IB Math IA: Does Pitchfork Influence An Artist's Popularity?

 This is my Internal Assessment (IA) for IB Math Studies, which I completed in senior year as part of my IB Diploma.  I wrote it on the correlation between Pitchfork reviews and artist popularity.  Though I'm not sure of the final IB grade, my IA received a 7 (A+) from my teacher.  IB students, feel free to use this as a reference.

Does Pitchfork Influence An Artist’s Popularity?

Statement of Task

Pitchfork.com is an American music website featuring primarily album reviews, covering chiefly the musical genres of rock, hip-hop, electronic, and experimental music.  Pitchfork’s reviewers rate albums on a scale of 10, with 10.0 being the highest possible rating and 0.0 being the lowest.  As Pitchfork is one of the most widely read English-language websites focusing on underground and “indie” music, many formerly obscure artists have gained wider audiences as a result of high album ratings from that site, while others have faded from the popular musical consciousness due to lower ratings from the site.  Due to the wide number of possible ratings (100 possible decimal scores can be given), few artists receive the same rating for two albums in a row.  

In my IB Math Studies project, I will attempt to determine whether or not a decrease or increase between two Pitchfork ratings for two consecutive albums in an artist’s oeuvre corresponds to a drop or increase in the artist’s popularity.  I have chosen only albums released at least a year before December 1, 2011, based on the common put-down “that’s so last year,” which indicates the general tenuousness of musical success and that an artist’s popularity may wane simply due to the passing of time.

I will select 20 bands/artists that have released two consecutive albums that were reviewed on Pitchfork--eight bands/artists whose Pitchfork ratings for two consecutive albums decreased, eight bands/artists whose Pitchfork ratings for two consecutive albums increased, and four bands/artists whose Pitchfork ratings stayed the same.  I will not include mixtapes (albums usually given away for free online that generally contain uncopyrighted covers/samples and thus cannot be sold for profit) or EPs (short albums, usually between 10 and 30 minutes long), as they are generally not as popular as albums.  For reasons that will be discussed, I also include only those albums that are available on iTunes.

I selected these albums based on a shuffle through the “Stuff Hipsters Like” playlist I created on iTunes.  (There is a stereotype that the musical taste of the subculture known as “hipsters,” who tend to appreciate the underground music Pitchfork champions, is dictated solely by Pitchfork reviews.)  My methodology required I exclude artists who have released only one album.  However, I manually selected four artists who have received the same Pitchfork rating for two albums--Deerhunter (9.2-9.2), Ghostland Observatory (1.5-1.5), LCD Soundsystem (9.2-9.2), and MGMT (6.8-6.8).

To determine the popularity of an album, I will rely on iTunes “likes,” the number of iTunes reviews, and the number of YouTube views for the album's most-viewed track (divided by 1,000, as the YouTube videos I used generally have view counts that dwarf the numbers of iTunes likes or reviews)--all divided by the number of days the album has been in the public consciousness (more on this below).  This will give me a number I will refer to as the “popularity coefficient.”  I will then compare the differences in the popularity coefficients of the two albums with the differences in the Pitchfork ratings they received.  I will then use the Spearman’s Rank Correlation Coefficient test to determine whether or not there is a correlation between the differences in popularity coefficients and the differences in Pitchfork ratings for albums.

Data Collection:

PROCESSED DATA

Artist	Difference in Pitchfork rating	Album 1 pop. coefficient	Album 2 pop. coefficient	Percent increase
AIR	-2.6	0.155	0.298	92.26%
Antony & the Johnsons	-0.9	0.872	1.532	75.69%
Blonde Redhead	-3.0	3.938	3.050	-32.79%
Califone	-0.6	1.215	0.307	-395.8%
jj	-3.2	0.506	0.461	-9.761%
M.I.A.	-4.5	17.81	13.18	-35.13%
No Age	-0.4	1.646	0.947	-43.47%
Vampire Weekend	-0.2	29.34	19.99	-46.77%
Deerhunter	0.0	1.428	6.396	447.9%
Ghostland Observatory	0.0	0.121	0.781	645.5%
MGMT	0.0	32.13	11.40	-281.8%
LCD Soundsystem	0.0	2.435	4.722	93.92%
Beach House	0.5	1.183	4.198	354.9%
Crystal Castles	0.7	9.962	19.63	97.05%
F*** Buttons	0.4	0.517	0.414	-24.88%
Charlotte Gainsbourg	2.6	0.643	1.516	235.8%
Grizzly Bear	0.3	4.701	12.85	273.3%
Titus Andronicus	0.2	0.165	1.229	744.8%
Wavves	0.3	0.878	2.249	256.2%
Kanye West	2.6	63.00	170.5	270.6%

The table above represents the artists and albums I use in this project, the difference between the Pitchfork ratings they received for two consecutive albums, and their popularity coefficients (calculations below).  The difference in popularity coefficients will be represented as a percent increase or decrease.

I determined the “popularity” coefficients shown on the preceding table using the following formula: 

(#Album reviews on iTunes + #iTunes “likes” + #YouTube views for most popular song from that album / 1000) / number of days since release

I chose to use iTunes because it is one of the world’s most popular methods of purchasing and downloading music, and YouTube because it is one of the most popular sites for listening to music free of charge.  Since albums’ lead singles are often posted to YouTube several weeks or even months before album releases, and since albums will sometimes disappear from iTunes and reappear (or be released after their initial release on CD or vinyl), I will use the variable t  to represent whichever is longer: the time since posting of the most popular song on YouTube or the time since the album was released on iTunes.  This accounts for albums that may fade momentarily only to be revived in popularity based on the sudden popularity of a single, such as M.I.A.’s Kala, whose most popular single “Paper Planes” became a massive hit after its use in the film Pineapple Express, which occurred several months after the release of the actual album.

I converted the differences between popularity coefficients into percent increases or percent decreases so all numbers could be evaluated equally.  

Data Analysis

To determine whether or not a correlation exists between the difference in Pitchfork ratings for two consecutive albums and the difference in those albums’ popularity coefficients, I calculated the Spearman’s Rank correlation coefficient using the data shown on the table below. 

Column A: artist name.  Column B: percent change in popularity coefficient/100.  Column C: Ranking of change in popularity coefficient from least to greatest.  Column D: change in Pitchfork rating.  Column E: Ranking of change in Pitchfork rating from least to greatest.  Column F: C-E.  Column G: F squared.

The table above shows my process for finding the Spearman’s Rank correlation coefficient for the two sets of data.  On this table, artists are ranked in ascending order by the size of the differences between the popularity coefficients of two consecutive albums with Titus Andronicus’s 744.8% increase (from The Airing Of Grievances to The Monitor) at the top and Califone’s -395.8% decrease (from Roots & Crowns to All My Friends Are Funeral Singers) at the bottom.  

To determine the coefficient, I ranked each difference in Pitchfork rating by size in the same way I ranked the differences in popularity coefficients.  I then found the differences between the rankings of the two, squared them, and added together the squares.  I then plugged the sum of the squares into the equation below to find the coefficient, as shown below:

or R = 1 - 6(719)/7980

The coefficient I obtained was 0.459.  This is a fairly weak correlation, though not so weak as to be negligible.  This suggests that while the Pitchfork ratings an artist receives may have an effect on their popularity, it is by no means sole cause.

From the table above, it can be observed that the artists whose popularity coefficients decreased from one album to the next tend to have had their Pitchfork ratings decrease as well, and vice-versa.  Of the eight artists whose popularity coefficients decreased, six suffered a decrease in their Pitchfork ratings, while one had the same Pitchfork rating for two consecutive albums and the other saw an increase in Pitchfork rating.  Of the twelve artists observed whose popularity coefficients increased, seven of them also saw an increase in their Pitchfork ratings, three of them did not see any change in their Pitchfork ratings, and two saw a decrease.  This gives credence to the existence of a correlation.

There is, however, an unusual anomaly with albums that saw no change in Pitchfork rating from one album to the next.  I studied four such artists: Deerhunter, Ghostland Observatory, LCD Soundsystem, and MGMT.  The former three artists experienced an increase in their popularity coefficients from one album to the next, while the latter experienced a decrease.  Of these artists, LCD Soundsystem experienced the smallest change in popularity: a relatively small increase of 93.92% from Sound of Silver to This Is Happening.  However, Deerhunter saw an increase of 447.9%, the third-highest increase observed among these albums, and Ghostland Observatory saw an increase of 645.5%, the second-highest increase observed.  

Though I started this project suspecting there might be some correlation, I did not expect a strong correlation.  Though Pitchfork has a reputation as one of the biggest tastemakers in American music media, it is by no means the only means by which the American population comes to know artists and make purchasing decisions.  (If that were true, perfect-10 recipients like Neutral Milk Hotel and ...And You Will Know Us By The Trail Of Dead would be more popular than Beyoncé, whose multi-platinum album I Am Sasha Fierce received a lukewarm 5.7.)

Conclusion & Evaluation

A number of factors may have affected the validity of my results.  It was extremely difficult for me to find a formula that would serve as an effective numerical proxy for an album’s popularity.  While it would be ideal to use the number of copies of an album sold, or even the album’s peak Billboard chart position, many of the artists I examined are relatively obscure, making it difficult if not impossible to find the number of copies sold (I also doubt many of these albums cracked the charts).  The formula I used was moderately effective, but it did not take into account an album’s popularity over time. 

 Albums generally tend to sell the most copies in their first month or so, and as my formula measured an album’s popularity from the time it was released to the time the data was collected, trends over time were not taken into account (e.g., MGMT, whose album Congratulations topped the charts upon its release but saw a subsequent plummet in popularity due to severe fan and critical backlash).  This is exacerbated by the step in my formula in which everything is divided by the number of days since an album’s release: if an artist were to hypothetically release two albums a year apart that both sold a consistent number of copies every day since their release dates, the division by number of days since the album’s release would result in the data indicating that the first album is considerably less popular.  (This may explain why most of the artists who saw no change in Pitchfork rating for two consecutive albums had much higher popularity coefficients for their second albums than their first albums.)

My study was also limited by my use of iTunes.  While iTunes is very popular, many people purchase albums from record stores, and these purchases were not taken into account in my study.  Many more people, however, do not even buy albums but rather download them for free from the Internet.  The number of people who download albums from the Internet is impossible to count, as many free download sites exist and few of them keep a record of the number of downloads.

In addition, the sample size could have been larger--Pitchfork reviews hundreds of albums a year, and the twenty artists and forty albums I use in this project only make up a small portion of the total artists and albums that have been reviewed by the site.  Had I devoted more study to artists who received the same Pitchfork rating for two albums in a row, I could have further examined the effectiveness of my formula over time and possibly found further evidence in favor of the correlation’s validity or lack thereof.  

APPENDIX

Pitchfork ratings received by albums:

Artist	Rating for album 1	Rating for album 2
AIR	Pocket Symphony 6.6	Love 2 4.0
No Age	Nouns 9.2	Everything In Between 8.8
jj	jj n. 2 8.6	jj n. 3 5.4
Blonde Redhead	23 7.0	Penny Sparkle 4.0
M.I.A.	Kala 8.9	MAYA 4.4
Antony & the Johnsons	The Crying Light 8.6	Swanlights 7.7
Vampire Weekend	Vampire Weekend 8.8	Contra 8.6
Califone	Roots & Crowns 8.7	All My Friends Are Funeral Singers 8.1
Deerhunter	Microcastle 9.2	Halcyon Digest 9.2
LCD Soundsystem	Sound Of Sliver 9.2	This Is Happening 9.2
MGMT	Oracular Spectacular 6.8	Congratulations 6.8
Ghostland Observatory	Robotique Majestique 1.5	Codename: Rondo 1.5
Charlotte Gainsbourg	5:55 5.8	IRM 8.4
Grizzly Bear	Yellow House 8.7	Veckatimest 9.0
Wavves	Wavves 8.1	King Of The Beach 8.4
F*** Buttons	Street Horrsing 8.6	Tarot Sport 9.0
Kanye West	808s & Heartbreak 7.6	My Beautiful Dark Twisted Fantasy 10.0
Beach House	Devotion 8.5	Teen Dream 9.0
Crystal Castles	Crystal Castles 7.8	Crystal Castles 2 8.5
Titus Andronicus	The Airing Of Grievances 8.5	The Monitor 8.7

View count and release date for most viewed YouTube video for Album 1 for each artist:

Artist	Album 1	Most Popular Song (by YT views as of 12/1/11)	Views	Released
AIR	Pocket Symphony 6.6	“Once Upon A Time”	242,020	3/5/07
No Age	Nouns 9.2	“Eraser”	191,089	10/29/09
jj	jj n. 2 8.6	“Things Will Never Be The Same Again”	325,749	7/11/09
Blonde Redhead	23 7.0	“23”	1,384,708	4/7/07
M.I.A.	Kala 8.9	“Paper Planes”	19,918,671	6/16/09
Antony & the Johnsons	The Crying Light 8.6	“Another World”	364,327	10/6/08
Vampire Weekend	Vampire Weekend 8.8	“A Punk”	19,516,752	1/7/08
Califone	Roots & Crowns 8.7	“The Eye You Lost In The Crusades”	31,070	9/25/07
Deerhunter	Microcastle 9.2	“Agoraphobia”	677,481	9/18/08
LCD Soundsystem	Sound Of Sliver 9.2	“All My Friends”	1,971,995	5/2/07
MGMT	Oracular Spectacular 6.8	“Kids”	41,638,285	10/2/07
Ghostland Observatory	Robotique Majestique 1.5	“The Band Marches On”	92,302	12/24/08
Charlotte Gainsbourg	5:55 5.8	“5.55”	550,318	4/24/07
Grizzly Bear	Yellow House 8.7	“Knife”	2,410,077	2/8/07
Wavves	Wavves 8.1	“No Hope Kids”	542,583	6/29/09
F*** Buttons	Street Horrsing 8.6	“Bright Tomorrow”	268,037	12/13/07
Kanye West	808s & Heartbreak 7.6	“Heartless”	60,070,156	6/16/09
Beach House	Devotion 8.5	“Heart of Chambers”	1,184,799	2/26/08
Crystal Castles	Crystal Castles 7.8	“Crimewave”	8,587,035	3/18/08
Titus Andronicus	The Airing Of Grievances 8.5	“Arms Against Atrophy”	80,471	2/7/2007

View count and release date for most viewed YouTube video for Album 2 for each artist:

Artist	Album 1	Most Popular Song (by YT views as of 12/1/11)	Views	Released
AIR	Love 2 4.0	“Love”	212,332	10/5/09
No Age	Everything In Between 8.8	“Fever Dreaming”	150,993	1/26/11
jj	jj n. 3 5.4	“My Life”	281,527	2/10/10
Blonde Redhead	Penny Sparkle 4.0	“Here Sometimes (4AD Session)”	1,202,589	8/24/10
M.I.A.	MAYA 4.4	“XXXO”	5,507,949	8/11/10
Antony & the Johnsons	Swanlights 7.7	“Thank You For Your Love”	586,862	8/20/10
Vampire Weekend	Contra 8.6	“Cousins”	8,655,477	10/19/09
Califone	All My Friends Are Funeral Singers 8.1	“Funeral Singers”	58,592	10/5/2009
Deerhunter	Halcyon Digest 9.2	“Helicopter”	892,710	9/3/10
LCD Soundsystem	This Is Happening 9.2	“Drunk Girls”	1,905,370	4/16/10
MGMT	Congratulations 6.8	“Flash Delirium”	3,050,900	3/26/10
Ghostland Observatory	Codename: Rondo 1.5	“Give Me The Beat”	116,093	10/7/10
Charlotte Gainsbourg	IRM 8.4	“Heaven Can Wait”	667,601	12/07/09
Grizzly Bear	Veckatimest 9.0	“Two Weeks”	5,446,100	5/23/09
Wavves	King Of The Beach 8.4	“King Of The Beach”	554,635	6/29/10
F*** Buttons	Tarot Sport 9.0	“The Lisbon Maru”	147,259	9/21/09
Kanye West	My Beautiful Dark Twisted Fantasy 10.0	“All Of The Lights”	58,765,002	2/18/11
Beach House	Teen Dream 9.0	“Zebra”	1,125,156	11/25/09
Crystal Castles	Crystal Castles 2 8.5	“Not In Love”	6,152,950	4/23/2010
Titus Andronicus	The Monitor 8.7	“A More Perfect Union”	457,147	3/29/10

Calculation of popularity coefficients:

ALBUMS

Air: Pocket Symphony

(25 + 1 + 242.0)/ 1732= 0.155

Air: Love 2

(21 + 1 + 212.3) / 787= 0.298

No Age: Nouns

(1032 + 33 + 191.1)/ 1304= 1.646

No Age: Everything In Between

(250 + 6 + 151.0)/ 430= 0.947

jj: jj n. 2

(111 + 5 + 325.7)/ 873= 0.506

jj: jj n. 3

(188 + 14 + 281.5)/ 659= 0.461

Blonde Redhead: 23

(5204 + 103 + 1384)/ 1699 = 3.938

Blonde Redhead: Penny Sparkle

(251 + 23 + 1202)/ 484 = 3.050

M.I.A.: Kala

(6402 + 1511 + 19919)/ 1563= 17.81

M.I.A.: MAYA

(397 + 384 + 5508)/ 477= 13.18

Antony & the Johnsons: The Crying Light

(602 + 37 + 364.3)/ 1151 = 0.872

Antony & the Johnsons: Swanlights

(125 + 5 + 586.9)/ 468= 1.532

Vampire Weekend - Vampire Weekend

(21271 + 994 + 19516)/ 1424= 29.34

Vampire Weekend - Contra

(6171 + 626 + 8655)/ 773= 19.99

Califone - Roots & Crowns

(1809 + 17 + 31.07)/ 1528 = 1.215

Califone - All My Friends Are Funeral Singers

(176 + 7 + 58.59)/ 787= 0.307

Deerhunter: Microcastle

(944 + 48 + 677.5)/1169= 1.428

Deerhunter: Halcyon Digest

(1968 + 48 + 892.7)/454= 6.396

LCD Soundsystem: Sound Of Silver

(2219 + 9 + 1972)/1725= 2.435

LCD Soundsystem: This Is Happening

(867 + 33 + 1905)/594= 4.722

MGMT: Oracular Spectacular

(6386 + 841 + 41638)/ 1521= 32.13

MGMT: Congratulations

(3128 + 831 + 3050)/ 615= 11.40

Ghostland Observatory: Robotique Majestique

(35 + 2 + 92.30)/ 1072= 0.121

Ghostland Observatory: Codename: Rondo

(171 + 41 + 116.1)/ 420= 0.781

Charlotte Gainsbourg: 5:55

(495 + 37 + 550.3)/ 1682= 0.643

Charlotte Gainsbourg: IRM

(405 + 25 + 667.6)/ 724= 1.516

Grizzly Bear: Yellow House

(6527 + 61 + 2410)/1914= 4.701

Grizzly Bear: Veckatimest

(6210 + 189 + 5446)/922= 12.85

Wavves: Wavvves

(263 + 87 + 542.6)/1017= 0.878

Wavves: King Of The Beach

(595 + 50 + 544.6)/ 529 = 2.249

F*** Buttons: Street Horrrsing

(251 + 41 + 268.0) / 1083 = 0.517

F*** Buttons: Tarot Sport

(169 + 15 + 147.3) / 801 = 0.414

Kanye West: 808s & Heartbreak

(5188 + 6125 + 60070) / 1133 = 63.00

Kanye West: My Beautiful Dark Twisted Fantasy

(8286 + 2000 + 58765) / 405 = 170.5

Beach House: Devotion

(413 + 27 + 1185) / 1374 = 1.183  0.575334143

Beach House: Teen Dream

(1814 + 151 + 1125) / 736 = 4.198

Crystal Castles: Crystal Castles

(4639 + 252 + 8587) / 1353 = 9.962

Crystal Castles: Crystal Castles II

(5156 + 212 + 6153) / 587 = 19.63

Titus Andronicus: The Airing Of Grievances

(90 + 16 + 80.47) / 1129 = 0.165

Titus Andronicus: The Monitor

(266 + 29 + 457.1) / 612 = 1.229