Data Science Portfolio Project： Is Fandango Still Inflating Ratings?

转载自：https://www.dataquest.io/blog/data-science-project-fandango/

Alex Olteanu
发表于

At Dataquest, we strongly advocate portfolio projects as a means of getting your first data science job. In this blog post, we’ll walk you through an example portfolio project.

The project is part of our Statistics Fundamentals course, and it assumes some familiarity with:

  • Sampling (simple random sampling, populations, samples, parameters, statistics)

  • Variables

  • Frequency distributions

  • pandas and matplotlib

If you think you need to fill in any gaps before moving forward, we cover the topics above in depth in our Statistics Fundamentals course. This course will also give you deeper instructions on how to build this project, and code it in your browser.

To learn more about pandas and matplotlib, check out our Data Scientist Path.

In October 2015, Walt Hickey from FiveThirtyEight published a popular article where he presented strong evidence that suggested Fandango’s movie rating system was biased and dishonest. In this project, we’ll analyze more recent movie ratings data to determine whether there has been any change in Fandango’s rating system after Hickey’s analysis.

We’ll work with two samples of movie ratings: the data in one sample was collected previous to Hickey’s analysis, while the other sample was collected after. This will help us compare the system’s characteristics previous and after the analysis. Fortunately, we have ready-made data for both these periods of time:

Walt Hickey made the data he analyzed publicly available on GitHub. We’ll use the data he collected to analyze the characteristics of Fandango’s rating system previous to his analysis.

One of Dataquest’s team members collected movie ratings data for movies released in 2016 and 2017. The data is publicly available on GitHub, and we’ll use it to analyze the rating system’s characteristics after Hickey’s analysis.

Let’s start by reading in the two samples (which are stored as CSV files: fandango_score_comparison.csv and movie_ratings_16_17.csv) and getting familiar with their structure.

1
2
3
4
5
6
7
8
import pandas as pd
pd.options.display.max_columns = 100 # Avoid having displayed truncated output

previous = pd.read_csv('fandango_score_comparison.csv')
after = pd.read_csv('movie_ratings_16_17.csv')

previous.head(3)
  FILM RottenTomatoes RottenTomatoes_User Metacritic Metacritic_User IMDB Fandango_Stars Fandango_Ratingvalue RT_norm RT_user_norm Metacritic_norm Metacritic_user_nom IMDB_norm RT_norm_round RT_user_norm_round Metacritic_norm_round Metacritic_user_norm_round IMDB_norm_round Metacritic_user_vote_count IMDB_user_vote_count Fandango_votes Fandango_Difference
0 Avengers: Age of Ultron (2015) 74 86 66 7.1 7.8 5.0 4.5 3.70 4.3 3.30 3.55 3.90 3.5 4.5 3.5 3.5 4.0 1330 271107 14846 0.5
1 Cinderella (2015) 85 80 67 7.5 7.1 5.0 4.5 4.25 4.0 3.35 3.75 3.55 4.5 4.0 3.5 4.0 3.5 249 65709 12640 0.5
2 Ant-Man (2015) 80 90 64 8.1 7.8 5.0 4.5 4.00 4.5 3.20 4.05 3.90 4.0 4.5 3.0 4.0 4.0 627 103660 12055 0.5 
1
2
after.head(3)
  movie year metascore imdb tmeter audience fandango n_metascore n_imdb n_tmeter n_audience nr_metascore nr_imdb nr_tmeter nr_audience
0 10 Cloverfield Lane 2016 76 7.2 90 79 3.5 3.80 3.60 4.5 3.95 4.0 3.5 4.5 4.0
1 13 Hours 2016 48 7.3 50 83 4.5 2.40 3.65 2.5 4.15 2.5 3.5 2.5 4.0
2 A Cure for Wellness 2016 47 6.6 40 47 3.0 2.35 3.30 2.0 2.35 2.5 3.5 2.0 2.5

Below, we isolate only the columns that provide information about Fandango, to make the relevant data more readily available for later use. We’ll make copies to avoid any SettingWithCopyWarning later on.

1
2
3
4
5
6
fandango_previous = previous[['FILM', 'Fandango_Stars', 'Fandango_Ratingvalue', 'Fandango_votes',
 'Fandango_Difference']].copy()
fandango_after = after[['movie', 'year', 'fandango']].copy()

fandango_previous.head(3)
  FILM Fandango_Stars Fandango_Ratingvalue Fandango_votes Fandango_Difference
0 Avengers: Age of Ultron (2015) 5.0 4.5 14846 0.5
1 Cinderella (2015) 5.0 4.5 12640 0.5
2 Ant-Man (2015) 5.0 4.5 12055 0.5 
1
2
fandango_after.head(3)
  movie year fandango
0 10 Cloverfield Lane 2016 3.5
1 13 Hours 2016 4.5
2 A Cure for Wellness 2016 3.0

Our goal is to determine whether there has been any change in Fandango’s rating system after Hickey’s analysis. The population of interest for our analysis is made of all the movie ratings stored on Fandango’s website, regardless of the releasing year.

Because we want to find out whether the parameters of this population changed after Hickey’s analysis, we’re interested in sampling the population at two different periods in time — before and after Hickey’s analysis — so we can compare the two states.

The data we’re working with was sampled at the moments we want: one sample was taken previous to the analysis, and the other after the analysis. We want to describe the population, so we need to make sure that the samples are representative. Otherwise we should expect a large sampling error and, ultimately, wrong conclusions.

From Hickey’s article and from the README.md of the data set’s repository, we can see that he used the following sampling criteria:

  • The movie must have had at least 30 fan ratings on Fandango’s website at the time of sampling (Aug. 24, 2015).

  • The movie must have had tickets on sale in 2015.

The sampling was clearly not random because not every movie had the same chance to be included in the sample — some movies didn’t have a chance at all (like those having under 30 fan ratings or those without tickets on sale in 2015). It’s questionable whether this sample is representative of the entire population we’re interested to describe. It seems more likely that it isn’t, mostly because this sample is subject to temporal trends — e.g. movies in 2015 might have been outstandingly good or bad compared to other years.

The sampling conditions for our other sample were (as it can be read in the README.md of the data set’s repository):

  • The movie must have been released in 2016 or later.

  • The movie must have had a considerable number of votes and reviews (unclear how many from the README.md or from the data).

This second sample is also subject to temporal trends and it’s unlikely to be representative of our population of interest.

Both these authors had certain research questions in mind when they sampled the data, and they used a set of criteria to get a sample that would fit their questions. Their sampling method is called purposive sampling (or judgmental/selective/subjective sampling). While these samples were good enough for their research, they don’t seem too useful for us.

At this point, we can either collect new data or change our the goal of our analysis. Let’s choose the latter and place some limitations on our initial goal.

Instead of trying to determine whether there has been any change in Fandango’s rating system after Hickey’s analysis, our new goal is to determine whether there’s any difference between Fandango’s ratings for popular movies in 2015 and Fandango’s ratings for popular movies in 2016. This new goal should also be a fairly good proxy for our initial goal.

With this new research goal, we have two populations of interest:

  1. All Fandango’s ratings for popular movies released in 2015.

  2. All Fandango’s ratings for popular movies released in 2016.

We need to be clear about what counts as popular movies. We’ll use Hickey’s benchmark of 30 fan ratings and count a movie as popular only if it has 30 fan ratings or more on Fandango’s website.

Although one of the sampling criteria in our second sample is movie popularity, the sample doesn’t provide information about the number of fan ratings. We should be skeptical once more and ask whether this sample is truly representative and contains popular movies (movies with over 30 fan ratings).

One quick way to check the representativity of this sample is to randomly sample 10 movies from it and then check the number of fan ratings ourselves on Fandango’s website. Ideally, at least 8 out of the 10 movies have 30 fan ratings or more.

1
2
fandango_after.sample(10, random_state = 1)
  movie year fandango
108 Mechanic: Resurrection 2016 4.0
206 Warcraft 2016 4.0
106 Max Steel 2016 3.5
107 Me Before You 2016 4.5
51 Fantastic Beasts and Where to Find Them 2016 4.5
33 Cell 2016 3.0
59 Genius 2016 3.5
152 Sully 2016 4.5
4 A Hologram for the King 2016 3.0
31 Captain America: Civil War 2016 4.5

Above we used a value of 1 as the random seed. This is good practice because it suggests that we weren’t trying out various random seeds just to get a favorable sample.

As of April 2018, these are the fan ratings we found:

Movie Fan ratings
Mechanic: Resurrection 2247
Warcraft 7271
Max Steel 493
Me Before You 5263
Fantastic Beasts and Where to Find Them 13400
Cell 17
Genius 127
Sully 11877
A Hologram for the King 500
Captain America: Civil War 35057

90% of the movies in our sample are popular. This is enough and we move forward with a bit more confidence.

Let’s also double-check the other data set for popular movies. The documentation states clearly that there’re only movies with at least 30 fan ratings, but it should take only a couple of seconds to double-check here.

1
2
sum(fandango_previous['Fandango_votes'] < 30)


1
2
0

If you explore the two data sets, you’ll notice that there are movies with a releasing year different than 2015 or 2016. For our purposes, we’ll need to isolate only the movies released in 2015 and 2016.

Let’s start with Hickey’s data set and isolate only the movies released in 2015. There’s no special column for the releasing year, but we should be able to extract it from the strings in the FILM column.

1
2
fandango_previous.head(2)
  FILM Fandango_Stars Fandango_Ratingvalue Fandango_votes Fandango_Difference
0 Avengers: Age of Ultron (2015) 5.0 4.5 14846 0.5
1 Cinderella (2015) 5.0 4.5 12640 0.5 
1
2
3
fandango_previous['Year'] = fandango_previous['FILM'].str[-5:-1]
fandango_previous.head(2)
  FILM Fandango_Stars Fandango_Ratingvalue Fandango_votes Fandango_Difference Year
0 Avengers: Age of Ultron (2015) 5.0 4.5 14846 0.5 2015
1 Cinderella (2015) 5.0 4.5 12640 0.5 2015 
1
2
fandango_previous['Year'].value_counts()


1
2
3
4
2015 129
2014 17
Name: Year, dtype: int64


1
2
3
fandango_2015 = fandango_previous[fandango_previous['Year'] == '2015'].copy()
fandango_2015['Year'].value_counts()


1
2
3
2015 129
Name: Year, dtype: int64

Great, now let’s isolate the movies in the other data set.

1
2
fandango_after.head(2)
  movie year fandango
0 10 Cloverfield Lane 2016 3.5
1 13 Hours 2016 4.5 
1
2
fandango_after['year'].value_counts()


1
2
3
4
2016 191
2017 23
Name: year, dtype: int64


1
2
3
fandango_2016 = fandango_after[fandango_after['year'] == 2016].copy()
fandango_2016['year'].value_counts()


1
2
3
2016 191
Name: year, dtype: int64

Our aim is to figure out whether there’s any difference between Fandango’s ratings for popular movies in 2015 and Fandango’s ratings for popular movies in 2016. One way to go about is to analyze and compare the distributions of movie ratings for the two samples.

We’ll start with comparing the shape of the two distributions using kernel density plots. We’ll use the FiveThirtyEight style for the plots.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
import matplotlib.pyplot as plt
from numpy import arange
%matplotlib inline
plt.style.use('fivethirtyeight')

fandango_2015['Fandango_Stars'].plot.kde(label = '2015', legend = True, figsize = (8,5.5))
fandango_2016['fandango'].plot.kde(label = '2016', legend = True)

plt.title("Comparing distribution shapes for Fandango's ratings\n(2015 vs 2016)",
 y = 1.07) # the `y` parameter pads the title upward
plt.xlabel('Stars')
plt.xlim(0,5) # because ratings start at 0 and end at 5
plt.xticks(arange(0,5.1,.5))
plt.show()

Two aspects of the figure above are striking:

  • Both distributions are strongly left skewed.

  • The 2016 distribution is slightly shifted to the left relative to the 2015 distribution.

The left skew suggests that movies on Fandango are given mostly high and very high fan ratings. Coupled with the fact that Fandango sells tickets, the high ratings are a bit dubious. It’d be really interesting to investigate this further — ideally in a separate project, since this is quite irrelevant for the current goal of our analysis.

The slight left shift of the 2016 distribution is very interesting for our analysis. It shows that ratings were slightly lower in 2016 compared to 2015. This suggests that there was a difference indeed between Fandango’s ratings for popular movies in 2015 and Fandango’s ratings for popular movies in 2016. We can also see the direction of the difference: the ratings in 2016 were slightly lower compared to 2015.

It seems we’re following a good thread so far, but we need to analyze more granular information. Let’s examine the frequency tables of the two distributions to analyze some numbers. Because the data sets have different numbers of movies, we normalize the tables and show percentages instead.

1
2
3
4
print('2015' + '\n' + '-' * 16) # To help us distinguish between the two tables immediately and avoid silly mistakes as we read to and fro

fandango_2015['Fandango_Stars'].value_counts(normalize = True).sort_index() * 100


1
2
3
4
5
6
7
8
9
2015
----------------
3.0 8.527132
3.5 17.829457
4.0 28.682171
4.5 37.984496
5.0 6.976744
Name: Fandango_Stars, dtype: float64


1
2
3
print('2016' + '\n' + '-' * 16)
fandango_2016['fandango'].value_counts(normalize = True).sort_index() * 100


1
2
3
4
5
6
7
8
9
10
2016
----------------
2.5 3.141361
3.0 7.329843
3.5 24.083770
4.0 40.314136
4.5 24.607330
5.0 0.523560
Name: fandango, dtype: float64

In 2016, very high ratings (4.5 and 5 stars) had significantly lower percentages compared to 2015. In 2016, under 1% of the movies had a perfect rating of 5 stars, compared to 2015 when the percentage was close to 7%. Ratings of 4.5 were also more popular in 2015 — there were approximately 13% more movies rated with a 4.5 in 2015 compared to 2016.

The minimum rating is also lower in 2016 — 2.5 instead of 3 stars, the minimum of 2015. There clearly is a difference between the two frequency distributions.

For some other ratings, the percentage went up in 2016. There was a greater percentage of movies in 2016 that received 3.5 and 4 stars, compared to 2015. 3.5 and 4.0 are high ratings and this challenges the direction of the change we saw on the kernel density plots.

Let’s take a couple of summary metrics to get a more precise picture about the direction of the change. In what follows, we’ll compute the mean, the median, and the mode for both distributions and then use a bar graph to plot the values.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
mean_2015 = fandango_2015['Fandango_Stars'].mean()
mean_2016 = fandango_2016['fandango'].mean()

median_2015 = fandango_2015['Fandango_Stars'].median()
median_2016 = fandango_2016['fandango'].median()

mode_2015 = fandango_2015['Fandango_Stars'].mode()[0] # the output of Series.mode() is a bit uncommon
mode_2016 = fandango_2016['fandango'].mode()[0]

summary = pd.DataFrame()
summary['2015'] = [mean_2015, median_2015, mode_2015]
summary['2016'] = [mean_2016, median_2016, mode_2016]
summary.index = ['mean', 'median', 'mode']
summary
  2015 2016
mean 4.085271 3.887435
median 4.000000 4.000000
mode 4.500000 4.000000 
1
2
3
4
5
6
7
8
9
10
11
12
plt.style.use('fivethirtyeight')
summary['2015'].plot.bar(color = '#0066FF', align = 'center', label = '2015', width = .25)
summary['2016'].plot.bar(color = '#CC0000', align = 'edge', label = '2016', width = .25,
 rot = 0, figsize = (8,5))

plt.title('Comparing summary statistics: 2015 vs 2016', y = 1.07)
plt.ylim(0,5.5)
plt.yticks(arange(0,5.1,.5))
plt.ylabel('Stars')
plt.legend(framealpha = 0, loc = 'upper center')
plt.show()

The mean rating was lower in 2016 with approximately 0.2. This means a drop of almost 5% relative to the mean rating in 2015.

1
2
(summary.loc['mean'][0] - summary.loc['mean'][1]) / summary.loc['mean'][0]


1
2
0.048426835689519929

While the median is the same for both distributions, the mode is lower in 2016 by 0.5. Coupled with what we saw for the mean, the direction of the change we saw on the kernel density plot is confirmed: on average, popular movies released in 2016 were rated slightly lower than popular movies released in 2015.

Our analysis showed that there’s indeed a slight difference between Fandango’s ratings for popular movies in 2015 and Fandango’s ratings for popular movies in 2016. We also determined that, on average, popular movies released in 2016 were rated lower on Fandango than popular movies released in 2015.

We cannot be completely sure what caused the change, but the chances are very high that it was caused by Fandango fixing the biased rating system after Hickey’s analysis.