14 October 2019 ~ 2 Comments

The Horowitz Method: A Metrics-Based Approach to Rank-Ordering Musical Groups

written by David Steffen (and no one else, alas)


Since time immemorial, one of the perennial topics of humankind has been to compare music.  Whether pop is better than country, whether this band is better than that band, or this song better than that song.  Before the invention of writing, one can imagine heated arguments about who was the best drummer.

(ANGELICA, if you’re reading this, I’m sorry. For everything. But most of all I’m especially sorry for taking what we had for granted. Don’t worry, the parts that are bold-and-italicized are only visible to you, keyed off of your IP address. I can only hope that even though you’ve changed your number and email address that you might have left this one thing unchanged. I know you would be mortified if this were public, and wouldn’t hear the end of it from Maurice. I wouldn’t do that to you!)

Arguments are powerful things.  Relationships have formed and relationships have ended over this subject matter (because some of us become complete assholes on the topic and don’t think about other people), and we believe that many relationships can be saved if we can apply some elements of scientific rigor.  The subject matter as it has been historically framed is inherently too subjective and therefore is a breeding ground for disputes and hard feelings.  Even scientists, we who pride ourselves on being able to set aside our emotions and think rationally, have been known to make this mistake, though we of all people should know better. 

We posit that our mistake has been rushing into the discussion without agreeing upon criteria (and also about using absolute statements in combination with invectives, statements like “Anyone who likes 98 Degrees more than The Four Seasons is a complete @*&@#$ @#*@! have no place in a laboratory”. I was not lying, but I should have considered your feelings. I didn’t know how hard you would take that until you replied to say that One Direction was better than Third Eye Blind. That still stings.), and so have entered the debate in bad faith with the conclusion in mind ahead of the evidence.  We considered what criteria might be used for the judging of musical bands.  As with the objective comparison of so many other types of subject matter, we have come to the conclusion that the answer lies in mathematics.  When we sent Voyager to journey beyond our solar system, we wrote our message to the universe in the languages of music and mathematics.  If it’s good enough for aliens, it’s good enough for resolving disputes with our fellow music-loving humans. (I would send you a gold record!)


Therefore, I propose The Horowitz Method (I hope you’re not upset that I named it after you. I know it’s traditional for the founder/inventor of a scientific method or discovery to be its namesake, and while you didn’t propose the method nor write this article to propose it to the public, I wanted to acknowledge the role that you played in its instantiation. You are the best research partner that I’ve ever had, so rigorous and well-spoken and hilarious when you want to be, and while yes I have at times been jealous of your success, that success was earned and anyone is lucky to work with you. I also admit that another factor in choosing your name was that I hoped you would hear about the proposed method via mutual colleagues and would be curious enough to visit this page where you could read these messages. If you’re upset about the naming, I promise I am willing to change it), an objective method of rank-ordering musical groups in a metric-based approach that is thus subject to peer review.

But what mathematical measure?  If we were talking about comparing one song with another, it might be easier, for the music itself is inherently mathematical–meter, tempo, time, number of notes, pitches.  But a single musical group could have any number of songs, and the number could grow every day–what particular songs would one use to judge a group?  Their newest?  The whole body of their work?  And some bands release songs so regularly that any conclusion drawn would have to be re-examined very frequently. And that’s not even to speak about what particular measure to use which, we know from personal experience, becomes a dispute of its own.

No, if we are going to compare musical groups and expect a somewhat stable outcome, we must not compare their songs, we must compare traits of the group themselves.  The genre?  The style?  Again, too subjective, one could argue that a group is one or another or maybe both or something entirely new.  We need to focus in on something entirely indisputable. 

The band name.  (Please hear me out and look at the data. And I look forward to seeing your refutation in a prestigious journal instead of publishing it on your own site)

And, in order to apply mathematical rigor to it, the dataset we will work with will be band names with numbers in them. (yeah, I know, but I figured we had to start somewhere)

“My favorite musical group doesn’t have a number in it,” (Black-Eyed Peas) some of you are declaring at this very moment (Faust, Lionel Richie, Adele).  Then take heart in knowing that your favorite band is incomparable, in the mathematical sense.  If you want to compare your group with others, I’m afraid you’re out of luck, at least for the time being.  You may as well try compare (8/0) to (10/0), or compare a walrus to a the clock speed of Pentium processor, or a raven to a writing desk, the question inherently has no meaning, and if you don’t like the system, propose an alternative. (I dare you. You know you want to!)

By using a mathematical system, we can define and rank and draw some mathematical conclusions about the dataset.  This system doesn’t define which band is the “best” because that is an inherently subjective concept, but it does define which is the GREATEST, mathematically speaking. (That’s right, that’s how sorry I am, I am resorting to PUNS . In PUBLIC. May the Flying Spaghetti Monster forgive me. )


Even in something so simple as numerical ordering, there were some corner cases that are worth noting, especially when other researchers consider peer review.

Only groups that had a number clearly as part of the name were included in the dataset. Groups that clearly had numerical etymology but did not contain what we would recognize as the word we commonly use for the number were not included. This excluded, for instance, Pentatonix, which was a corner case in itself, but if we included root words then we felt it would have to include any other names that include root words, which might not always be easy to determine in every word that it may not be common knowledge that they are numerically based, such as “quarantine”.

But a number may be part of a larger word and still be included as long as the number itself is clearly visible and appears to clearly refer to the number. So, Sixpence None the Richer was included as the number 6 and Oneohtrix Point Never was included as the number 1, but Bone Thugs and Harmony was not included because “Bone” clearly is not meant to refer to the number “one” even though it contains the letter sequence.

At first, ordinal were included, like Third Eye Blind, as its integer number (in this case, 3). But, after considering the earlier decisions about not allowing words with number etymology in them, this seemed inconsistent with that. In an attempt at greater consistency, these were still included in the dataset, but as fractions whenever the word was correct–so Third Eye Blind was included as 1/3 rather than as 3. We expect that this will be a point of contention in peer review and we welcome the debate. (Note that I didn’t do this just so that One Direction would be greater than Third Eye Blind, and how dare you suggest I would undermine my own scientific integrity)

Roman numerals were included, but only when the numeral clearly referred to a number. So, King’s X was excluded even though the X might be considered a 10, because that doesn’t appear to be how it’s used. But Boyz II Men was included, because it is spoken as the number representation, rather than being pronounced “Boyz Eye Eye Men”.

Musical groups with more than one number in their name, like The 5,6,7,8’s, or Seven Mary Three, were treated as a dataset, included once for each number. This means that Seven Mary Three is both greater than and less than The Four Tops.


Many of the results of this dataset are illustrative of the problems inherent in trying to summarize a dataset with extreme outliers. At the same time, the usual methods for excluding outliers seemed inappropriate for this particular application, because if we are to determine which band is greater than another, but exclude the greatest bands in the dataset, this would undermine. Note that, among other things, this means that the GREATEST band is also the ONLY band that’s above average.

The Greatest (Maximum): Six Billion Monkeys

The Least (Minimum): Minus Five

Average: 28,846,316.88

Standard Deviation: 416,025,135.8

Median: 5 (see data list below to see the bands with value 5)

Mode: 3

Again, note how the average and standard deviation in particular were skewed very high by the high outliers in the dataset, particularly the number of 6,000,000,000, when the majority of the rest of the numbers were less than 100.


While the dataset as a whole is very spread out to make a displayable histogram, since 90% of the datapoints are between the values of 0 and 100, that a histogram of the data within this range could be interesting.


If this measure were widely adopted, it is possible that it would have the consequence of encouraging musical groups to be more likely to pick names with numbers in them, or to add numbers to existing names. We see this as a positive result in itself, though it could make future results require more peer reviews as bands try to pick the greatest number to improve their placement, which may bias the data.

Although we explicitly avoided ranking individual songs here, the same method has potential for that as well as albums or movie titles or books (i.e. 1984 is greater than Slaughterhouse Five) or really anything else that has titles that might include numbers in them.

(And the most important under the topic of further study is whether you will see this as the olive branch it is meant to be. My research is lesser without you, and I hope you feel the same way about me. You know how to reach me, and I hope you do contact me. Most of all, and you know that I’m not good at the touchy-feely stuff, is that I miss you as a person. You are an incredible human being.)


Here is a list of the complete set of datapoints used in this study. While this is meant to be as complete a list as possible, it is recognized that this is likely not a comprehensive list, as with the Internet publishing where it is it can be hard to define whether a band is a band or not–i.e. what if there is a musical YouTube channel with a numerical username, or what if someone self-publishes a CD on their own website that no one has heard of. Further studies can propose methods of defining what exact musical groups should be included and which ones should not.

Six Billion Monkeys
10,000 Maniacs
Powerman 5000 (Yeah, I know, but numbers don’t lie)
Andre 3000
Death From Above 1979
The 1975
1000 Homo DJs
MC 900 Foot Jesus
Galaxie 500
Appollo 440
Front 242
Blink 182
Zuco 103
The 101ers
100 Flowers
Haircut One Hundred
98 Degrees
Old 97’s
Revenge 88
Combat 84
Link 80
Seun Kuti & Fela’s Egypt 80
Resistance 77
69 Eyes
Sham 69
Eiffel 65
The Dead 60s
Ol ’55
The B-52’s
50 Cent
45 Grave
Loaded 44
June of 44
Level 42
Sum 41
36 Crazyfists
Thirty Seconds To Mars
Apartment 26
Section 25
23 Skidoo
Catch 22
Twenty One Pilots
Matchbox Twenty
East 17
Heaven 17
16 Horsepower
13 & God
Thirteen Senses
13 Enginers
Thirteen Senses
12 Stones
Finger Eleven
Ten Seconds Over Tokyo
Ten Years After
10 Years
Nine Inch Nails
Sound Tribe Sector 9
The 5,6,7,8’s
The 5,6,7,8’s
Seven Mary Three
Zero 7
School of Seven Bells
Avenged Sevenfold
School of Seven Bells
7 Seconds
7 Year Bitch
Shed Seven
The 5,6,7,8’s
Six Organs of Admittance
Slow Six
Appollonia 6
Eve 6
Sixpence None the Richer
Three Six Mafia
Six Feet Under
Nikki Sixx
Vanity 6
Delta 5
The 5,6,7,8’s
Pizzicato Five
Five Finger Death Punch
Maroon 5
Five Iron Frenzy
Ben Folds Five
The Jackson Five
Family Force 5
Dave Clark Five
Section 5
Count Five
5 Seconds of Summer
Grandmaster Flash and the Furious Five
Jurassic 5
John 5
We Five
The Five Satins
five star
Gang of Four
Four Tet
The Four Seasons
The Four Tops
The Brothers Four
The 4-Skins
The Four Pennies
The Fourmost
4 Non Blondes
4 Jacks and a Jill
Funky 4*1
Unit 4 + 2
The Three O’Clock
Dirty Three
Fun Boy Three
Seven Mary Three
3 Leg Torso
Bike For Three!
Three Mile Pilot
Dirty Three
Mojave 3
Opus III
Alabama 3
Three Dog Night
Three Doors Down
3 Mustaphas 3
3 Mustaphas 3
Three Six Mafia
Three Days Grace
The Three Degrees
Spacemen 3
Timbuk 3
The Juliana Hatfield Three
Fun Boy Three
The Big Three
3 Colours Red
Secret Chiefs 3
Two and a Half Brains
Boyz II Men
Two Gallants
U2 (Sorry Bono)
Soul II Soul
Two Door Cinema Club
The Other Two
Aztec Two-Step
Two Man Sound
2 Live Crew
Unit 4 + 2
2 Chainz
Secondhand Serenade
2 Minutos
1-2 Trio
The Other Two
Faith + 1
Oneohtrix Point Never
One Republic
One Night Only
One Direction
The Only Ones
The Lively Ones
Funky 4*1
1-2 Trio
One Dove
Third Eye Blind
Third Ear Band
The Sixths
Eleventh Dream Day
13th Floor Elevators
Zero 7
Remy Zero
Edward Sharp and the Magnetic Zeros
Authority Zero
Zero Boys
The Minus Five

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