TV Ratings Myths

August 28, 2013
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(This article was first published on jacobsimmering.com, and kindly contributed to R-bloggers)

TV Show Cancellations: Myths and Models

TV shows are amazing ways to waste time and, on occasion, the story is so good that you actually start to care. The problem is that some shows get cancelled before they jump the shark. Classic examples are shows like Firefly or Arrested Development. With the increasing serialization of TV shows, having the show be cancelled early means the story will potentially be unresolved or have a rushed conclusion.

As a result, a cottage industry of decision rules for predicting cancellation has emerged over the past few years. A lot of rules have come up such as “If it is good and it is on Fox, they will cancel it” or “If it airs on Friday, it will not return for next season.” But how accurate are these rules?

The most sophisticated method of tracking viewership I have seen is the Renew/Cancel Index by TV By The Numbers. Their insight is that a network is unlikely to cancel many of their shows in a given season. New series are typically just as costly to make but are not a known quantity. Many shows are cancelled during the course of the first season. For every new series that a network wants to air, they have to order \( cS \) series where \( c > 1 \) and \( S \) is number of ordered new series. As such, a network is loath to cancel too many shows due to the added cost of a new project and possible replacement for the new project. Like the old joke, you don't have to outrun the bear, you just have to outrun the slowest guy in the group.

The Renew/Cancel Index produced by TV By The Numbers takes this to heart. Instead of just looking at the number of viewers or share, they divide the number of viewers of the \( i^{th} \) show on the \( N \) network by the average number of viewers of all shows on \( N \) during that week. Now it doesn't matter that a show that would be a good performer for NBC would be a dud on Fox because they are normalized to the mean for each network.

If this index holds up as accurate, it provides an interesting way to test those two major “TV Myths.” From the TV By The Numbers website, I pulled 303 renewal decisions for the networks ABC, CBS, FOX and NBC from 2009-2010 to the 2012-2013 seasons.

Data Overview

When we look at the density of the index values split by network, we see that this normalization makes them roughly equal. Each network has some outstanding shows with index values over 1.5 and all have a few duds around 0.5.

ggplot(bigFour, aes(x = index, color = network)) + geom_density() + scale_x_continuous("Renew/Cancel Index")

bigFour$adjusted <- bigFour$index + bigFour$friday * 0.2
ggplot(bigFour, aes(x = adjusted, color = network)) + stat_ecdf() + geom_vline(aes(xintercept = 0.75)) + 
    geom_vline(aes(xintercept = 0.9)) + scale_x_continuous("Adjusted Renewal/Cancel Index") + 
    scale_y_continuous("Cumulative Density")

The “slow runners” on each network are also made clear. The people at TV By The Numbers use the following breaks for their predictions:

  • Index values over 0.90, renewal
  • Index values over 0.75 but under 0.90 are toss-ups
  • Index values under 0.75 will probably lead to a cancellation And shows that air on Friday's are given a slight bump of about 0.2 index units to account for the Friday Night Death Slot. These values are the vertical lines in the ecdf plot.

So how well does the index work?

bigFour$adjusted <- bigFour$index + bigFour$friday * 0.2
ggplot(bigFour, aes(x = adjusted, y = status)) + geom_point() + geom_vline(aes(xintercept = 0.75)) + 
    geom_vline(aes(xintercept = 0.9)) + scale_x_continuous("Adjusted Renewal/Cancel Index") + 
    scale_y_continuous("Renewal Status") + geom_smooth(method = "loess", alpha = 0.25)

It captured the expected sigmoidal shape of the response curve! That is something! Looking at their suggested breaks, they nicely land at about 30% and about 70% probability of renewal. Not too shabby for simple rules. Now, if we accept this index as a valid measure of cancellation risk, lets ask the hard questions.

Mythbusting: Does FOX Hate TV?

The cancellation of Firefly and Arrested Development in the early 2000s lead to the idea that Fox cancels everything good. Is that true? Does FOX really hate TV? Or more accurately, does FOX have a higher requirement for show performance than the other networks? Lets test that with a model. Let \( Y_{i, N} \) be the renewal status of the \( i^{th} \) show on network \( N \) and \( I_{i, N} \) be the renew/cancel index for the \( i^{th} \) show. I looked at three models, one that did not have a network effect (M1), a model with an intercept that varied by network (M2) and a model with both variable intercept and slope parameters (M3).

bigFour$reference <- ifelse(bigFour$network == "FOX", 1, ifelse(bigFour$network == 
    "ABC", 2, ifelse(bigFour$network == "CBS", 3, 4)))
bigFour$network <- reorder(bigFour$network, bigFour$reference)
m1 <- glm(status ~ adjusted, data = bigFour)
m2 <- glm(status ~ adjusted + network, data = bigFour)
m3 <- glm(status ~ adjusted + network + adjusted * network, data = bigFour)
summary(m1)
## 
## Call:
## glm(formula = status ~ adjusted, data = bigFour)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.1782  -0.3110  -0.0048   0.3421   0.8238  
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -0.3152     0.0673   -4.68  4.3e-06 ***
## adjusted      0.9635     0.0673   14.31  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for gaussian family taken to be 0.1426)
## 
##     Null deviance: 70.833  on 293  degrees of freedom
## Residual deviance: 41.629  on 292  degrees of freedom
##   (9 observations deleted due to missingness)
## AIC: 265.6
## 
## Number of Fisher Scoring iterations: 2
summary(m2)
## 
## Call:
## glm(formula = status ~ adjusted + network, data = bigFour)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.0951  -0.3131  -0.0147   0.3393   0.8944  
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.26429    0.07965   -3.32    0.001 ** 
## adjusted     0.95144    0.06759   14.08   <2e-16 ***
## networkABC  -0.05954    0.06359   -0.94    0.350    
## networkCBS   0.00875    0.06236    0.14    0.888    
## networkNBC  -0.11536    0.06578   -1.75    0.081 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for gaussian family taken to be 0.1416)
## 
##     Null deviance: 70.833  on 293  degrees of freedom
## Residual deviance: 40.919  on 289  degrees of freedom
##   (9 observations deleted due to missingness)
## AIC: 266.6
## 
## Number of Fisher Scoring iterations: 2
summary(m3)
## 
## Call:
## glm(formula = status ~ adjusted + network + adjusted * network, 
##     data = bigFour)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.1760  -0.3031  -0.0172   0.3297   0.9497  
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -0.2709     0.1477   -1.83    0.068 .  
## adjusted              0.9584     0.1472    6.51  3.4e-10 ***
## networkABC           -0.0740     0.1876   -0.39    0.693    
## networkCBS            0.1497     0.2016    0.74    0.459    
## networkNBC           -0.2308     0.2083   -1.11    0.269    
## adjusted:networkABC   0.0167     0.1901    0.09    0.930    
## adjusted:networkCBS  -0.1415     0.1972   -0.72    0.474    
## adjusted:networkNBC   0.1240     0.2099    0.59    0.555    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for gaussian family taken to be 0.1421)
## 
##     Null deviance: 70.833  on 293  degrees of freedom
## Residual deviance: 40.655  on 286  degrees of freedom
##   (9 observations deleted due to missingness)
## AIC: 270.7
## 
## Number of Fisher Scoring iterations: 2

We see in all three models that the show's Friday-adjusted Renew/Cancel Index is a powerful predictor (OR of around 2.75!) but that the network effects were not significant.

Looking at this visually…

bigFour$fox <- ifelse(bigFour$network == "FOX", "FOX", "Others")
ggplot(bigFour, aes(x = adjusted, y = status, lty = fox)) + geom_smooth(alpha = 0.25, 
    method = "loess") + scale_x_continuous("Adjusted Index") + scale_y_continuous("Renewal Probability")

This is interesting. Fox is slightly less likely to cancel low performing shows (see Fringe) than other networks. However, Fox is more likely to cull shows with a more middling performance. This might be the results of shows like Fringe having favorable economics ( syndication rights) that leads to the higher renewal rates for FOX at the lower index values. However, it is fairly clear that FOX's reputation as a killer of all that is good on TV is (at least since 2010) unfounded.

Mythbusting: Friday Night Death Slot

One of the most interesting questions regarding the Friday Night Death slot is whether airing on Friday night kills the shows (due to the lack of viewers on Friday evening) or whether being moved to Friday night is the result of a lack of viewership on other nights. That is an interesting question but can't be addressed by the current form of the data I have. I can, however, answer whether Friday night is actually a death slot or a safe harbor.

Because Friday nights are going to have lower viewer numbers regardless of what show airs and because the networks want to have programming on Friday night, shows airing on Friday night might be renewed at viewership numbers that would have resulted in cancellation with extreme prejudice on any other night. This is because the cost of making a new series, and the midseason replacement in case the new project is a flop, is no cheaper and often more expensive than airing the known quantity.

m4 <- glm(status ~ index + friday, data = bigFour)
m4
## 
## Call:  glm(formula = status ~ index + friday, data = bigFour)
## 
## Coefficients:
## (Intercept)        index       friday  
##      -0.300        0.953        0.134  
## 
## Degrees of Freedom: 293 Total (i.e. Null);  291 Residual
##   (9 observations deleted due to missingness)
## Null Deviance:       70.8 
## Residual Deviance: 41.5  AIC: 267

Looking at the two models, shows on Friday don't get a huge break relative to shows airing on other days during the week (about 0.14 boost compared to the suggested 0.2 used by TV By The Numbers). Here is the same thing visually:

ggplot(bigFour, aes(x = index, y = status, color = as.factor(friday))) + geom_smooth(span = 0.75, 
    method = "loess")

The shows on Friday all have lower viewer counts by are more likely to be renewed at those lower counts than other nights. In this sense, Friday night time slots may offer a chance for shows with cult followings, like Fringe or Chuck to find an economically viable timeslot and audience. At the very least, the networks do not hold Friday shows to Thursday standards.

Hopefully this year I won't have to worry about getting my six seasons and a movie but if I do, I can rest confident knowing that the network doesn't matter and Friday offers a refuge for cult shows.

To leave a comment for the author, please follow the link and comment on his blog: jacobsimmering.com.

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