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Statistician’s Approach to Coincidences: What Are the Odds

Unlikeliness characterizes coincidences. A common kind of coincidence, for example, is one in which you think of a friend and that friend calls you. Your first thought might be, “What are the chances?”

In the previous post, we bumped into difficulties estimating the probability of this coincidence.

The main issue is that there are so many unique variables for each situation; it’s difficult to estimate the rate of occurrence (base rate) for each part of the coincidence. How long has it been since the friend has contacted you? How often do you think of the friend? Many more intricacies complicate the issue.

Estimating the probability of other coincidence types seems equally, if not more, difficult. Since unlikeliness characterizes coincidences, clarifying their probabilities is a necessary task in better understanding them.

View the full article Dr. Beitman’s Psychology Today blog »

The Promise & Problems of Probability in Coincidence Studies

Coincidences attract our attention because they seem weird, odd, or unlikely. Their improbability stimulates wonder—“what are the odds of this happening?” Probability theory, which is a branch of mathematics, promises to shed light on this defining aspect of meaningful coincidences.

Carrying this banner, I valiantly strode forward into probability’s thicket of mathematical concepts and formulas and emerged to write a report. My confidence was bolstered by having gotten a Double A in a probability theory seminar at Swarthmore College.

Here’s what I found in the thicket…

View the full article Dr. Beitman’s Psychology Today blog »

Using Coincidences to Push a Sale

Coincidences can be used for a variety of purposes including making a sale. In this story, the salesman sought links of similarity with Diane as a way to establish connections in the hopes of increasing the possibility of a better deal for him and his company.

Diane wrote:

“Two summers ago, I was faced with the task of buying a new car. After a long, arduous search, I finally found the car I wanted at a local dealership in my city. The salesman was surprisingly wonderful. A retired school teacher who seemed forthright and honest. When all the preliminaries were done, I was passed along to the financing department. The fellow I met there was also quite pleasant. As he entered in my information, he asked me questions about my job, kids, etc., and we did seem to have a few things in common. For example, he lived in the county where I work, we both had a child in the second grade and also had a friend in common.

After each of these links were uncovered, he would note that it was a funny coincidence. When he was finished entering in my information into the system, he gave me a big smile, pushed a long form in front of me and said, “And now let’s talk about our extended warranty”. At that point, I felt as if he was trying to use the links we had in common to gain my trust and make an even bigger sale…”

Was Diane being a bit paranoid? She truly felt she was “being had”.  Coincidences do draw people together. When they are sought or manufactured and money is about to change hands, it is better to pay more attention to the deal than to the coincidences.

Tell Your Coincidence Story!

Coincidences can make great stories. Telling them can be entertaining both for the teller and the listener. The surprise factor adds juice to the tale. Talking about a coincidence can also help initiate difficult discussions.

A reader sent this one:

“A work colleague said he wanted to get to know me better. I thought it might be fun so we arranged to meet on a Friday at 2PM at a coffee shop in a shopping mall about a mile from our office building. Punctual person that I am, I was there a few minutes before 2, got a coffee and waited. By 2:15 he had not shown up. I emailed him by phone. No response. We had not exchanged phone numbers. By 2:20, hurt and angry, I wandered off to a nearby bookstore where my phone did not register a signal for some reason.  After leaving the bookstore and regaining the signal, I saw an email from him. “En route,” it said. The time was 2:25.

“At 2PM on the same Friday, my wife was waiting for a work colleague at a different coffee shop. They too wanted to get to know each other better having had only brief conversations in their office building. By 2:30, the woman had not shown up.

“My wife and I were involved in the same pattern: Meeting work colleagues at a coffee shop at 2PM on the same Friday to get to know them better. And neither showed up at the agreed upon time.

“My wife contacted the woman who apologized profusely. She had forgotten.

“I ran into my work colleague a few days later. I did not realize how upset I was. When he implied that it was my fault that we did not get together, I got mad. He then stormed off. No apology.

“After too much deliberation and much anxiety, I arranged to meet with him to discuss what happened between us. I was trying to be a mature adult. I was very anxious when we started. So I told him about the 2PM coffee-shop-no-show coincidence. That broke the ice for me. Smooth sailing. We have since met for lunch and are thoroughly enjoying getting to know each other.”

Intense emotion marks memory.  Our amygdalae (almond shaped organs deep in both sides of the brain) fire when recognizing something to be feared or something new. This firing tells their nearby cousins, the hippocampi, to store the event in memory. The surprise of coincidences marks them for storage in your memory. Recall and tell your story! Something positive can happen.

The Non-Diamond Earrings

A student in my first class at the University of Virginia did her homework! She wrote this coincidence story:

“A few years ago after moving to Charlottesville to raise my small son alone, I was feeling confirmed in the wisdom of my move but realizing life would be comfortable while not luxurious. I was OK with that although, truthfully, I would have been happy with more money in the bank account.  Many of my friends wore diamond stud earrings given them by loving partners or brought with their own income. I liked the stud earrings but knew they were not in my budget.

I returned to Kansas to visit my mom and the two of us went downtown to a small farmers’ market. As we were leaving, I stepped on a small glassine envelope. Inside were small, stud earrings. Rhinestone, perhaps. Nothing very valuable except to me.

I experienced this coincidence as an affirmation that I was not alone and that—while I would never be rich—I could know that somehow I would be provided basic needs.”

The Several Meanings in a Meaningful Coincidence

In this post I examine a basic element of meaningful coincidences—the several aspects of meaning in each of them. While the poet William Wordsworth suggested that sometimes “we murder to dissect”— that analysis can remove meaning from the experience—I believe that by taking apart coincidences and examining their qualities, we can more fully appreciate them.

View the full article Dr. Beitman’s Psychology Today blog »

Why Study Coincidences? Part 2

I study coincidences because they are fascinating. I study them because I’ve discovered they are useful in ways most people never considered. Once you become aware of them, you realize what a ubiquitous part of life they are. They are intertwined with so many of the things we hold to be important.

In Part 1, I looked at how coincidences are used in career development and in finding just what you need when you need it. Now, I’ll explore how they help with personal growth, inunderstanding the connections we have with the world around us, and in our relationships with others.

A common coincidence happens as follows: you think of someone you haven’t seen, or even thought of, in years. All of a sudden, you run into that person. You think, “How in the world did what I was thinking about just appear before my eyes?!” In such cases, you’re pushed to look at how your mind connects to the outside world. You’re made more aware of what was in your mind when the coincidence occurred.

View the full article Dr. Beitman’s Psychology Today blog »

Why Study Coincidences? Part 1

When I ask myself why I’ve embarked on a mission to establish Coincidence Studies, the simplest answer is that coincidences are fascinating. They jolt us into an awareness of mysterious connections between ourselves and the world around us.

I am curious about how they work and what they can do. When I work on trying to figure out something about them and write about it, time passes quickly. I am immersed in the learning-entertainment interface.

They are also useful in ways most people never considered.

Psychotherapists can use them to treat patients; they can help people become self-aware and introspective, leading to positive changes. Coincidences have proven useful in professional development. People often “coincidentally” find exactly what they need when they need it. Coincidences have helped scientists make great discoveries. They have the power to comfort people, to aid healing from traumatic experiences. Through them, people can build stronger relationships.

View the full article Dr. Beitman’s Psychology Today blog »

Life is But a Dream

As my coincidence colleague Tara MacIsaac in Peterborough, Ontario and I ended our conversation over the internet on 8/28/15, I asked her if she had seen the movie Waking Life. She replied that about 6 years ago this was her favorite movie. She had seen it many times, but hadn’t seen it since then. A few days earlier she had spontaneously thought about watching parts of it on YouTube.

For the previous 10 days, I had been slowly watching Waking Life, carefully enjoying each of its many interesting sections, laughing and wondering about how it was made.  Tara seemed to have picked up my energizing the idea of the movie.

I think my excitement about it 650 miles away in Charlottesville, Virginia helped to initiate her seeking the movie again.  She would not have been triggered by my energizing the idea if she had not sometime earlier energized the idea herself.

Waking Life uses cartoonized versions of real actors as the story follows a young man’s encounters with a series of people who lecture him on the nature of reality. The movie suggests to us that what we think of as reality is one of many dream states to which we have access.  Coincidences may be windows for this expansive perspective.

The Same Birth Date

Thursday, June 19, 1986

On June 19, 2015, I met with a new friend for coffee to discuss my upcoming talk on coincidences. He knew the audience well and could help guide me to better communicate with them.  He was also interested in knowing more about Coincidence Studies.

He started the conversation with “today is my son’s 29th birthday” and then described his continuing amazement at how quickly time passes. Startled, I waited until he finished to tell him that today was the 29th birthday of one of my sons.  Our sons were born on the same day!

Earlier that day, I had finally completed a four month negotiation to settle an ugly dispute with a business associate.  It was a great relief to have agreed on a final dollar number.

On my son’s birthday, I received two presents—an improbable birthday coincidence and finalizing an agreement to receive a substantial amount of money.

How did it happen that I received two such great presents on my son’s birthday?


Base rates

Sons having same birth date. Millions of people were born on June 19, 1986. What are the odds of two people 5 years apart in age having a child with the same birth date?  Not birthday but birth date.  Not particularly unlikely given their closeness in age.

Meeting on their birthday. It was a convenient Friday for my friend and me to meet. We did not see each other regularly. This was only the second time we had met outside of social gatherings. Did I pick the day in part because it was my son’s birthday? The likelihood of our meeting on their birthday was about 1/365.

Discussing the birthday. What are the odds that one of us would bring up the birthday of his son? Pretty high because it was close to the surface for each of us.

So the key question is what are the odds of two people within 5 years of age having children with the same birth date meeting on their children’s birthday and discussing it?  Not so astronomical actually. Still pretty amazing.

Discussing Coincidences. I write and email about coincidences but rarely meet with the primary purpose of talking about them. Lately, I have avoided discussing the idea unless someone else does. So to meet to discuss coincidences was unlikely.

Reaching a settlement on my son’s birthday. The business problem had been going on for four months. Lots of verbal pushing and threatening. Earlier in the week I threatened my adversary for a third time. After avoiding any negotiation, he finally agreed to discuss a settlement figure with me. From past experience, I knew that Friday was the day he liked to have these discussions. The Friday of that week was June 19.  So I picked the week to do the third threat that had the Friday that was my son’s birthday. Yet I was not at all confident that he would be willing to negotiate with me.

My son was very much involved with my initiating the settlement conflict. He was my advisor at the beginning of the dispute. I had wanted him to do the deal for me because he is a better negotiator. 

Probability summary

There is a moderately low probability for each of us to have sons with the same birth date. Meeting on their birthday, decreases the coincidence probability. That we were together to discuss coincidences decreases the probability even more.

There was no guarantee that my adversary would negotiate that week. But if he were going to, then it would most likely be on the Friday of that week, June 19.  This element lowers the total coincidence probability even further.


Personal contributions
I had something to do with creating both coincidences. I picked June 19 to meet with my friend and selected the June 19th week to hopefully finalize the negotiation.

The purpose of the meeting was to discuss my first formal coincidence lecture.  Coincidences seem to be increase during transitions. 

In addition to probability and my own decision making, I feel that something else I don’t know about, a mystery, made some contribution.  The probabilities seem too low to just attribute to chance and to me.

The coincidence increased my feeling of connection with my son. He had been so helpful with the difficult negotiation.  It also raised a question about my new friend because he had been involved with another meaningful coincidence of mine. Is he a coincidence magnet for me?