Pure stupidity

Today, my colleague Rachel Stassen-Berger and our competitor J. Patrick Coolican had a Twitter fight about how Patrick reacted to one of Minnesota’s senators attending a rock concert.

It was, everyone involved readily admitted, pretty stupid.

But Patrick made a further claim: that the exchange was, in fact, the stupidest Twitter fight of the day (to that point, about 12 hours old). Rachel disagreed:

After Patrick’s co-worker Ricardo declared himself to be on #TeamCoolican, Rachel asked me to back her up. This was a mistake:

As of Rachel’s comment at 12:06 p.m. today, there had been an estimated 416 million tweets, at the average rate of about 9,500 tweets per second.

About 0.7% of tweets are negative in tone, according to one study. (Other studies have found higher rates of negativity on Twitter, particularly when discussing subjects like politics. But I’m going to go with the lowest number I found, in part because it’s universal and we’re not just interested in political Twitter fights, and in part because we don’t need to consider a higher rate to settle this.)

That’s 2.9 million negative tweets in this first 12 hours. This particular Twitter fight had seven tweets (including Ricardo’s interjection but not Brian’s query), so for the sake of simplicity, let’s take seven as our average Twitter fight length and divide out for about 417,000 Twitter fights. Scale the following smaller if you prefer a different definition of the number of tweets per fight, though we’re really just making numbers up left and right here.

Let’s further assume the intelligence of those tweets follows a normal distribution, with tweets of average intelligence the most common and really smart and really dumb tweets of decreasing frequency. We’ll apply a scale of 0 to 100, where 0 is peak stupidity, 50 is average intelligence and 100 is peak intelligence.

All sides have stipulated that these tweets are, in fact, dumb. So we’re limited to just one side of the normal distribution: this fight is somewhere between 0 and 50 on the intelligence scale.

What is in dispute is to what degree this fight is dumb. Is this the dumbest Twitter fight humanly possible (a 0)? I suspect we can all imagine dumber possible Twitter fights. But that’s not necessarily fatal to Patrick’s argument that this is the dumbest fight of the day — or even, in our sample, of the first half of the day.

Now, the exact stupidity level of this fight is so subjective that it’s impossible to know for sure. But we can speak probabilistically. We know the stupidity value, which we’ll call S, is somewhere in the range 0 <= S <= 50.

But most values of S are immaterial. If this conversation is a 45, then it’s clearly not the stupidest Twitter fight of the day. In fact, we only care about about the extreme low values.

With a population size of about 417,000 fights, our normal distribution can tell us how many Twitter fights we can expect for each stupidity score range:

Stupidity score Number of fights
0 - 5 1
5 - 10 12
10 - 15 84
15 - 20 466
20 - 25 2,025
25 - 30 6,894
30 - 35 18,362
35 - 40 38,281
40 - 45 62,468
45 - 50 79,798

For example, we can expect almost 80,000 fights between 45 and 50 — just slightly stupid fights. But there will be just 84 fights between 10 and 15, where the stupidity is becoming impressive.

Fortunately for Patrick, you can still be the dumbest Twitter fight in the day without being the dumbest Twitter fight possible (a score of 0). Unfortunately, you have to get pretty darn close. A score of 6 would put you among the two dumbest fights, and the “winner” likely has to achieve a score of 5 or less.

The odds of that happening are one in 294,319, an 0.00034 percent chance.