Analyzing Rudy Gay Trades Using the CausalImpact Package

Introduction

I have been meaning to learn more about time-series and Bayesian methods; I'm pumped for a Bayesian class that I'll be in this coming semester. RStudio blogged about the CausalImpact package back in April—a Bayesian time-series package from folks at Google—and I've been meaning to play around with it ever since. There's a great talk posted on YouTube that is a very intuitive description of thinking about causal impact in terms of counterfactuals and the CausalImpact package itself. I decided I would use it to put some common wisdom to the test: Do NBA teams get better after getting rid of Rudy Gay? I remember a lot of chatter on podcasts and on NBA Twitter after he was traded from both the Grizzlies and the Raptors.

Method

I went back to the well and scraped Basketball-Reference using the rvest package. Looking at the teams that traded Gay mid-season, I fetched all the data from the “Schedule & Results” page and from that I calculated a point differential for every game: Positive numbers meant the team with Rudy Gay won the game by that many points, while negative numbers meant they lost by that many points. I ran the CausalImpact model with no covariates or anything: I just looked at point differential over time. I did this separately for the Grizzlies 2012-2013 season and the Raptors 2013-2014 season (both teams traded Rudy mid-season). The pre-treatment sections are before the team traded Gay; the post-treatment sections are after the team traded Gay.

Code for scraping, analyses, and plotting can be accessed over at GitHub.

Results

The package is pretty nice. The output is easy to read and interpret, and they even include little write-ups for you if you specify summary(model, "report"), where model is the name of the model you fit with the CausalImpact function. Let's take a look at the Grizzlies first.

	Actual	Predicted	Difference	95% LB	95% UB
Average	4.4	3.6	0.82	-5	6.6
Cumulative	167.0	135.8	31.22	-190	252.5

The table shows the average and cumulative point differentials. On average, the Grizzlies scored 4.4 points more than their opponent per game after Rudy Gay was traded. Based on what the model learned from when Gay was on the team, we would have predicted this to be 3.6. Their total point differential was 167 after Rudy Gay was traded, when we would have expected about 136. The table also shows the differences: 0.82 and 31.22 points for average and cumulative, respectively. The lower bound and upper bound at a 95% confidence interval fell on far opposite sides of zero, suggesting that the difference is not likely to be different from zero. The posterior probability here of a causal effect (i.e., the probability that this increase was due to Gay leaving the team) is 61%—not a very compelling number. The report generated from the package is rather frequentist—it uses classical null hypothesis significance testing language, saying the model “would generally not be considered statistically significant” with a p-value of 0.387. Interesting.

What I really dig about this package are the plots it gives you. This package is based on the idea that it models a counterfactual: What would the team have done had Rudy Gay not been traded? It then compares this predicted counterfactual to what actually happened. Let's look at the plots:

The top figure shows a horizontal dotted line, which is what is predicted given what we know about the team before Gay was traded. I haven't specified any seasonal trends or other predictors, so this line is flat. The black line is what is actually happened. The vertical dotted line is where Rudy Gay was traded. The middle figure shows the difference between predicted and observed. We can see that there is no reliable difference between the two after the Gay trade. Lastly, the bottom figure shows the cumulative difference (that is, adding up all of the differences between observed and predicted over time). Again, this is hovering around zero, showing us that there was really no difference in the Grizzlies point differential that actually occurred and what we predicted would have happened had Gay not been traded (i.e., the counterfactual). What about the Raptors?

The Raptors unloaded Gay to the Kings the very next season. Let's take a look at the same table and plot for the Raptors and trading Rudy:

	Actual	Predicted	Difference	95% LB	95% UB
Average	4.4	-0.37	4.8	-0.88	10
Cumulative	279.0	-23.22	302.2	-55.59	657

The posterior probability of a causal effect here was 95.33%—something that is much more likely than the Grizzlies example. The effect was more than five times bigger than it was for Memphis: There was a difference of 4.8 points per game (or 302 cumulatively) between what we observed and what we would have expected had the Raptors never traded Gay. Given that this effect was one (at the time, above average) player leaving a team is pretty interesting. I'm sure any team would be happy with getting almost 5 whole points better per game after getting rid of a big salary.

Conclusion

It looks like trading Rudy Gay likely had no effect on the Grizzlies, but it does seem that getting rid of him had a positive effect on the Raptors. The CausalImpact package is very user-friendly, and there are many good materials out there for understanding and interpreting the model and what's going on underneath the hood. Most of the examples I have seen are simulated data or data which are easily interpretable, so it was good practice seeing what a real, noisy dataset actually looks like.

Quantifying "Low-Brow" and "High-Brow" Films

I went and saw Certain Women a few months ago. I was pretty excited to see it; a blurb in the trailer calls it “Triumphant… an indelible portrait of independent women,” which sounds pretty solid to me. The film had a solid point in that it exposed the mundane, everyday ways in which women have to confront sexism. It isn't always a huge dramatic thing that is obvious to everyone—instead, most of the time sexism is commonplace and woven into the routine of our society.

The only problem is that I found the movie, well, pretty boring. Showing how quotidian sexism is in a film makes for a slow-paced, quotidian plot. A few days ago, I happened upon the Rotten Tomatoes entry for the movie. It scored very well with critics (92% liked it), but rather poorly with audiences (52%). It made me think of the divisions between critics and audiences; I thought that the biggest differences between audience and critic scores could be an interesting way to quantify what is “high-brow” and what is “low-brow” film. So what I did was got critic and audience scores for movies in 2016, plotted them against one another, and looked at where they differed most.

Method

The movies I chose to examine were all listed on the 2016 in film Wikipedia page. The problem was I needed links to Rotten Tomatoes pages, not just names of movies. So, I scraped this table, took the names of the films, and I turned them into Google search URLs by taking "https://google.com/search?q=rottentomatoes+2016+" and using paste0 to add the name of the film at the end of the string. Then, I wrote a little function (using rvest and magrittr) that takes this Google search URL and fetches me the URL for the first result of a Google search:

# function for getting first hit from google page
getGoogleFirst <- function(url) {
  url %>% 
    read_html() %>% 
    html_node(".g:nth-child(1) .r a") %>% 
    html_attr("href") %>% 
    strsplit(split="=") %>% 
    getElement(1) %>% 
    strsplit(split="&") %>% 
    getElement(2) %>% 
    getElement(1)
}

After running this through a loop, I got long vector of Rotten Tomatoes links. Then, I fed them into two functions that gets critic and audience scores:

# get rotten tomatoes critic score
rtCritic <- function(url) {
  url %>% 
    read_html() %>% 
    html_node("#tomato_meter_link .superPageFontColor") %>% 
    html_text() %>% 
    strsplit(split="%") %>% 
    as.numeric()
}

# get rotten tomatoes audience score
rtAudience <- function(url) {
  url %>% 
    read_html() %>% 
    html_node(".meter-value .superPageFontColor") %>% 
    html_text() %>% 
    strsplit(split="%") %>% 
    as.numeric()
}

The film names and scores were all put into a data frame.

Results

Overall, I collected data on 224 films. The average critic score was 56.74, while the average audience score was 58.67; while audiences tended to be more positive, this difference was small, 1.93, and not statistically significant, ,t(223) = 1.34, p = .181. Audiences and critics tended to agree; scores between the two groups correlated strongly, r = .68.

But where do audiences and critics disagree most? I calculated a difference score by taking critic - audience scores, such that positive scores meant critics liked the film more than audiences. The five biggest difference scores in both the positive and negative direction are found in the table below.

“High-Brow” Films

Film	Critic	Audience	Difference
The Monkey King 2	100	49	51
Hail, Caesar!	86	44	42
Little Sister	96	54	42
The Monster	78	39	39
The Witch	91	56	35
Into the Forest	77	42	35

“Low-Brow” Films

Film	Critic	Audience	Difference
Hillary's America: The Secret History of the Democratic Party	4	81	-77
The River Thief	0	69	-69
I'm Not Ashamed	22	84	-62
Meet the Blacks	13	74	-61
God's Not Dead 2	9	63	-54

Interactive Plot

Below is a scatterplot of the two scores with a regression line plotted. The dots in blue are those films in the tables above. You can hover over any dot to see the film it represents as well as the audience and critic scores:

I won't do too much interpreting of the results—you can see for yourself where the movies fall by hovering over the dots. But I would be remiss if I didn't point out the largest difference score was an anti-Hillary Clinton movie: 4% of critics liked it, but somehow 81% of the audience did. Given all of the evidence that pro-Trump bots were all over the Internet in the run-up to the 2016 U.S. presidential election, I would not be surprised if many of these audience votes were bots?

Apparently I'm a low-brow plebian; I did not see any of the five most “high-brow” movies, according to the metric. Both critics and audiences seemed to love Hidden Figures (saw it, and it was awesome) and Zootopia (still haven't seen it).

Let me know what you think of this “low-brow/high-brow” metric or better ways one could quantify the construct.

Sentiment Analysis of Kanye West's Discography

Introduction

Last time, I did some basic frequency analyses of Kanye West lyrics. I've been using the tidytext package at work a lot recently, and I thought I would apply some of the package's sentiment dictionaries to the Kanye West corpus I have already made (discussed here). The corpus is not big enough to do the analyses by song or by a very specific emotion (such as joy), so I will stick to tracking positive and negative sentiment of Kanye's lyrical content over the course of his career.

Method

For each song, I removed duplicate words (for reasons like so that the song “Amazing” doesn't have an undue influence on the analyses, given that he says “amazing"—a positive word—about 50 times). I allowed duplicate words from the same album, but not from the same song.

The tidytext package includes three different sentiment analysis dictionaries. One of the dictionaries assigns each word a score from -5 (very negative) to +5 (very positive). Using this dictionary, I simply took the average score for the album:

afinn <- kanye %>% # starting with full data set
  unnest_tokens(word, lyrics) %>% # what was long string of text, now becomes one word per row
  inner_join(get_sentiments("afinn"), by="word") %>% # joining sentiments with these words
  group_by(song) %>%  # grouping dataset by song
  subset(!duplicated(word)) %>% # dropping duplicates (by song, since we are grouped by song)
  ungroup() %>% # ungrouping real quick...
  group_by(album) %>% # and now grouping by album
  mutate(sentiment=mean(score)) %>%  # getting mean by album
  slice(1) %>% # taking one row per every album
  ungroup() %>% # ungrouping
  subset(select=c(album,sentiment)) # only including the album and sentiment columns

The other two dictionaries tag each word as negative or positive. For these, I tallied up how many positive and negative words were being used per album and subtracted the negative count from the positive count:

bing <- kanye %>% # taking data set
  unnest_tokens(word, lyrics) %>% # making long list of lyrics into one word per row
  inner_join(get_sentiments("bing"), by="word") %>% # joining words with sentiment
  group_by(song) %>% # grouping by song
  subset(!duplicated(word)) %>% # getting rid of duplicated words (within each song)
  ungroup() %>% # ungrouping
  count(album, sentiment) %>% # counting up negative and positive sentiments per album
  spread(sentiment, n, fill=0) %>% # putting negative and positive into different columns
  mutate(sentiment=positive-negative) # subtracting negative from positive

# all of this is same as above, but with a different dictionary
nrc <- kanye %>% 
  unnest_tokens(word, lyrics) %>% 
  inner_join(get_sentiments("nrc"), by="word") %>%
  group_by(song) %>% 
  subset(!duplicated(word)) %>% 
  ungroup() %>% 
  count(album, sentiment) %>%
  spread(sentiment, n, fill=0) %>% 
  mutate(sentiment=positive-negative)

I then merged all these data frames together, standardized the sentiment scores, and averaged the three z-scores together to get an overall sentiment rating for each album:

colnames(afinn)[2] <- "sentiment_afinn" # renaming column will make it easier upon joining

bing <- ungroup(subset(bing, select=c(album,sentiment))) # getting rid of unnecessary columns
colnames(bing)[2] <- "sentiment_bing"

nrc <- ungroup(subset(nrc, select=c(album,sentiment)))
colnames(nrc)[2] <- "sentiment_nrc"

suppressMessages(library(plyr)) # getting plyr temporarily because I like join_all()
album_sent <- join_all(list(afinn, bing, nrc), by="album") # joining all three datasets by album
suppressMessages(detach("package:plyr")) # getting rid of plyr, because it gets in the way of dplyr

# creating composite sentiment score:
album_sent$sent <- (scale(album_sent$sentiment_afinn) + 
                    scale(album_sent$sentiment_bing) + 
                    scale(album_sent$sentiment_nrc))/3
album_sent <- album_sent[-7,c(1,5)] # subsetting data to not include watch throne and only include composite
# reordering the albums in chronological order
album_sent$album <- factor(album_sent$album, levels=levels(album_sent$album)[c(2,4,3,1,5,7,8,6)])

Results

And then I plotted the sentiment scores by album, in chronological order. Higher scores represent more positive lyrics:

ggplot(album_sent, aes(x=album, y=sent))+
  geom_point()+
  geom_line(group=1, linetype="longdash", size=.8, alpha=.5)+
  labs(x="Album", y="Sentiment")+
  theme_fivethirtyeight()+
  scale_x_discrete(labels=c("The College Dropout", "Late Registration", "Graduation",
                            "808s & Heartbreak", "MBDTF", "Yeezus", "The Life of Pablo"))+
  theme(axis.text.x=element_text(angle=45, hjust=1),
        text = element_text(size=12))

Looks like a drop in happiness after his mother passed as well as after starting to date Kim Kardashian…

This plot jibes with what we know: 808s is the "sad” album. Graduation—with all the talk about achievement, being strong, making hit records, and having a big ego—peaks at the album with the most positive words. This plot seems to lend some validity to the method of analyzing sentiments using all three dictionaries from the tidytext package.

Some issues with this “bag-of-words” approach, however, was that it was prone to error in the finer level of analysis, like song. “Street Lights,” perhaps one of Kanye's saddest songs, came out with one of the most positive scores. Why? It was reading words like “fair” as positive, neglecting to realize that a negation word (i.e., “not”) always preceded it. One could get around this with maybe n-grams or natural language processing.

Nevertheless, there's the trajectory of Kanye's lyrical positivity over time!