SUCK SO HARD AT MATH! I could never do this.
kilodaltonkilodalton on May 10th, 2013 08:30 pm (UTC)
Haha np at all! And I'd be happy to plot the other show for you - I already have this set up as a template, so all I'd need is the ratings =D
(no subject) - arabian on May 12th, 2013 04:19 am (UTC) (Expand)
(no subject) - kilodalton on May 12th, 2013 01:09 pm (UTC) (Expand)
sherrilina: Doomsday Ten/Rosesherrilina on May 10th, 2013 04:00 am (UTC)
Wow, I am still a bit confused, but I like your general gist--because it means we aren't the only ones who think the last few seasons have progressively sucked! ;) (Although some of the episodes with Clara haven't been so bad...it's nice to have some fresh blood). Moffat desperately needs to leave, stat, for the survival and well-being of the show!
kilodaltonkilodalton on May 10th, 2013 08:31 pm (UTC)
Yeah there is definitely something going on ... I have to agree with fogsblue here, I think the improvement may be too little too late =/ (plus Eleven isn't new and shiny anymore - although that didn't seem to hurt Ten's popularity so idk)
betawhobetawho on May 10th, 2013 04:16 am (UTC)
It's still possible things can go back up. Since this series still has two episodes to go, they can also swing the trend back up the way the last two episodes of most of the other series did. (Although that won't negate that it's also fallen lower than any other series so far.)

If you take out the last two episodes of Series 1-6, the difference in the trends doesn't appear as great. It will be interesting to see this graph again once the series is complete.

(I'm still hoping that the Gaiman/Cybermen episode and the "Trensalore" episode, with Clara's mystery, the Doctor's name mystery, and the return of River Song, can help swing those numbers back up.)

I agree, the attraction of the show has seemed to have waned a a lot this season, not just for me (although I'm at my lowest "rewatch" ebb ever) but in the mainstream media reviews and general ratings too. Although, oddly, the AI still seems to be high. (It would be interesting to see a graph on the AI as well. - Especially how 2 parters AI* compares to single parters, as well as for full series' as well.)

*Audience Appreciation Index.

Cool graph! Six would be proud!

Edited at 2013-05-10 04:18 am (UTC)
kilodaltonkilodalton on May 10th, 2013 08:35 pm (UTC)
Oh sure it could go up! Honestly judging from the flatter lines that s5 and s6 have shown, I would be surprised - but it's possible and I'll continue to map that to see where s7 ends up relative to the others.

Re the AI - I'm actually not surprised that this remains pretty high from what I've seen. DW fans are nothing if not pathologically loyal lol - so even if perhaps more casual viewers were to be leaving (and not tuning in at all), if die-hards are still tuning in every week then the AI isn't going to budge much.
fogsbluefogsblue on May 10th, 2013 06:00 am (UTC)
I've actually noticed a number of people on my fb for example who are losing interest, but they loved S5 and at least some of S6, so... *shrug*

I've actually found a few of the latest episodes to the best in a long time, but too little, too late comes to mind as an answer for that.

But I've seen a few reports around lately about how the numbers are dropping a fair bit... MAYBE THE BBC WILL LISTEN SOON AND LOSE MOFFAT!

The Captain Of My Ship, The Master Of My Soulgonzo21 on May 10th, 2013 11:57 am (UTC)
Yes, I agree, the last few episodes have definitely included some improvements.
(no subject) - kilodalton on May 10th, 2013 08:35 pm (UTC) (Expand)
Eli-chan: 9 - *wibble*silverlunarstar on May 10th, 2013 07:10 am (UTC)
*sighs* It's sad to see what was once such a fantastic show shoot down like that.

kilodaltonkilodalton on May 10th, 2013 08:35 pm (UTC)
Claireyumimum on May 10th, 2013 08:43 am (UTC)
I am both impressed and depressed at the same time.

Someone send this to the Moff, please?
kilodaltonkilodalton on May 10th, 2013 08:36 pm (UTC)
Haha I have no doubt that he's seen something like this (and that his bosses have as well) - the BBC has to be tracking this in depth and with much more powerful software than I have!! XD
(no subject) - yumimum on May 10th, 2013 08:43 pm (UTC) (Expand)
(no subject) - kilodalton on May 10th, 2013 09:39 pm (UTC) (Expand)
Rosa | ¯\(ºдಠ)/¯rosaxx50 on May 10th, 2013 10:06 am (UTC)
I am sad about this, because I've enjoyed the second half of s7 so far.

Hahaha, I loved calculus in high school, but now I've forgotten almost every single thing about it.
kilodaltonkilodalton on May 10th, 2013 08:37 pm (UTC)
I adore calculus. It's one of those topics that I totally thought I was going to hate but that I fell head over heels in love with!!
The Captain Of My Ship, The Master Of My Soulgonzo21 on May 10th, 2013 11:55 am (UTC)
What a brilliant analysis. Well done. I was hoping somebody with sharper maths skills than me might be able to prove what the gut feeling was about these numbers. And this does indeed prove it.
kilodaltonkilodalton on May 10th, 2013 08:38 pm (UTC)
Thank you!! Yeah there's only so many times you can chock up ratings to bank holidays or nice weather, or 2-for-1 hot dog sales at Tesco's XD No statistics are perfect but this does illustrate a powerfully convincing trend imo.
(no subject) - gonzo21 on May 14th, 2013 02:44 pm (UTC) (Expand)
(no subject) - kilodalton on May 14th, 2013 10:11 pm (UTC) (Expand)
kelkat9 on May 10th, 2013 12:58 pm (UTC)
Worships at the alter of your math wizardry!
kilodaltonkilodalton on May 10th, 2013 08:38 pm (UTC)
((Blush)) glad you find it helpful!! =D
ebartonebarton on May 10th, 2013 02:04 pm (UTC)
I'd be interested to see how season 3 stacks up when looked at on it's own - this was surely the weakest season of the RTD era so it seems more natural to compare the weakest season of the moffat era to that rather than s1-4 combined.

And I reckon the last two episodes of 7.2 will definitely be a help to the ratings... hopefully anyway!?
kilodaltonkilodalton on May 10th, 2013 08:56 pm (UTC)
Yeah I'll definitely keep tracking s7 to see where things end up vis a vis the others - truth be told, s5 and s6 were pretty flat overall in terms of ratings so I'm not hopeful for much of a bump but who knows!! =)

Re s3 ... LOL THAT'S MY FAVORITE ONE!! I thought s2 was the weakest personally, and that s5 and s6 were weaker than s7 - just goes to show haha!!!
(no subject) - ebarton on May 10th, 2013 09:24 pm (UTC) (Expand)
(no subject) - kilodalton on May 10th, 2013 09:37 pm (UTC) (Expand)
(Deleted comment)
kilodaltonkilodalton on May 10th, 2013 08:57 pm (UTC)
Why ty!! =D
bloose09: Angstbloose09 on May 10th, 2013 05:26 pm (UTC)
I am a card carrying Aerospace Engineer and I, too, approve this post!

It is all about the trends and they certainly do not look good. Viewers mean sponsors, and sponsors mean money. You do not need an engineering degree to figure that one out. It also shows that established viewers are leaving the show faster than new ones can find it. That is something that the BBC will certainly understand and have to address.

No matter what the Moff does for the 50th, it is bound to be a ratings bonanza. Once he blows his wad on that episode, he can safely leave and claim that everything was perfect when he handed over the reins. It is the perfect time to leave and blame the next person for the slip in ratings. He is in a win-win scenario because it happens to be 2013.

Thank you for this post :)
kilodaltonkilodalton on May 10th, 2013 08:58 pm (UTC)
Why thank you! And totally agreed!
eve11eve11 on May 10th, 2013 06:21 pm (UTC)
Sorry, I am a card-carrying statistician and all I see is a general trend for all seasons, bucked by the end of season 4 with its specials.

For your positively curved red and blue lines, re-calculate with the last 3 episodes removed as you have for the S7 data. Willing to bet they will also trend down. You are fitting a trend line that looks like some kind of cubic... why that particular line? ETA: my mistake, quadratic. That is pretty highly parametric, which means the format of line is going to be susceptible to outliers, and especially susceptible to boundary points. If you get a new data point that changes inflection it has the possibility to severely affect the form of the line. And you don't really have a lot of points to fit something like a smoother. You could take the mean of each episode crosswise and see if any seasons lie "more likely above" or "more likely below", maybe?

ETA: and one last thing which is that anyone can look at the above chart and see that S4 is an obvious outlier at the end. So the big uptick in the blue line in your chart is mostly due to incorporating the s4 outlier.

I think you should also include at least the month of airing as a covariate.

Gonna have to wait for the next few episodes to see if s7 trends upward again like the previous seasons or if it goes down.

Edited at 2013-05-10 06:30 pm (UTC)
eve11eve11 on May 10th, 2013 06:37 pm (UTC)
My mistake, it's the end of series 4 (not the specials) that is the outlier. eg, Turn Left, The Stolen Earth and Journey's End.
(no subject) - hammard on May 10th, 2013 06:42 pm (UTC) (Expand)
(no subject) - kilodalton on May 10th, 2013 09:18 pm (UTC) (Expand)
hammard: tennanthammard on May 10th, 2013 06:41 pm (UTC)
You should read Tom Spilsbury's post on this subject he did back during Season 6 where he analysed ALL the ratings and showed the change was very little:

Whilst we cannot analyse all the recent ratings in this way due to lack of data (Iplayer stats will not be available for a while) it is probable to be the same.

What the figures are possibly mapping is the move from TV to online watching (just as the strong downwards trend from S1 to S2 tracks people moving to repeat vieiwings).

Also, out of curiousity, would you really say r-squared is valuable for such a small data set for a trend of fit. Perhaps it's different in other sbjects but I studied statistics and we would not consider it a relaiable measure of trend for a data set this small. As for example, your r-squared function for this season is 0.81 based on only 7 variables but it can only explain every 4 in 5 variances so the trend cannot be said to be solid.

Anyway, don't want to start a flame war on your own blog. I love maths too :D

Edited at 2013-05-10 06:53 pm (UTC)
eve11eve11 on May 10th, 2013 07:39 pm (UTC)
Another interesting story would be to start with eg, episode 4 in each series, and plot the quadratic curves point by point as you gain new points with each new episode, and see how much the prediction changes with the next new data point. The future predictive trend depends rather massively on where it estimates the inflection point.
(no subject) - kilodalton on May 10th, 2013 09:08 pm (UTC) (Expand)
(no subject) - eve11 on May 10th, 2013 09:16 pm (UTC) (Expand)
(no subject) - kilodalton on May 10th, 2013 09:20 pm (UTC) (Expand)
(no subject) - eve11 on May 10th, 2013 09:24 pm (UTC) (Expand)
(no subject) - kilodalton on May 10th, 2013 09:33 pm (UTC) (Expand)
(no subject) - eve11 on May 10th, 2013 10:00 pm (UTC) (Expand)
(no subject) - kilodalton on May 10th, 2013 10:01 pm (UTC) (Expand)
(no subject) - eve11 on May 11th, 2013 05:31 am (UTC) (Expand)
(no subject) - kilodalton on May 11th, 2013 01:58 pm (UTC) (Expand)
(no subject) - eve11 on May 11th, 2013 09:35 pm (UTC) (Expand)
(no subject) - kilodalton on May 12th, 2013 12:55 pm (UTC) (Expand)
(no subject) - eve11 on May 12th, 2013 01:05 pm (UTC) (Expand)
(no subject) - kilodalton on May 12th, 2013 01:09 pm (UTC) (Expand)