The Myth of Supermarket Line Karma

Supermarket line karma is a myth. Yes, yes, I know, it happens to you all the time. Whatever line you get in at the supermarket (or airport, or concert, or fast food restaurant, or …) moves slower than the one beside it, and almost certainly slower than every other frickin’ line in the place.

I know I always feel like it happens to me. I usually warn people who get in line behind me at supermarkets or airports that they should pick another line. I have bad queuing karma — the line I’m in is always the worst.

But it’s almost certainly not true. Look at it this way: Assume there is a supermarket with four equal-length lines. Call them a, b, c, and d. For the sake of argument, let’s say that each line has an equal chance of being “fastest”, where fastest is defined as being the one where the person in position Nx (queue position N, line x), reaches the front first. Assuming the probabilities hold, it’s straightfowardly obvious that there is a seventy-five percent chance your line won’t be first. In other words, most of the time some other line will be fastest.

You protest, however, that there are plenty of times when your line starts out shorter than the other lines, and so I should finish first. Not so fast though. In general shorter lines should finish first, but keep in mind that the amount of time people spend at the front is a random variable, one with significant positive skewness. In other words, while the distribution of checkout times (unadjusted for scanner or bagger skill) is kinda normal, it has a significant right skew with a correspondingly fat right tail (i.e., those darn people with suitcase-sized purses who full-arm fish for a checkbook about three feet down). Further, there is a cumulative effect, where small delays cascade quickly, with a single tiny problem (“Can someone get me a price for organic, free ranch avocados?”) rapidly causing the queue to go out of kilter.

All of this is, of course, just Queueing Theory For Dummies, but I’m sitting in an airport lounge right now, having just spent the last twenty minutes in a line that went slower than all the ones around me. Hey, I needed some way to pacify myself.

Related posts:

  1. RiteAid, Queuing Theory, and the Law of the Slowest Line
  2. Power line is bigger bandwidth?
  3. The Google Guidance Myth
  4. The Myth of the Myth of Disruptive Technology
  5. The Myth of the Drinker’s Bonus

Comments

  1. flambeee says:

    this is an example of the availability heuristic.
    basically, people tend to recall instances which retain significant cognitive or emotional salience. and since “losses loom larger than gains” then we tend to recall instances in which we lost at something much easier than instances where we broke even or won a bit. so getting the raw end of the line lottery, which is really simple chance, just seems like it happens every time because we remember better those times when it does occur.
    the availability heuristic was discovered and described by danny kahneman and amos tversky. kahneman is a social cognitive psychologist who won the nobel prize in economics for his (and tversky’s who unfortunately passed away before the award) explication of prospect theory.
    their work with heuristics and prospect theory served as the foundation of behavioral economics although one would never know it by the rigid and stagnating mockery economists and other posers have made of the field…
    in other news, call me poo poo head but i really do hope the consumer blows the doors off of march and april and gives the fed no other choice but to choke the economy once and for all. the sooner we take this bitter medicine the sooner we can enter a collective 12 step recovery program, gluttonous americans anonymous, admit that we are helpless in our addiction and offically begin the healing and recovery process…
    “hi, my name is flambeee and im a gluttonous american swine…”
    thanks for allowing me this space to rant a bit…

  2. Zoli Erdos says:

    “darn people with suitcase-sized purses who full-arm fish for a checkbook about three feet down” … and of course they wouldn’t start writing that check until the cashier is all done:-(

  3. JohnD says:

    “The New Yorker” discusses line queues– http://www.newyorker.com/talk/content/articles/030113ta_talk_parker (This article from a 2003 issue mentions why supermarkets can’t have a first-come, first-serve system like some banks and airlines.)

  4. I was thinking about this just last night and I think it’s not so random: something like….speed of cashier x NÂș people in queue x amount of goods x age of each person in the queue :)

  5. The late Stephen Jay Gould had a typically eloquent solution. After a lenghty discourse on the uncontrollable factors affecting the speed of any given line, he suggested always using one of the extreme outside lines; with only one adjacent line, the odds of being faster than your neighbors goes from 1/3 to 1/2.

  6. Roger Bohn says:

    But there are some situations where the apparent bias against you is actually true. As my stochastic process prof said (one of the few things I remember ): “Crowded buses have more people on them.” So on average, the bus you are on will be more crowded than the average bus!

  7. An elegant description, Paul — and totally correct, of course. And yet, I bet you still have a niggling feeling that your line does go slower than others. The human brain wants to see patterns, even when there are none. And for what it’s worth, a research study showed that a surprisingly large proportion of otherwise reasonable people also believe that their presence at a sporting event affects the outcome.

  8. I agree with Mathew– we do look for patterns when there are none to be found.
    That said, I can provide a way to avoid long waits at the DMV: Bring reading material. The act of preparing for a long wait actually eliminates it. With 99% certainty. I Promise.
    Thanks for the diversion.

  9. Franklin Stubbs says:

    There is also a significant variation in the speed of the cashiers.
    The other day my wife and I were checking out with about fifty bucks worth of stuff. I noticed that our checker was the hair-twirling talkative type. On a whim we decided to switch to the next line, which was at least two customers longer but had a no-nonsense type behind the cash register.
    We were done and gone before the woman previously in front of us even had her stuff on the belt.