The Case for More Card Readers: How Bechtel’s Single Entrance Costs Students 1,454 Hours Yearly

1. The Problem

$130,000. That is my estimate of waste at Bechtel.

Most visitors to Caltech’s newest residence were probably surprised when they first found out that the 212-room building has just one entrance, an issue which, as a resident of Bechtel myself, has been more inconvenient than I originally anticipated. There are various doors around Bechtel, as shown by the circles in the below floor plan. However, only the southern main gate indicated in green has a card reader, while every other door indicated in red has no card reader and can thus only be used as exits. Therefore, due to their inability to use these doors as entrances, Bechtelites often spend a minute more than necessary to journey back to their room.

My goal in this article is to add up all of these seemingly negligible wastes, summing over all students, over many years. I will then propose and justify ways of valuing (in cold hard dollars) these massive collections of tiny time intervals, ultimately to illustrate the scale of the benefit which just one small change can make.

(Source: Floor Plan of Level 1 of Bechtel Residence)

2. The Time

Having found a document detailing the precise number of students living in each region of Bechtel, I approached this problem by considering each possible combination of approach direction and region. This is because, in the best case, a student returning from the south to his room in region A wastes no time by going through the main entrance; in the worst case, a student returning from the north to her room in region B must walk around the outside of Bechtel rather than simply entering through the northern door, adding roughly 2 minutes to her journey. I therefore estimated the added time for each of the 28 combinations of direction and region, taking into account the positions of stairs in estimating the times for levels 2 and 3.

Additionally, students don’t return to Bechtel from each direction equally: the south, for example, being the direction of the main campus, is more likely to be approached from than the north. I therefore also estimated the weekly rates with which students would return from each direction and factored those rates into my calculations. With just the above assumptions, I arrived at the following values:

Average Number of entrances (per student per day)	4.3
Average wasted time (per entrance)	25 seconds
Wasted time (per student per week)	12.47 minutes
Academic weeks per year	33
Wasted time (per student per year)	6.86 hours
Number of students	212
Total wasted time (per year)	1454 hours

1454 hours per year. Just consider that. What would you do if you could get that many extra hours? How much would you value that?

3. The Money

How valuable is a Caltech student’s time? That’s hard to say, especially given the peculiar situation I am currently considering. Most people would intuitively feel that 60 separate one-minute chunks have a different value to a single uninterrupted hour; as Ec 11 students might say, the marginal value of time is not constant. On one hand, working on a problem set for 60 minutes probably gives more than 60 times the benefit of working on it for 1 minute. On the other hand, there are situations where a single minute can have a large effect: consider the fact that there is only a 5-minute gap between class periods, making each gap especially valuable. A single minute might be the difference between whether or not a forgetful EE student has time, between back-to-back lectures in the Moore Sub-basement, to go back to his Bechtel room to get his homework (the one that Prof. Glen George as usual insists be done on paper). In this case, a single minute can be what decides whether the hours spent on the homework pay off. Given the examples on either side, therefore, on average, whether the time was wasted as big chunks or small intervals has no crucial impact on the total value of that time.

What about the argument that the time wasted from walking wouldn’t have been productive anyway? The value of leisure and work is equal to an ideal logical student (because the student is already operating at the margin of the trade-off between work and leisure). Even if someone assigns a value of 0 to the inherent value of leisure, it is still a fact that, after a certain amount of work, leisure allows them to be more productive in future work. Even someone who only cares about pure productivity would value leisure.

So, values should be assigned to this situation in a utilitarian manner, even if doing so seems intuitively ridiculous. Since I saw no reasonable way of personally estimating the average worth of a Caltech student’s time, I chose to calculate a range of possible total values using a range of possible hourly rates:

Possible valuations of the 1454 wasted hours per year:

	Hourly rate	Total wasted value (per year)	per student per year	Over 5 years
Federal minimum wage	$7.25	$10,543	$50	$52,715
Pasadena minimum wage	$17.50	$25,449	$120	$127,243
Maximum Caltech UG pay	$38	$55,260	$261	$276,298

Five years is a confident estimate of the lifespan of a card reader. Therefore, taking the middle of the above range, $130,000 is a reasonable estimate for the waste that a set of five card readers installed on the five exit-only doors can prevent. Sure, any individual estimate I made could be criticized. Maybe students enter 3 times a day on average, not 4; maybe journeys from the north are far rarer than I guessed. What is almost certainly accurate, though, is the order of magnitude of my estimation—that the value wasted over 5 years is somewhere between $50,000 and $500,000.

I can hardly imagine that card readers (installation costs and all) require tens of thousands of dollars apiece. So, I hope that Caltech can consider my calculations, invest in five card readers, and solve this problem for present and future Bechtelites.