Sound Transit 3 and Cost/Benefits Detailed

Last week I published a post outlining ways to start evaluating the benefits of rail extensions in terms of costs and benefits. I used projected ridership, projected cost and a discount rate (because future benefits aren’t as valuable as present benefits) to derive an approximate subsidy per ride for a given rail extension. I emphasize approximate in part because a single number derived from a single ridership estimate for a single year can only provide so much information. But I also say approximate because I wasn’t as precise as I could have been with the costs and benefits. With Sound Transit proposing its draft Sound Transit 3 ballot measure, a decided to do a more detailed analysis of the costs and benefits of the proposal.

The basics of the analysis are the same. I still use Sound Transit’s ridership numbers and project costs and continue to use annuities to assess benefits over time. I increased my discount rate to 3% and assumed that the capital benefits last in perpetuity from the date the service is expected to open (these changes mostly cancel each other out). I also included annual operational costs into the analysis and I assumed that taxpayers pay taxes to cover project costs annually. Finally, I looked at scenarios where ridership was constant and where ridership increased by 0.5% per year. All ridership estimates use Sound Transit’s numbers, which estimate ridership in 2040.

For projects, I looked at all the rail projects (including infill stations) for which reliable ridership estimates existed, plus the two large BRT projects that are proposed as part of the ST3 draft proposal. This should cover well over 95% of proposed spending.

Before diving into the data, it’s worth defining what “subsidy per ride” means because it is the basis for analyzing the benefits of the investment. Subsidy per ride is the amount of social value we place on the average ride on the transit service. Since transit (or at least this transit) doesn’t pay for itself at the fare gates, we need to have some value for the amount that we are willing to subsidize a ride. This value comes from positive externalities such as emissions reductions and congestion alternatives. Coming up with an exact value is difficult, but farebox recovery rates for bus service provide a good litmus test.

Theoretically, bus subsidies should on average be higher than rail subsidies because buses also provide lifeline service, a social equity concern that rail systems don’t address. King County Metro has a 29% farebox recovery rate and fares ranging from $2.50 to $3.00. Sound Transit has a 22% farebox recovery rate and fares ranging from $2.25 to $5.75 for Sounder commuter rail. Given these numbers rail investments should probably have at least a 30% farebox recovery rate per dollar of subsidy though the case can be made for higher or lower subsidies.

In the tables below an $8.33 subsidy per ride corresponds to a 30% farebox recovery rate with $2.50 fare. Similarly, a $10 subsidy per ride corresponds to a 25% farebox recovery rate and a $7.00 subsidy per ride corresponds to a 35.7% farebox recovery rate. Unfortunately, Sound Transit does not provide more detailed fare information.

Here is the data on the net benefits and return on investment for each subarea and the region as a whole with dollar values in millions of dollars. Edit: Detailed formulas posted at the end of the post. For those not familiar with subarea system, the Sound Transit district is divided into five subareas and every dollar raised in a given subarea must also be spent in that subarea.


Net benefits (in millions of dollars) with 0.5% annual ridership growth.

Cumulative c-b table 5% growth net

Return on investment (1 = break even) with constant annual ridership.

Cumulative c-b table 5% roi

Net benefits (in millions of dollars) with constant annual ridership.

Cumulative c-b table no growth net

Return on investment (1 = break even) with constant annual ridership.

Cumulative c-b table no growth roi

The data tells a fairly sad story.

The most basic problem is that under less generous assumptions, the net value of the package is actually negative. That’s really troubling given that capital investments of this sort should have at least a 15% return on investment given the deadweight losses associated with taxes. And return on investment should probably be five to ten percentage points higher given that Sound Transit 3’s revenue will come from nasty regressive sales taxes. Only three out of the six scenarios meet the 15% threshold.

But the more harrowing issue is the hugely inefficient use of resources. Three of the five subareas (South King, East King and Snohomish) have a negative return on investment even with the most generous assumptions. There are lots of big projects here whose benefits do not come remotely close to covering their costs. Of course, some amount of pork to grease the wheels for a vote is inherent to the political process. But the amount of extremely wasteful spending in this proposal is rather shocking and far higher than Sound Transit 2. Notice all the red in the tables below, which show the data project by project. The net benefits for many projects are negative (and usually extremely negative) even under the most generous $10 subsidy per rider assumptions.

Table 1 c-b

Table 2 good c-b

If there is a silver lining to this analysis it is as a reminder for why rail investment in Seattle proper is so important. Even under more conservative assumptions, North King projects create over $2.7 billion dollars of value for the region and a 57% return on investment.

Overall, given these numbers and the amount wasteful spending in this project, I don’t see myself voting for it as it stands. Fortunately, the plan is not final and you can still give feedback to Sound Transit.


*EDIT: the actual specific formulas for calculating costs and benefits are:

Y = Projected Opening Year – Current Year

Benefit with .5% ridership growth

Benefit = (Subsidy * (Ridership / (1.005 ^ Y)) * 365 – Operational Costs) * (1/.025  – (1 – (1.005/.03) ^ Y) / .025)


Benefit with constant ridership

Benefit = (Subsidy * Ridership * 365 – Operational Costs) * (1/.03  – (1 – (1/.03) ^ Y) / .025)



Cost = Annual Paymnet * (1 1.03^25)/0.03 where

Sticker Price = Annual Payment * (1 – (1/.99) ^ 25) / -.01 (assumes tax base grows by 1% a year).

Assuming population increases by 1% per year reduces total cost by about 1.5% over 0 population growth.



U-Link’s Value: An Introduction to Costs

Yesterday, Sound Transit’s University Link extension finally opened to much fanfare. And deservedly so. Sound Transit projects that the extension will serve between 71,000 and 78,000 riders per day by 2030. At a 1.9 billion total cost, the project’s cost per daily rider is between $24,000 to $27,000 or roughly speaking $25,000.

Now quick question: is $25,000 per rider for a subway project too much, a bargain or a fair cost?

The answer to this question is not obvious and the overwhelming majority of Americans, including and even many ardent transit supporters, would probably not have a sound argument about the cost-effectiveness of the project. Most arguments on public transit talk in general platitudes about the importance of regional transit, growth, the environment, and world class cities or, on the other side argument, general platitudes about how transit won’t work here or transit should pay for itself.

This is a problem and the reason it’s a problem is that the actual benefits of public transit are within an order of magnitude of the costs. A project may be worth twice its cost or even maybe four times its cost, but it’s impossible to find a project worth ten times its cost, at least in a developed country. This means that if $25,000 is a fair (per rider) price for a project we should wonder whether an $100,000 project is a fair (per rider) cost for a project and be extremely skeptical of projects whose costs per rider are in the range of $250,000.

So how valuable is a $25,000 per rider subway extension? The simplest way to answer this question is to assume constant ridership over 50 years with a 2% discount rate and then determine the value per ride that makes the project worth it’s cost. For my calculations I estimated 73,000 riders and a 1.9 billion dollar cost. At those figures U-Link breaks even if we value a ride on U-Link today at $2.20. More realistically we would need to value each ride at at least $2.40 for the project to be worthwhile as break-even is generally not worth government investment.

This type of analysis represents a useful starting point for reasoned conversation about costs and benefits. If instead of $2.40 per ride the calculations suggested that the minimum benefit necessary to justify the project was five times higher at $12 per ride, the conversation would be much different. At almost five times the current fare, $12 per ride is a lot of money to spend for each rider. But $2.40 per rider is well within a realm of reason and compares favorably to current U.S. public transportation spending. U.S. transit agencies’ farebox recovery is typically around 30% (King County Metro is 29.1%) meaning that if the fare is $2.50 then $5.83 is being spent to subsidize that trip. Now this is comparing operating costs to capital costs and comparing what is often lifeline transit service with premium transit service, but overall $2.40 is a reasonable subsidy per ride compared to existing public spending, while $12 should require serious justification. 

Now this dollar per ride analysis is at best a proxy for the actual benefit of the investment. For starters, different ridership estimates may project different numbers of years into the future or use different nominal dollars and so the comparison is not always apples to apples. It also ignores systematic benefits. Many riders using Lynnwood Link will take advantage of the new tunnel between downtown and Husky stadium even if they don’t get off at one of the two stations. For this reason, core segments are more valuable than their ridership numbers would suggest.

But the more fundamental problem is that a particular ridership projection likely ignores some of the long-term growth potential around the station. Areas that have the opportunity for long range major development over 20 or 30 years should score higher than 10 year ridership estimates would suggest. Inversely, areas with minimal growth opportunities should score lower than 10 year ridership estimates would suggest. Nonetheless, cost per rider should serve as the jumping off point when discussing the merits of various high capacity transit investments.

Sound Transit is currently planning it’s ST3 ballot measure for November 2016. So with that in mind below is a table below showing the cost effectiveness of some potential Sound Transit 3 projects as well as Sound Transit 2 projects that are in the planning or construction phase.

cost per rider 2


The Concrete Fallacy

The “Concrete Fallacy” succinctly defined is the erroneous belief that building public transit infrastructure within a given neighborhood is the investment that maximizes that neighborhood’s per dollar utility. In simpler words, a useful infrastructure project in the neighborhood may be less useful for said neighborhood than an infrastructure project outside the neighborhood. Note that this fallacy applies to road networks too, but this post will focus on public transit, as people fall for the fallacy less when thinking about road networks.

The basic fact that makes the concrete fallacy possible is that transit trips, by definition, do not start and end at the same location. The speed at which one can traverse any particular part of the trip is equally important as any other part.

Let’s say you work in a neighborhood called Jobville. It isn’t particularly valuable for transit to move really fast in your home residential neighborhood if you just get stuck in horrible traffic near your job in Jobville anyways. In fact, you may find it more valuable for the transit agency to spend some money getting the bus out of traffic in Jobville so that you don’t have to waste 10 minutes each day sitting in traffic to traverse the final mile of your commute. Saving those 10 minutes near work can far outweigh any value dedicated right of way or other improvements near your relatively traffic free home could possibly bring (especially if your bus spends less than 10 minutes in your neighborhood!). Failure to realize where capital investment would most help you is to succumb to the concrete fallacy.

Of course on the individual level people rarely make this mistake, as the costs and benefits will be readily apparent. But on the neighborhood level the concrete fallacy is still a trap because most of your neighbors don’t work where you work and don’t see the value in spending transit dollars near there. There may be a fraction of people in your neighborhood that work in that area, but not nearly enough to make the immense benefits to you and those with a similar commute, outweigh the near uselessness of the investment for everyone else in the neighborhood. In this instance, your neighborhood is likely to support the investment of dollars locally. Small benefits to a large swath of neighborhood residents will be viewed as superior to acute benefits for a smaller subset of neighbors. Moreover, if you are not actually planning to regularly use the service, it is easier to see how an investment physically located in your neighborhood will benifit you and your community than one outside the neighborhood.

Up to this point I have been discussing what I’d describe as the strict concrete fallacy, wherein the benefits of capital investment in the neighborhood is less valuable for the neighborhood than investing those same dollars elsewhere. However, the more common concrete fallacy occurs when we consider many neighborhoods making spending decisions.

Let’s use the Jobville example again. In all likelihood, your residential neighborhood isn’t the only neighborhood from which people commute to Jobville, assuming it contains enough density, employment, and activities to attract people from a wide variety of neighborhoods similar to yours. If those neighborhoods pool their money together to improve trip times near Jobville, each neighborhood only pays a small fraction of the total cost of the project. So while forking up for the entire project doesn’t pencil out for any given neighborhood, the coordinated spending in Jobville may benefit the average resident of each neighborhood much more than each neighborhood spending their money locally.

Mathematically we can say that if N is the number of neighborhoods, X is the value of a local project for the neighborhood and Y is the value of the Jobville project for each neighborhood and the costs for the projects are Xc for each local project and Yc for the single Jobville project then choosing the Jobville project is the optimal outcome for each neighborhood if:

Y – (Yc/N) > X – Xc

For example, if the value in each neighborhood for the Jobville project is 12, the cost of the project is 50, the value of each local project is 15 and the cost is 11 and there are 10 neighborhoods then: 12 – 50/10 = 7 > 4 = 15  – 11.

Note that this equation does not include the residents of Jobville in calculating the merits of the project. If Jobville is mixed-use then they will presumably also benefit from the capital investment in their neighborhood. Indeed, this subtlety is a key aspect of the concrete fallacy. When people look at a map they often instinctively view rail in another neighborhood as for other people (in this case the residents of Jobville) even if it is not just for people living there but also people who want to go there, including some of their neighbors.

The concrete fallacy is insideious and has a tremendous effect on rail planning. Instead of investing in a denser rail network in the center of the city, regions tend to build large sprawling rail systems. These sprawling systems serve people’s desire to “have rail in their neighborhood,” but tend to fail to actually provide all that much mobility for those neighborhoods because they don’t effectively serve enough destinations where people from all over the city actually want to go.

Public Transit Defined

I going to make the claim that public transit isn’t buses, streetcars, light rail or any physical real world object or system, but rather a concept. Public transit is distinct from private transit in that with public transit, patrons who don’t know each other share a vehicle in order to economize operational costs and/or space. Economizing operational costs generally entails reducing labor or fuel costs. Packed trains require much less labor and fuel than a fleet of taxis carrying the same number of people. Economizing space entails taking up less space on limited capacity travel ways (generally roadways, but this could also refer to railways, airspace etc.). As long as the space available to travel through an area or city is finite there will always be theoretical value in modes of transport that use that space more efficiently per passenger. Thus, public transit is a mode or system of transportation that economizes some combination of space, labor, and energy over private transit.

The are good reasons to quibble with this definition. The most notable issue is that this definition ignores notions of social well-being, the public realm and positive externalities, attributes that are typically baked into the word “public.” Indeed, social justice is a central motivation for much bus service today. Buses are partially intended to provide affordable transportation to those who can’t drive, such as children, the elderly, and persons with disabilities as well as persons who can’t afford a car. When a transit agency proposes to cut a low ridership local bus route, people often bring up elderly people with limited mobility being unfairly burdened as a reason to oppose the proposal. Thus, most public transit service today isn’t even ostensibly ridership maximizing, because that would go against the social justice component of the service.

However, the is nothing inherent about public transportation serving social justice or the public good. Society could just as easily (though likely at a higher cost) provide vouchers for elderly people etc. to use on taxis, ubers or rideshare vans, while focusing limited public transit dollars entirely on ridership maximization. Indeed, with automated cars, this is exactly what will probably happen as hiring a cab will be far cheaper than it is today and it will make little sense to provide a local bus route, with such a reasonable alternative available. In contrast, as long as private vehicles don’t economize space, cost or labor compared to other alternatives, public transportation will have some value, regardless of what types of vehicles we might have.

With this definition in mind, public transit’s value comes into clearer focus. Public transit enables people to live in dense areas while still maintaining mobility for everyone. Cars take up too much space to make such an arrangement possible. And while denser living is not for everybody, it is for some people at certain times of their life. Dense living is also associated with reduced environmental impact, healthier living, economies of scale in social services and broadly speaking economic growth. Moreover, public transit, by making dense living more viable enables people to have more choices when deciding where to live. Urban dwellers in general strongly support local taxes for public transit for precisely the selfish reason that it enhances their living situation. Clarity on the purpose and function of public transit makes it possible to analyze how public transit achieves its goal effectively.

Hello World

Hello World

After mulling it over for quite some time, I am finally starting my own blog. The blog will be a technical blog (as opposed to personal) and will principally cover my thoughts on public transportation. However, focusing on public transportation alone would miss key aspects of the larger issues around mobility and the nature of cities that make public transit worthwhile in the first place. Thus, the blog will also include discussion on land use and transportation generally. In addition, a lot of posts will be spent looking into the not so distant future when automated vehicles become commonplace. The rise of vehicular automation over the next 15 to 25 years will have substantial implications for transportation and especially public transportation. This blog will explore some of these issues, which are shockingly absent from discussion on public transportation investments.

My next post will be a primer on public transportation, how it works and why it matters. The goal of the post is to provide a basis for conversation about more nuanced public transit issues. In other words to get everyone up to speed and on the same page. Subsequent posts will be less verbose and will by and large be independent of each other, such that they need not be read in a linear fashion. I hope to post content at least once a week on Monday mornings, but we will see how well those expectations are met.

Finally, I’d like to thank Jarrett Walker, Jeff Speck and Jane Jacobs, whose writings and ideas represent much of the foundation on which these ramblings will be built. Thanks for reading this and I hope you enjoy the blog.