At 11:26 p.m. Monday, a laid-off journalist sent out a single tweet that would ignite the media and force the Trump campaign onto the defensive at the Republican National Convention. Melania Trump’s speech, he found, was eerily similar to one given by Michelle Obama at the Democratic National Convention eight years earlier.
The argument that it was purely a coincidence was always on slim ground. At least statistically speaking, the Trumps didn’t have basic probability on their side. Indeed, it’s less likely she and Obama independently wrote these speeches than if she were struck by lightning. Twice. (I'm not the only one to think of this comparison.)
To understand the math, let's begin with a calculation that gives Melania Trump the benefit of the doubt. Let’s assume she actually did have the same ideas, and express them in the same words, as Obama.
Even then, as a McGill University astrophysicist described in a Facebook post, the chances that Trump and Obama’s speeches would come out so similar is near-zero. There are, by his count, 14 distinct copied phrases between the two speeches — phrases like "willingness to work for them" that could be reordered in almost any configuration and still make a coherent speech.
In reality, not all of these orderings are created equal — some may create a more logical flow than others, giving them a higher probability to be chosen. So the estimates below should be treated as a ballpark rather than concrete figures, with some probabilities a bit high or low depending on how Obama and Trump's logical flow compares to that of other possible phrase orderings.
With that in mind, the probability that two orderings of 14 items come out the same is incredibly small. There are 14 possible phrases you could put first, then 13 remaining phrases you could put second, and so on, yielding 87 billion total possible orders. (In middle school math terms, that's 14 factorial.)
That means, the chance Trump’s order, chosen out of those 87 billion, matched the one order Obama chose is 1 in 87 billion. For comparison, you’re about 300 times more likely to win the Powerball jackpot on any given play.
But even that 1-in-87-billion figure may be generous.
Those assumptions — that Melania Trump happened upon the same ideas as Michelle Obama and described them in the same words — are huge. If we make the situation slightly more realistic, but still very generous to Trump — say there were two viable ways of wording each of the 14 phrases — those chances fall to about 1 in about a 15 hundred trillion. You’re about 14,000 times more likely to have your name pulled out of a hat that contained the name of every human that ever lived.
And plagiarism software confirms this incredible improbability. As published by the Washingtonian, according to Turnitin, which makes plagiarism detection software for use in schools, the chance Trump’s words weren’t plagiarized is well below 1 in 1 trillion.
It’s no surprise someone at the Donald Trump campaign finally had to fess up. The odds were not in their favor.
