Apophenia, Paradelia, and The Hot Hand…Oh My!

Virgin Mary Toast

Most people think they can tell when a process is random.

Once, when I was at the Mark O. Hatfield Courthouse building in downtown Portland (surprisingly to serve as a juror not as defendant) four groups of jurors were called forward to be impaneled. One of the groups was overwhelmingly composed of women. A guy next to me grumbled: “Random? Yeah, right.” He had the intuitive (but wrong) feeling that randomness correlates with equitable distribution. To him a random process meant that all four groups of jurors should be basically mixed in equal parts.

But the court did follow a random process. The thing of it is over a long period of time randomized selection processes will produce groups that are anything but evenly distributed, and our intuitions aren’t trained to recognize this.

Let’s say you walk into a classroom where you find a giant blackboard covered in four long lines of H’s and T’s standing for heads or tails. The teacher tells you that three of the lines are random, created by using a coin flip; one of the lines was generated by a student asked to create a random string of heads and tails. She then asks you to examine the lines and write down which you think was created by the student.

Think you could tell?

To a normal person randomness means you should only expect a coin to produce a few heads before you see a tail. It begins to feel weird if this doesn’t happen. So, when a person tries to create a random string of heads and tails you will rarely see more than a string of three heads or tails in a row; you will probably never see a string longer than four. But, in a long series of, say, a hundred flips, a random process will commonly produce long streaks of heads or tails in a row- streaks that feel spooky and anything but random. Except random is exactly what they are.

Our tendency to see patterns where none exist, apophenia, or paradelia, imagining we see the Virgin Mary in a piece of toast, can get us into trouble. Especially when it comes to making decisions. Sports offers us the most well known example of imagining patterns in randomness: the hot hand. Players, coaches, and spectators alike are positive they can feel when a player has become “hot”- meaning, they’re experiencing some kind of streak such that they are more likely to hit a three or sink a putt. People perceive that some kind of inner or outer force is at play, and if you can, you should try to get the ball into the control of the player with the hot hand.

Sigh… Alas, the hot hand is about as real as the image of the Virgin Mary you were sure you saw popping up in your toaster. Thomas Gilovich produced the first study disproving the hot hand theory. More recently, a 2013 study using larger sets of data indicates a tiny correlation between the probably a player who made a basket will make their next shot as well. But, whether you think Gilovich is right or this more recent study- all the researchers agree that there’s nothing like a magic “hot hand” so many of us think we see. Rather, there are better players and worse players- and worse players, over a long period of time, will still experience streaks. But then, according to what statisticians call regression to the mean, after their streak they will experience of a string of misses you don’t notice because it’s so much less exciting.

This happens in scripture, too. In First Samuel 4 the Philistines were attacking the Israelites the Israelites were losing battle after battle. Finally, the elders, sick of losing, came up with the game changing idea to retrieve the Ark of the Covenant. (Cue Indy!) Even though the Israelites had been losing, they all gave a huge shout when the Ark arrived. The Ark is like a symbol of God’s presence and the hot hand. Surely, with the Ark the hot hand would be theirs! Emotion and momentum, as the sports commentators say, was theirs. And on the other side the Philistines were duly frightened. They had never fought against a people with “gods in their camp.” (First Samuel 4:7) According to the hot hand theory, the Israelites should have kicked butt and taken names. Alas. The hot hand the ark was supposed to produce never materialized. The Philistines won, as usual, and they took the ark into their possession.

The same kind of dynamic takes place in the crucifixion of Jesus. With Jesus’ healings and deeds of power the disciples felt like if anyone had the hot hand it had to be Jesus. Hence, Peter rebukes Jesus for his defeatist prediction of crucifixion (and gets called Satan in the process.) At the foot of the cross the gawkers felt the same way: surely if Jesus really was the Son of God he could just call out for help, invoke his hot hand, and come down. But in the deepest way the Gospels don’t promote a hot hand Christology. Jesus, fully divine but fully human, wasn’t some kind of god marked by fortune. The hot hand wasn’t going to save him any more than it will any of us. Jesus was subject to the same weaknesses and laws as we all are- including the laws of statistics. And because of this he died a very real death on the cross.

It’s impossible to overstate how much we want to believe in the hot hand. We are just wired to feel that momentum is with us or not and that we are directly impacted by this emotional power. Church leaders are among the most prone to this. We love to talk about “call” and “feeling the Spirit,” and we get grumpy when people ask us, after the manner of First John, to test these spirits. If you are helping to lead a governing body, and you begin to feel that emotions are beginning to run high and individuals are beginning to substitute a kind of hot hand hope in place of considered arguments, this is a dangerous time. I don’t recommend you challenge the hot hand directly. I’ve never found this to be productive. I do recommend that you slow down the pace. Ask for a time of prayer and moments of silence. Then, ask as many questions as possible. Probe assumptions and discern for where the body is trying to move too quickly. Finally, expand creative, doable alternatives as much as possible keeping in mind that doing nothing is nearly always a valid option. It’s surprising how quickly groups forget the option of just staying the course is an option. Doing nothing isn’t always the most exciting option; but sometimes it is the wisest. Obviously, these measures won’t ensure you always make the best decisions as a group, but they can at least help you to avoid the emotional blindness the hot hand bias brings.

Churches are great places. And being called to ministry is fantastic. But it doesn’t exempt us from being human and the law of statistics. My favorite verse (I'd have it tattooed on my face except for the length…) comes from Ecclesiastes. After Qoheleth laments how nothing can give him a sense of ultimate he finally exhorts us to simply love the world we are in as much as we possibly can for, as he puts it, time and chance (yes, Calvin, CHANCE!) happen to all.

4 But whoever is joined with all the living has hope, for a living dog is better than a dead lion. 5 The living know that they will die, but the dead know nothing; they have no more reward, and even the memory of them is lost. 6 Their love and their hate and their envy have already perished; never again will they have any share in all that happens under the sun. 7 Go, eat your bread with enjoyment, and drink your wine with a merry heart; for God has long ago approved what you do. 8 Let your garments always be white; do not let oil be lacking on your head. 9 Enjoy life with the wife whom you love, all the days of your vain life that are given you under the sun, because that is your portion in life and in your toil at which you toil under the sun. 10 Whatever your hand finds to do, do with your might; for there is no work or thought or knowledge or wisdom in Sheol, to which you are going. 11 Again I saw that under the sun the race is not to the swift, nor the battle to the strong, nor bread to the wise, nor riches to the intelligent, nor favor to the skillful; but time and chance happen to them all.
Harper Bibles (2011-11-22). NRSV Bible with the Apocrypha (Kindle Locations 30123-30132). Harper Collins, Inc.. Kindle Edition.