As indicated by the title, this is part 2 of the analysis of movie sequels.

In the first post I described the IMDB data used for the analysis and shared some preliminary statistics on the distribution of number of movie installments in movie series.

In part 2 I focused on comparing IMDB ratings for the original movie and its sequel.

This post looks at series with 3 or more installments.

Looking at multiple installments is a little tricky. Can I compare the average IMDB rating change between installments 1 and 2 with the change between installments 2 and 3? Probably, but only if I look at the same sample. Let me explain myself. To compute the change between installments 1 and 2 I might have 1000 series to look at (2000 movies then). But when looking at the change between 2 and 3, my sample will be smaller (I will no longer have all the series that only had two installments). Is that so much of an issue? It could be if there is what is called a "lurking third variable". Perhaps moviemakers only make a third installment when the second installment wasn't too bad, so series with only two installments could be biased in the sense that they are the ones where the second installment did really terrible and so no third installment was made. So if we really want to compare the drop-off between 1 and 2 with the drop-off (I am assuming it is another drop-off!) between 2 and 3, we should restrict the analysis to only series with at least three installments.

So there are a couple of things we might want to look at:

1) average change between installments 1 and 2 for all movies that have 2 and only 2 installments

2) average change between installments 1 and 2 for all movies that have 3+ installments

3) average change between installments 2 and 3 for all movies that have 3+ installments

Comparing 1) and 2) will give us an idea whether third installments are favored for series where second installments didn't do too badly. Comparing 2) and 3) will allow us to compare the 1 -> 2 and 2 -> 3 effects.

Here are the results:

So it does seem that series with exactly 2 installments had a larger 1 to 2 installment drop-off (-0.92) than those with 3 or more installments (-0.78), however another (unpaired) t-test revealed that the difference was not significant. Budget and revenue are probably more important factors than IMDB ratings taken into account at Hollywood before deciding whether to make a third movie, but I suspect there is still some correlation between rating and revenue (no worries a future post will address this!).

Another interesting finding is that the drop-off from 2 to 3 is much smaller than from 1 to 2. This can make sense:

1) First of all, an IMDB rating can only go so low, you can't keep losing a full point rating everytime.

2) It is safe to assume the original movie was seen by a rather diverse crowd, whereas the second might have been seen only by the first movie's fan base, and very likely that those were about the same as those who saw the third. In other words, a much bigger overlap is to be expected between those who saw the second and third as opposed to first and second, which translates into more similar ratings.

For more than three installments, the sample starts to shrink quite rapidly, which is why I went for a more visual approach. I normalized all first installments to a score of 100 in order to track the evolution of all subsequent installments. This graph will allow us to shed some light on some hypotheses from the previous section: ratings go down but at a slower pace and tend might eventually converge with the same hard-core fan base rating the movies.

A slightly more confusing plot where trends are harder to establish but which nonetheless conveys both the initial rating drop-off as well as the sharp decrease in series length is the spaghetti-plot, where each line represents the evolution of a given series rating installment after installment.

From the previous two graphs, it appears that the decrease we observed over the first few installments continues until the fourth installment which is typically a series all-time low, with installments 5 and 6 usually bouncing surprisingly back. However, as shown in the spaghetti plot, the sample size is severely reduced and it would be dangerous to draw any strong conclusions.

It also seemed that quite a few series ended on surprisingly good ratings, sometimes the best or second best after the first installment:

Also, in the cases mentioned above, the last installment was usually declared as such, in which case also ratings might be higher from fans saddened to witness the final installment.

What have we learned? The primary conclusion is that the common belief that sequels do worse than the original is definitely valid. Although not proven here, the most likely explanation is that Hollywood doesn't care about making terrible movies as long as they generate a profit but more importantly (since good movies are more likely to generate greater profits than terrible movies, a priori) they want as little risk as possible involved. A guaranteed million dollar profit is better than a 50/50 chance of generating either three million or losing a million.

In the first post I described the IMDB data used for the analysis and shared some preliminary statistics on the distribution of number of movie installments in movie series.

In part 2 I focused on comparing IMDB ratings for the original movie and its sequel.

This post looks at series with 3 or more installments.

**The sequel has a sequel!!!**Looking at multiple installments is a little tricky. Can I compare the average IMDB rating change between installments 1 and 2 with the change between installments 2 and 3? Probably, but only if I look at the same sample. Let me explain myself. To compute the change between installments 1 and 2 I might have 1000 series to look at (2000 movies then). But when looking at the change between 2 and 3, my sample will be smaller (I will no longer have all the series that only had two installments). Is that so much of an issue? It could be if there is what is called a "lurking third variable". Perhaps moviemakers only make a third installment when the second installment wasn't too bad, so series with only two installments could be biased in the sense that they are the ones where the second installment did really terrible and so no third installment was made. So if we really want to compare the drop-off between 1 and 2 with the drop-off (I am assuming it is another drop-off!) between 2 and 3, we should restrict the analysis to only series with at least three installments.

So there are a couple of things we might want to look at:

1) average change between installments 1 and 2 for all movies that have 2 and only 2 installments

2) average change between installments 1 and 2 for all movies that have 3+ installments

3) average change between installments 2 and 3 for all movies that have 3+ installments

Comparing 1) and 2) will give us an idea whether third installments are favored for series where second installments didn't do too badly. Comparing 2) and 3) will allow us to compare the 1 -> 2 and 2 -> 3 effects.

Here are the results:

Series length | Sample Size | From Installment ... | To installment ... | IMDB Rating Difference |
---|---|---|---|---|

All series | 606 | 1 | 2 | -0.87 |

Exactly 2 | 410 | 1 | 2 | -0.92 |

3 or more | 196 | 1 | 2 | -0.78 |

3 or more | 196 | 2 | 3 | -0.33 |

So it does seem that series with exactly 2 installments had a larger 1 to 2 installment drop-off (-0.92) than those with 3 or more installments (-0.78), however another (unpaired) t-test revealed that the difference was not significant. Budget and revenue are probably more important factors than IMDB ratings taken into account at Hollywood before deciding whether to make a third movie, but I suspect there is still some correlation between rating and revenue (no worries a future post will address this!).

Another interesting finding is that the drop-off from 2 to 3 is much smaller than from 1 to 2. This can make sense:

1) First of all, an IMDB rating can only go so low, you can't keep losing a full point rating everytime.

2) It is safe to assume the original movie was seen by a rather diverse crowd, whereas the second might have been seen only by the first movie's fan base, and very likely that those were about the same as those who saw the third. In other words, a much bigger overlap is to be expected between those who saw the second and third as opposed to first and second, which translates into more similar ratings.

**More than 3?**For more than three installments, the sample starts to shrink quite rapidly, which is why I went for a more visual approach. I normalized all first installments to a score of 100 in order to track the evolution of all subsequent installments. This graph will allow us to shed some light on some hypotheses from the previous section: ratings go down but at a slower pace and tend might eventually converge with the same hard-core fan base rating the movies.

A slightly more confusing plot where trends are harder to establish but which nonetheless conveys both the initial rating drop-off as well as the sharp decrease in series length is the spaghetti-plot, where each line represents the evolution of a given series rating installment after installment.

From the previous two graphs, it appears that the decrease we observed over the first few installments continues until the fourth installment which is typically a series all-time low, with installments 5 and 6 usually bouncing surprisingly back. However, as shown in the spaghetti plot, the sample size is severely reduced and it would be dangerous to draw any strong conclusions.

It also seemed that quite a few series ended on surprisingly good ratings, sometimes the best or second best after the first installment:

- The
*Rocky*series was strictly decreasing from the start: 8.0, 6.9, 6.3, 6.2, 4.7 but finished with 7.2 - The
*Rambo*series had a similar pattern: 7.5, 6.0, 5.2, and... 7.1! - The
*Harry Potter*series has ratings grouped between 7.2 and 7.6 for the first 7 installments but the eight and final finished at 8.1

*Rocky*whereas the first 5 came within an average of 3 to 4 years apart from each other. Same for*Rambo*within a 20 year lapse compared to the three year gaps for the first movies.Also, in the cases mentioned above, the last installment was usually declared as such, in which case also ratings might be higher from fans saddened to witness the final installment.

**Closing thought**What have we learned? The primary conclusion is that the common belief that sequels do worse than the original is definitely valid. Although not proven here, the most likely explanation is that Hollywood doesn't care about making terrible movies as long as they generate a profit but more importantly (since good movies are more likely to generate greater profits than terrible movies, a priori) they want as little risk as possible involved. A guaranteed million dollar profit is better than a 50/50 chance of generating either three million or losing a million.

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