Every week a new set of charts is released by Billboard, encompassing what’s hot in music right now across all music media (the radio, streaming on digital sources, and physical sales). This chart encompasses data from around the world for every major genre. Is it possible to devise an equation that could predict chart placement?
First, we need to know some information on what we want to do. Our goal is to get into the Top 20 range, since that is considered the best place to be on the charts besides number one. According to Billboard, about 50 albums are released a week, or 200 in a month. We can assume that every 10 in these 200 is a collection album (‘Best of _______’ is an example), so we can slim that figure down to 190 albums. If each of these albums releases two songs as singles per month, then there are 280 original songs vying for 20 spots during that month, or a 7.1% chance of getting on that month’s chart. These are somewhat slim odds at first – 7 in 100. However, there is more here to consider in chart placement.
Sales. It’s all about the sales. Let’s say we have twenty music acts being sold at one store (I’m going to use various groups and musicians here).
Music Act
Single
The Beatles
“Can’t Buy Me Love”
Diana Ross
“It’s Your Move”
a-ha
“Take on Me”
Klaatu
“A Routine Day”
Pink Floyd
“Another Brick in the Wall (Part 2)”
Justin Bieber
“Sorry”
David Bowie
“Space Oddity”
Eminem
“Lose Yourself”
Oasis
“Wonderwall”
Nirvana
“Smells Like Teen Spirit”
Lemon Demon
“Ultimate Showdown (of Ultimate Destiny)”
Elvis Presley
“Blue Suede Shoes”
The Buggles
“Video Killed the Radio Star”
Lady Gaga
“Bad Romance”
Bruno Mars
“24k Magic”
Drake
“Hotline Bling”
AC/DC
“TNT”
Eric Clapton
“Layla”
Metallica
“Enter Sandman”
Weird Al Yankovic
“I Lost on Jeopardy”
Now, Billboard charting does affect sales, as someone is going to be more familiar with a song they’ve heard on the radio than an independent or little known group unless they get a boost in popularity. However, sales also affect Billboard chart placement, so you can’t get up there unless you sell some music first. So that creates the first part of our equation, which is just s=p, where s represents store sales and p equals placement. Now, let’s assume that after the first week sales come in. These sales can be based off of many variables, such as popularity of the group. We’ll assume that each group’s popularity here is based off a random number between 1 and 100, with 1 being really popular and 100 being really unknown, since it’s hard to determine the popularity of a musician. Let’s say that the store has 150 of each record and divide by 20 (the number of bands listed, since one usually buys more than one record at a store). Popularity is converted with the highest number being a 20 (which is #1, AC/DC) and the lowest (in this case, a-ha at #93) being a 1.
Music Act (Popularity)
Popularity Ranking
Sales (r*150/20)
The Beatles (38)
13
98
Diana Ross (39)
12
90
a-ha (93)
1
8
Klaatu (19)
17
128
Pink Floyd (42)
11
83
Justin Bieber (30)
15
113
David Bowie (92)
2
15
Eminem (83)
4
30
Oasis (58)
8
60
Nirvana (60)
7
53
Lemon Demon (55)
10
75
Elvis Presley (57)
9
68
The Buggles (27)
16
120
Lady Gaga (65)
5
38
Bruno Mars (6)
18
135
Drake (3)
19
143
AC/DC (1)
20
150
Eric Clapton (35)
14
105
Metallica (90)
3
23
Weird Al Yankovic (64)
6
45
All in all, the week’s winner at this store for sheer popularity was AC/DC, selling out. In some cases, sales alone help the song get onto the charts (especially in this day in age with Spotify and YouTube). Now, if we consider ten stores in the area (as Billboard originally did early on), we get sales ranging from 80 to 1500. This is good and all, but it’s just not enough.
Let’s move onto radio play. The more popular an act is, the more radio play they get. This variable will be r in our equation, which is now s*r=p. The more you’re heard on the radio, the more sales you get. Now, let’s say sales increase by half the original total (s in the table above times .5, then added) every time a song is heard on the radio, because if one person hears the song and goes “huh, I really like it”, then they will go out and buy it. If you hear AC/DC’s “TNT” once on the radio, then their weekly sales go up from 150 to 225 sales per store. If a song is as popular as “TNT” is, though, it’s going to be played more than once; it’ll probably be played twice a day (once during morning traffic, once during rush hour traffic jams). Going by this, we can conclude that the song is being played 14 times a week. Each time adds 75 copies. For the sake of the equation, however, we’ll set it to 20 times, since there’s those odd times in the middle of the night)
Times Played on Radio
Original Sales + 75x (half of sales at one store times how many times said song is played)
Total Sales
0
150+0
150
1
150+75
225
2
150+150
300
3
150+225
375
4
150+300
450
5
150+375
525
6
150+450
600
7
150+525
675
8
150+600
750
9
150+675
825
10
150+750
900
11
150+825
975
12
150+900
1,050
13
150+975
1,125
14
150+1050
1,200
At the end of the week, AC/DC has sold 8 times what they were originally selling per store from previous listeners alone. These 10 stores, then, report sales of 12,000 copies of “TNT” sold per week thanks to the radio exposure. If the song remains at a constant 14 plays per week for those four months with constant sales, then AC/DC sells 48,000 copies a month
So with sales (s) and radio airplay (r), we’re almost ready to determine an equation that could possibly predict a chart placing. We need to consider how the competition will affect it on the radio. This is the variable l, for level average. Our ten stores are only a fraction of the nation’s music stores. To truly get an average, let’s say that AC/DC placed 6th in terms of sales and radio play combined nationwide. Our equation comes out to:
S*R/L=P
But then there’s the last thing we need to consider: the other songs that were released. With 280 songs per week, the final equation is:
S*R/L/280=P
So, let’s see our stats for AC/DC’s “TNT”:
12,000 record sales total for every ten stores
20 plays on the radio per week (constant)
6th in radio play nationwide
279 other songs vying for Billboard charting
The equation: 12000*20/6/280=p
The result: 142nd on Billboard’s Top 200 chart
That’s not bad. The Billboard 200 is a good starting spot for many bands, especially if the group is on an independent label, and the song just missed the Bubbling Under chart, which goes up to #125. The equation, however, seems flawed. Take the best selling single of all time, “White Christmas” by Bing Crosby. It’s estimated at 50 million copies sold. Slimming that down to sales per year (since 1941) that’s 1,315,789 copies per year. Once we get that down to one week (27,412 sales), we can use our equation. With that, the song comes out at 326th; this does make some sense, estimated for the fact that it’s a Christmas song, meaning less airplay and lower ranking.
Perhaps it’s not possible to predict where your song will place on Billboard, but this equation can give you at least some idea. Maybe it’s all based on sales and comparisons between those figures. Or perhaps it takes a more complex equation, maybe in statistics. Perhaps some experience in sociology is important too. All in all, you could possibly make an equation to predict chart placement, it’s just on a higher level than a mix of Algebra II and Statistics.