The luck of the judge: Why surprising but meaningless coincidences arise all the time

Jeffrey S. Rosenthal is a professor of statistics at the University of Toronto. His new book is Knock on Wood: Luck, Chance, and the Meaning of Everything.

Washington has lately been gripped by yet another scandal, this one involving allegations of sexual assault against a judge nominated for the U.S. Supreme Court.

Amid all the bitter debate, the conservative outlet Pacific Pundit introduced a novel argument. They said that Christine Blasey Ford was accusing Brett Kavanaugh merely as an act of revenge. Why? Because Justice Kavanaugh’s mother, also a judge, had issued a ruling back in 1997 about the foreclosure of Prof. Blasey Ford’s parents' house.

The outlet sarcastically referred to this as “an amazing coincidence.”

And at first glance, it does seem striking. What are the odds that the two primary figures in the scandal would have parents who had previously interacted in such a way?

However, as with many surprising-sounding coincidences, this one is actually less meaningful than it appears. Why? Because to evaluate it properly, we need to consider not just the one single unusual event, but also all of the other ways that an equally unusual event could have arisen, but didn’t. I call this the “out of how many” principle.

So, we should consider not just Prof. Blasey Ford’s parents, but also all of her other relatives and friends and associates – since we would have been equally surprised if one of them had been involved in a case judged by Justice Kavanaugh’s mother instead. And we should consider all of Justice Kavanaugh’s relatives and friends, too, since we would have been equally surprised if the case had actually been judged by his father or aunt or best friend.

We should also consider all of the other ways that those various people could have interacted with each other, not only in court but in any of their many other activities, during all of the years of their lives. The possibilities add up very quickly.

Out of all of these many different possible interactions, it is much less surprising that one of them came to pass between one set of relatives on one particular occasion – especially since they both grew up in the same area (Maryland, just outside of Washington). It could be just a meaningless coincidence, happening by pure chance alone. As William Shakespeare might put it, full of sound and fury but signifying nothing.

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Indeed, surprising but meaningless coincidences arise all the time. Back when I was a teenager, I once travelled with my family to Disney World in Florida. While there, we ran into my father’s cousin Phil – who lived in Connecticut and, to our complete surprise, just happened to be visiting Disney World at the very same time as us.

What are the odds? Not as low as you might think. Indeed, when I give lectures about probability, and ask the audience to indicate if they have any similar such story, usually more than half of them raise their hand.

This is the “out of how many” principle again. Out of all the places you have travelled, and all the crowds you have waded through, and all the relatives and friends you could have run into, it’s not so surprising that one time you happened to see a familiar face just by luck.

Fortune tellers and astrologers take advantage of this principle in their own way. They make predictions that are very general, and therefore have lots of different ways of coming true. For example, my latest horoscope advised me that “what you are scared of this weekend … is just one more illusion that can safely be ignored.”

Well, most people worry unnecessarily about lots of things. So, it was quite likely that, by luck alone, there would be something that concerned me during the weekend but was actually harmless. And this applies not just to me, nor just to those who share my astrological sign, but to virtually everyone everywhere. The “out of how many” principle practically guarantees that the astrologer’s prediction would come true through nothing more than random chance.

Last month, sports pages lamented that the Cleveland Browns National Football League team had failed to win any of their previous 19 games, a terrible streak. Was this an extraordinary occurrence, indicating that they were supernaturally cursed, and would never win a game again? Hardly.

Out of all the teams in all the sports in all the years, occasionally one team will have a very bad run – not because of any special curse, but just through a combination of poor ability and some plain old bad luck. So it was with the Browns. In fact, they had come close in several previous games, so their skill was not so low, and their streak surely involved some bad luck, too. Indeed, a couple of weeks ago, they finally won a game against the New York Jets, thus (hopefully) ending wayward talk of a curse once and for all.

So what about that Supreme Court nominee? Out of all the different possible connections between all the different relatives and friends of the accuser and the accused, the one single interaction years ago between their parents could easily be just a meaningless coincidence.

Nevertheless, the interaction did occur. So, you may be thinking, it could still have provided Prof. Blasey Ford with a motive. After all, who wouldn’t feel some animosity towards the a judge whose mother had ruled against their parents, in any capacity, however long ago, even if just by pure coincidence. Right?

Wrong. It turns out that the 1997 ruling by the judge’s mother was simply to accept an agreed-upon settlement which cancelled the foreclosure, and allowed Prof. Blasey Ford’s parents to keep their house, where they still live to this day. Her ruling wasn’t “against” the parents at all. So, in fact, it provided no motivation for revenge whatsoever. Rather, it was just another in a long, long list of fascinating but meaningless coincidences due to nothing more than random luck.