(Submitted by reader Daniel S)

I hurt my back on Monday. Nothing severe just have to stay in bed and take muscle relaxers for a couple of days. I’m not sure exactly how I did it because the pain wasn’t instant, it just got worse as the day progressed until I couldn’t get out of bed Tuesday morning. I’m pretty  sure I hurt it that morning when I stopped to change a tire for a little old lady who had a blowout on the side of the interstate. She was very sweet and thankful and said that normally her husband would have come to help her but he was out of state. She offered me money but I wouldn’t accept it. I just told her to remember to be nice to others.

Fast forward to today. I get a call from my Mom about an hour ago that she has had a blowout on the interstate and it’s pretty close to the same place that I had stopped to help the lady on Monday. I feel helpless because I can’t get up to go help her so I tell her that if she can’t get it changed to call me back and I will start calling friends who may be near her. About half an hour goes by and she calls me back. She got the lug nuts off but the tire wouldn’t budge. It was stuck on. Just then a little old man pulled up and asked her if she needed help. He got a hammer out of his pickup and got the tire off for her and changed it. She offered him money but he wouldn’t accept. He said that his wife had a blowout around the same place two days ago and he was out of town and felt helpless that he couldn’t come help her. He said that she told him that someone stopped and changed the tire for her and wouldn’t accept money but told her to be nice to others and he was just paying it forward.

[EDITOR: I have nothing snarky to add to this. It’s a genuinely sweet story and stands on its own.]

Updated 5/22/2012

Below are the exact notes provided by Barbara Drescher for use in Skepticality Episode 183. Take a look and leave your comments below.

As with all of these stories, the odds of these events rely on answers to a number of questions and the list is shorter than one might think:

  1. What is the probability that the author’s mother would have a blow-out within a few days of the first event?
  2. What is the probability that this would occur in the same general area?
  3. What is the probability that the woman’s husband would be driving in the same general area at the same time?

You might be thinking that the question of whether the husband would stop to help is also a factor, but I’m going to argue that it is insignificant.

Pro-social behavior has been a topic of intense study by psychologists since modern psychology began and it continues today because it is much more complicated than most people think. We tend to view the behavior of others as driven by personal values and
personality, yet this view is mostly inaccurate. One finding which was apparent in early studies and has stood the test of time is that our behavior is driven much more by situations than by anything else. This is a good thing, because it means that there are things we can do to increase pro-social behavior in general and as recipients of it.

One early finding is that people are more likely to take responsibility for the welfare of others (or even for another’s property) if they are simply asked to do so. This is due, in part, to our feelings of obligation, both because we agreed to it and because it is expected. However, more recent research suggests that a large part of the effect can be attributed simply to the fact that a pro-social attitude is easily accessed when we are reminded (a kind of priming).

In this case, the woman the author helped specifically asked her to “pay it forward”. The added feeling of gratitude and debt that she felt was certainly a factor, but the effect of noting that she could do the same for someone else is not insignificant. Additionally, pro-social behavior is contagious; we want to smile at people who smile at us. We are more likely to help someone if we have been on the receiving end of such help in the past.

In this way, ideas like those put forward in “The Secret” or those that motivational speakers promote (e.g., the power of positive thinking) can appear to be effective means of personal gain.

In some ways, they can be. However, it is important to keep in mind that 1) there is nothing supernatural about this effect, 2) it cannot be guaranteed or forced, 3) we are talking about human reciprocity. A positive attitude will not help you win a sweepstakes or ensure that your cake comes out delicious. Asking for special treatment is also not a good way to convince others to provide it, either. However, a positive attitude toward others, both in providing help to others when they need it without expecting something in return and in trusting that others are willing to help when you ask for it yourself, will improve everyone’s chances of acting pro-

So, after addressing the probability that the husband would stop to help the mother and concluding that it is highly likely, given the events two days prior, the other questions are the statistically-interesting ones.

The probability of getting a flat tire is relatively small in modern times in comparison to 30 years ago, but it happens. It is rare enough that the probability is mired in enough factors to make it difficult to calculate. Questions such as how often one drives affect this probability a great deal, but they also effect the other factors. For example, if you drive a lot, you have more opportunities to get a flat tire, but you are less likely to allow those tires to wear down to unsafe tread depths. Where you drive is a factor as well. If these two women were the victims of flats this close together, perhaps there is a large amount of sharp debris in the roadway, increasing
everyone’s chance of getting a flat tire.

The location and likelihood of a flat are tied together for other reasons as well. The author of the post clearly lives close enough to where his mother’s flat occurred that he could have helped if he had not been injured. Although humans may travel great distances, the majority of us live most of our daily lives within a relatively small “home range”. The fact that most accidents occur in the home is not due to our homes being unsafe, but simply due to the amount of time we spend there.

Likewise, the probability that the woman’s husband was driving in the same general area is not exactly low, nor is the probability that he was driving at that time. The fact is that humans share enough of a pattern of activity that we can predict the flow of traffic fairly well and make reasonable assumptions about the operating hours of businesses.

So we are left, once again, with the question of why this particular gentleman stopped to help when nobody else did. That, I think, rests on the fact that the author made the gesture he made when he made it.

The one question remaining is, what is the probability that neither woman would be a member of AAA? That, it turns out, is quantifiable.

Estimates of the number of drivers in the United States range from 250 to 300 million. AAA boasts a membership of 51 million. Conservatively, one in five drivers is a member of AAA, so the probability of a given driver not being a member is roughly .8. The distribution is probably clustered somewhat geographically, but ignoring that, the probability, choosing two drivers at random from this population and neither being a member can be written:

P(approximately) = .8 x .8 = .64.

This is better than a coin toss.