Confessions: An Alternate Take on "The Fraud of Saved Time Calculations"

John Ragan

I've been reading Confessions of a Recovering Engineer, and I've reached Chuck's criticism of saved time calculations, of which I have always been skeptical. However, I have a different interpretation of the problem than Chuck does.

The book focuses mainly on the issue of assigning a monetary value to time and the fact that humans don't actually behave according to their "hourly rate". Given the prevalence of people struggling to use their time in a rational manner, especially in the age of gamified social media, I don't buy this argument.

I think that the "fraud" in saved time calculations is fundamentally a mathematical error, not an economic or philosophical one. I see the problem as twofold:

1. The Way Time is Quantized. Most humans plan their day in increments of 5, 10, 15, 30, 60, etc. minutes depending on the activity. Saving 30 seconds on a trip might save some people from being late for work, but it won't have any meaningful effect on most people's daily schedules. When I plan a trip in Google Maps, 44 minutes and 46 minutes are effectively the same number to me. The real amount of time "saved" on average when 30 seconds is shaved off a trip is considerably less than 30 seconds. To use a money analogy, it's the difference between digital and physical currency. Corporations engaged in "microtransactions" can make millions of dollars by having computers earn $0.01 billions of times. A penny, on the other hand, is a uselessly low-value coin from a human perspective, and it's a disgrace that the U.S. Mint still produces them. Or nickels. Or dimes. Pennies end up discarded on the side of the road like the trash they are (don't litter, kids), but highway expansion advocates are using "microtransaction" accounting practices and assuming that everyone will actually go to the store and spend their pennies.

2. The Inherent Imprecision of Multiplying Very Small Numbers By Very Large Numbers. I'm tempted to call this a "floating point error", but that might be a controversial description. In any case, multiplying a very small estimate by a very large estimate is a very reliable way to arrive at results that make absolutely no sense... or at least have a very high level of uncertainty. First, any subtle uncertainties or inaccuracies in the estimate of the smaller number are massively amplified. For a highway project, if the average trip is actually shortened by only 20 seconds instead of the 30 seconds estimated, that difference of 10 seconds has massive implications when multiplied by millions of trips. Moreover, bad actors trying to purposefully "massage" a study to reach the conclusion they want have an extremely powerful lever for tipping the results in their favor. But it goes deeper than that. As alluded to above, 30 seconds is, practically speaking, a very small amount of time. "Negligible", as an engineer might say. Choosing to include one negligible-number-multiplied-by-a-big-number (time savings) in an analysis but to exclude other negligible-numbers-multiplied-by-a-big-number (increased health risks due to air and noise pollution, social damage to the fabric of neighborhoods, etc.) is a mathematical catastrophe. You can use the wild imprecision of such logic to justify literally anything. And the "Infrastructure Cult", as Chuck calls them, certainly do.

I think that Chuck does implicitly capture a lot of the "missing" stuff unfairly discounted as "negligible" in my Point #2 in his analysis by focusing on empirical results instead of theoretical estimates (i.e. bad design destroys community ∴ net value is obviously negative), but I think he's wrong about the mechanism of the "saved time" error.

Anyway, I'm pretty sure that 50% of my day job is paid for based on economic assumptions that the American coal industry will continue to grow exponentially through 2060, so the question of "What if the people coming up with these numbers are idiots?" is near and dear to my heart.



Please sign in to leave a comment.