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A Preliminary Essay on Intra-Community Speculations on Rapper Quality

For this blog post, I’ll take a break from my usual ranting about measuring things in industry. Everybody who knows me relatively well knows that the only music genre I am really familiar with on any level is hip hop, as well as whatever music that hip hop artists in turn sample — e.g., I know a lot of Parliament. I was pretty disappointed as a teenager to realize that The Chronic in a lot of cases loops some Parliament and just adds drums on top. Not that I don’t like sampling.

I also know some stuff about statistics. And this is pretty niche — but I also know some rap verses that make odd references to statistics. 

First, let me dispense with the most obvious song — Yasiin Bey’s, formerly Mos Def’s, “Mathematics” on Black on Both Sides. I want to not focus on this because, while I like the song, it mostly puts together a bunch of numbers in terms of facts, but doesn’t make any oddly complicated references to more statistical things.

I’ll mainly focus on two songs that seemingly contradict each other.

Issues with Confusion on Central Tendency Measures

First, in Run the Jewels’ song Lie, Cheat, Steal”, El P, allegedly quantifying his prowess as an MC, says in one line:

“Got a average of bein’ excellent the median just dove
Like the ratio of heroin to laxative that’s sold”

Now the first thing my brother and mother might notice is “a” should be “an”. But WHO CARES.

Now, someone on Genius contends that El-P says “dope”, but then one commentator (whoM I agree with) says “dove” makes more sense. But let’s break this down: El-P, while I appreciate the whole Run the Jewels thing, and while I admire your trying to bring in some nuanced statistical phenomena to the rap game, I also have to point out that this probably doesn’t make sense: the whole point of the median as a measure is that outliers don’t measurably affect it. The median stays the same. What El-P is trying to say is that he’s so far above the average that he’s pulling up the average. Ok, cool idea, but the median didn’t change, just the average.

UNLESS?

It so happens that the median before El-P recorded this verse was pretty high, and by adding one more data point to the mix, it drops down to the next rapper below. Could that happen? Well let’s see if this makes any sense. Let’s make a simple world where there are 11 rappers before El-P joins the dataset of rappers, in order from 1-11, and each have an arbitrary score of an integer of > 0, where larger values indicate a higher quality of rap. Here’s the data pre El-P:

Rapper 1 — 1000 (this is like, Nas or something)
Rapper 2 — 500
Rapper 3 — 100
Rapper 4 — 75
Rapper 5 — 50
Rapper 6 — 40 (this is Wiz Khalifa, our current median rapper. Maybe this is giving him way too much credit though.)
Rapper 7 — 30
Rapper 8 — 20
Rapper 9 — 10
Rapper 10 — 5
Rapper 11 — 0 (this is like, Kobe, Shaq, or Justin Bieber, or some hideous amalgamation of those 3 styles)

Notice I do not assume a Gaussian or symmetric distribution, which comes back into play in the next section. The average is currently 166.4 and the median 40.
Now, let’s assume here comes El-P, and he’s now so respected that he bumps Nas down. Here’s the new dataset, indexed from 0 now.

Rapper 0 — 1500 — El-P’s claim
Rapper 1 — 1000 (this is like, Nas or something)
Rapper 2 — 500
Rapper 3 — 100
Rapper 4 — 75
Rapper 5 — 50
Rapper 6 — 40  —> most statisticians would say the median is now 45 … a mix between Wiz Khalifa and, let’s say, Shyne, when he had Barrington Levy singing that one time
Rapper 7 — 30
Rapper 8 — 20
Rapper 9 — 10
Rapper 10 — 5
Rapper 11 — 0 

The average is now 277.5, and the median is 45. So, El-P, I appreciate you trying to fit some stats into this verse (and I realize you’ve gotta make it sound okay in your rhyme scheme).. but I suggest you change it to:

“The median’s just stagnant; the average just rose
Like the ratio of heroin to laxative that’s sold”

So this fits the rhyme scheme (better even maybe? stagnant and laxative said with the right cadence might work…) and makes a lot more sense.

Austin_furcoat

My brother back in his golden era of his most prolific rhyming. Nobody ever noticed the half-off rack sign before today, somehow.

The Distribution of Quality in Rappers: A More Accurate Statistical Assessment

Despite its fallacy, El-P’s verse would lead one to assume that the distribution of quality in rap is skewed to the right. I think most fans would agree, and that’s likely true for any genre.

Big K.R.I.T.’s verse on Joey BADA$$’s “Underground Airplay” (which is awesome by the way) validates El-P’s assessment. Here’s a line:

“Half of these [rappers] ain’t even average/
How easy the word classic gets tossed around”

K.R.I.T. is telling us that the averages is at least above the median — yet this time he correctly doesn’t get into any problems of distorting the wrong metric.

So, by process of elimination, what does this rule out? The distribution of rappers is not a normal or uniform distribution. But it could be a log-normal, a Pareto distribution, a Beta distribution (if scaled to a 0-1 quality index)… and so on and so forth. Future studies may want to examine, say, Pitchfork review score data for Hip Hop albums to estimate an approximate distribution of rapper quality, though being cognizant that the review scale of most such sites is bounded (e.g., scores of <=10). This apriori effectively biases out the possibility of estimating that rappers follow, for example, a Fréchet distribution.

Discussion

2 responses to ‘A Preliminary Essay on Intra-Community Speculations on Rapper Quality

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