Waiting in Airports
Analyzing the tradeoffs all around us through the lens of an eccentric quote
“If you’ve never missed a flight, you spend too long waiting in airports”
Long ago I read this quote. At the time it was attributed to an anonymous eccentric professor. The quote has quite a few layers and it’s topical right now because I personally came very close to missing my flight on my recent vacation. So I would like to spend this post analyzing the various layers of this quote and I think we’ll touch on quite a few interesting points along the way.
To start off with, what is the surface meaning of the quote? What is it getting at by suggesting that we should sometimes miss flights? What it’s getting at is the idea of tradeoffs. How do we avoid missing a flight? By aiming to arrive at the airport earlier. The earlier we aim to arrive the more of a buffer we have against unexpected delays that otherwise might cause us to miss our flight. Unexpected delays could be things like car crashes on the highway while driving to the airport, extra-long lines at baggage check or security, oversleeping an alarm or anything else you can think of that might cause you to be later than you expected. But aiming to arrive earlier isn’t completely free. In the case that we don’t have any unexpected delays every minute we arrive early to the airport is an extra minute that we have to spend waiting at our gate. Which is not an activity that most people find to be a particularly fun or productive use of their time. So, aiming to arrive earlier has both a cost (the extra time spent waiting at the airport) and a benefit (the reduced chance of a missed flight) and aiming to arrive later also has both a cost (the increased chance of missing a flight) and a benefit (the reduced time waiting in the airport). So, which one should we do? well, that depends on which benefit is higher which in turn depends upon many factors one of the largest of which is what time are we currently aiming to arrive. If we are currently aiming to arrive 15 minutes before the gate closes, we are risking a very significant chance of missing our flight if anything goes wrong and thus it would almost certainly be worth it to spend an extra 15 minutes in the airport by aiming to arrive 30 minutes early instead in order to significantly reduce our flight missing probability. On the other hand, if we are currently aiming to arrive 5 hours early, we can easily save ourselves an hour by aiming to arrive 4 hours early instead and the increase in flight missing probability will be very small as 4 hours is still a huge buffer. To summarize if the marginal cost (ie the small amount of time we spend to arrive at the airport earlier) is less valuable than the marginal benefit (the small amount of reduced flight missing probability we enjoy from aiming to arrive a little earlier) then we should aim to arrive earlier. If the marginal cost is more valuable than the marginal benefit we should aim to arrive later. And somewhere in the middle there will be a point (or possibly multiple points depending on the shape of the marginal benefit curve) where the marginal cost equals the marginal benefit, and this will be the ideal time to shoot for. So, what is that optimum? that depends upon a lot of factors, and it will likely be different for each person and each flight. The goal here isn’t to find a specific number but to understand the factors that go into the calculation.
The idea of thinking in terms of tradeoffs and setting the marginal benefit equal to the marginal cost is ubiquitous in economics but may seem strange or overly cold to people not used to it. Most people instead use a more intuitive form of reasoning, going by what seems “reasonable”. This intuitive thinking sometimes captures most of the important considerations but other times it can have serious deficits.
So now that we’ve seen what the quote was getting at, I want to answer two more questions. Firstly, is the quote true when read literally. And secondly, was the concept of waiting in airports vs missing flights a good example to illustrate the general point about the benefit thinking in terms of tradeoffs instead of using naive intuitive reasoning?
Is it true? Maybe for some people but not for most people and certainly not for everyone. In order for the quote, read literally, to be true, we would need that the optimal flight missing probability is high enough that when extrapolated to the number of flights taken in a lifetime it leads to a high probability of at least one missed flight. There’s one very big open variable, the number of flights taken in a lifetime. For some people this might be 1000 but for others it might only be 10. Suppose the optimal flight missing probability is 2% (this is a random guess, but it feels about right to me) then in order for someone to have a 95% or greater chance of having missed at least one flight assuming they were hitting that optimal flight missing probability exactly they would have to have taken at least 149 flights. That’s a lot of flights. A 35 year old who took 2 flights per year (1 annual vacation round trip) throughout their first 18 years of childhood and then took 6 flights per year (1 annual vacation and 2 annual work trips) throughout their 17 years of adulthood would have taken 138 flights, just under the threshold. So in conclusion, for reasonable values of the optimal flight missing probability the quote will be literally true for a frequent business flyer but dubious for a more modest flyer and certainly false for the kinds of people who have only taken a handful of flights in their lifetimes.
Was it a good example? Yes and no. On the one hand the smooth decrease in flight missing probability with the amount of time aimed to be early to the airport provided a good illustration of marginal costs and benefits so as a conversation starter it certainly succeeded on that front. However, on other fronts I think the example has some serious flaws. Firstly, we can’t neglect the fact that we just found that for the majority of people the quote is literally not true. That’s a big deal. Sure, we could make a true version by adding some caveats and making sure it was only applied to the relevant population but that inevitably detracts from the snappiness of the quote. And I don’t think this is an accident. I think the reason we need these caveats and restrictions in order to make the snappy quote true is that fundamentally airport waiting times are not good example of an area where explicit cost-benefit analysis is superior to intuitive analysis. In fact I would claim it’s quite the opposite, airport waiting times has all the qualities that make intuitive reasoning preform well.
What are the qualities of a decision that makes intuitive reasoning more or less likely to succeed? Intuitive reasoning succeeds when both the costs and benefits can be felt in a visceral way and the numbers involved aren’t too big or too small. In these cases, the brain is pretty good at adjusting its intuition to a point that’s at least somewhat close to optimal. Airport waiting times fits that description well. When you get to your gate early and have to wait the whole cost is very apparent. This is very different from questions of healthcare public policy where costs might be spread out over millions of taxpayers and benefits are spread out over millions of patients and neither one is very obvious. These are the kinds of cases where relying on what intuitively “feels reasonable” can lead to incoherent policy and where doing the math of cost-benefit analysis can save billions of dollars.
In conclusion, the original quote isn’t really true, at least not for many people, and it probably wasn’t the best example of an area where intuitive reasoning fails. But it still succeeded in providing us with a jumping off point to discuss the idea of cost benefit analysis and the idea of finding an optimum by setting equal marginal cost and marginal benefit.