Coincidence

I had a weird thing happen on my way in to work this morning. On the main road just a short distance from my parking lot I noticed that the SUV in front of me had the same three letter combination on their license plate as mine, “YGK”. Then I noticed that the car in front of THEM had the SAME three letter combination! Wow. What are the odds of that happening? Well, I’m not going to tell you the odds of that happening, because I don’t really know. But it did happen. An odd coincidence for sure, but maybe not as cosmically-connected as you might be inclined to think.

First off, let’s think about the odds of drawing the same 3-letter combination from a hat with 26^3 combinations two times in a row (approximating what happened here- because my license plate is fixed). That’s how many different possible 3-letter combinations there are- I suppose probably subtracting one or two for words that aren’t allowed, like “ASS” and, ummm, well maybe there’s another. This is 17,576. The chances of drawing two of the same out of a hat would be 1/17,576 X 1/17,576 – 1 in 300 million. So this means that you could sit and draw letters out of this hat every second (that is drawing two sets of three letters out every second) for about 10 years before you’d be likely to have this happen. Now clearly I’m simplifying here- but still. So for my license plate story I’d be unlikely to have this happen in my lifetime since I’m only driving every now and then and I’m not generally even paying attention to other people’s license plates to see if this has happened or not.

So here are some reasons why it’s not TOO surprising that it did happen. First, assuming all combinations are used, there are 1000 other vehicles in WA state with the same letters, which narrows the field a bit- but only a bit since there are ~6 million registered vehicles (at least in 2012, though some portion of these have the longer 7 number/letter plates). Second, is that it is likely that these are issued in order (though I’m not 100% sure about that, it would seem to make sense) of request. That means that vehicles purchased about the same time as mine (2001) are probably far more likely to have the same set of letters.That’s been about 13 years, which means that those vehicles are going to be of a certain age.  I would also include geography – since that could be another influencing factor as to which numbers/letters you get, but I did get my license plate on the other side of the state. I don’t have a clear idea of how this would bias the probability of seeing three license plates in a row, but it fits in to my next point, which is hidden or partially hidden explanatory variables.

When my wife and I lived in Portland, far before we had such encumbrances as kids to drag us down, we often did a bunch of activities on a weekend. I started to be surprised to notice some of the same people turning up at different places, parks, restaurants, bookstores, museums, etc, far across town. This happened more than you’d expect in a moderately-sized city. Interestingly, in Seattle when we had a kid this also happened. And it happens all the time in our current city(ies), which are much smaller. My idea about this is that it’s not surprising at all. Our choice of activities and times is dictated or heavily influenced by our age, interests, kidlet status, etc. – as are other peoples’. So instead of thinking of the chances of repeatedly bumping in to the same set of people out of the entire population, think about the chances if the background distribution is much more limited, constrained (in part) by those interests and other personal constraints. The probability of this happening then rises considerably because your considering a smaller number of possible people. I’m sure this has been described before in statistics and would love it if someone knew what it’s called (leave a comment).

How does this fit in to my license plate experience? I don’t really have a clear idea, but it is evident that there can be multiple underlying and often hidden explanatory variables that may be influencing such probabilities. Perhaps my work is enriched in people who think like me and hold on to vehicles for a long time- AND purchased vehicles at about the same time. I think that’s probably likely, though I have no idea how to test it. If that’s true then the chances of running in to someone else with the same letters on their plates, or two people at the same time, would have to go up quite a lot. Still, what are the odds?

10 thoughts on “Coincidence

  1. By assuming that all 300 million plates are possible observations we get the erroneous 3.24e-09 probability. This type of assumption is known as the population assumption in Statistics.

    http://en.wikipedia.org/wiki/Statistical_assumption

    Using the knowledge that only 6 million plates are even in circulation we get a more correct version of the probability at 2.78e-08, but as you say, that isn’t that much better.

    Sounds to me like Synchronicity.

    en.wikipedia.org/wiki/Synchronicity

    You’re going through the same thing as Wolfgang Pauli, but with license plates instead of broken scientific equipment. I think we should call it the McDermott Effect.

    • I heartily approve (the McDermott Effect- I like it!). However, I’m sure someone’s described this before- it may be a sampling assumption, i.e. that the population you think you’re sampling from is the larger population (of all 6 million) but it’s actually much smaller because of the hidden explanatory variables. Interesting and thanks for your input.

  2. So I realize this blog entry is a bit dated, but I had to ask something regarding coincidences and license plates and hope you might see it

    About a year ago I had a weird license plate popup around a specific life event that seemed surreal enough I was compelled to take a picture of it. It was a quadruple ‘7777’ digit license plate. The fact that it was quadruple digit didn’t make it surreal, but it was the timing of it. Since then I have seen a total of four more quadruple ‘7777’ license plates. What’s more there have been no other quadruple digits that I have seen. Only sevens. I know they are out there, but I have seen none and trust me I am looking. Even more, these cars were passing by at a time and a manner I was able to get a photo of each one. Weird huh?

    • THat’s very weird. I wonder if the 7s could be selected because some people think they’re lucky? Like they might want to hold on to a license plate like that rather than change it when they have the decision to? I have seen at least 5-7 more YGK license plates in our area since I posted this. I still can’t decide if this is just confirmation bias (I’m looking for it so I see it) or if there’s something else going on. I’m leaning toward the latter. I’ve tried to start collecting photos too but never seem to have my phone at the handy when one passes me 🙂

      • Thank you so much for your response. So quick question about this confirmation bias. I could see having an attention to ‘YGK’ that your senses pick them up readily. How would confirmation bias apply to NOT seeing alternatives to ‘7777’, such as ‘5555’. My bias would have to be so strong I would subconsciously block others out. I feel fairly certain this isn’t happening. What I am left with is a statistically unlikely occurrance. Let’s disregard for a moment that seeing quadruple digit license plates is an uncommon occurrance. So all things being equal, when ever I cross a quadruple digit license plate (only numerics not characters), I have a 1 in 10 chance it being ‘7777’, more so if your hypothesis is correct about there being more out there. So to see five in a row would be about 1 in 1,000,000 chance, correct? Not impossible, but very unlikely.

        Long story short, I am compelled to keep this up until a different quadruple digit pops up. Not the best use of my time, but this is nuts.

        • Yeah- it applies to my problem, but not really to yours. I can’t see how you’d (reasonably) have confirmation bias against seeing other quad-numbers. If we had access to license plate records you could check if there are just more of those. Really my guess is it’s somehow related to superstition about the lucky 7 – but I have no idea about the mechanism. That is, do people request this license plate (can they even?) or is it some other way?

  3. Once I made in my mind that if I see a yellow colour car or vehicle on my way then whatever I am thinking would come true , I didn’t see it on that day but after few days I started seeing yellow colour car , bikes very frequently , even if I watch television I suddenly find the same. I don’t know if it is a coincidence,.

  4. Something similar has happened to me recently. I live in Arizona and I’ve seen cars with the same first three letters of the license plate as I have. 17 cars to be exact. This is in the last three months. On one occasion there was five, including mine at the same place. Can I you tell me the odds of that??

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