Updated May 17 at 11:00 pm: Richard Gilbert has responded to this article. Rather than leave his remarks and my replies in the comment stream, I have placed them at the end of this article.

Urban consultant and former city Councillor Richard Gilbert has an article on the Globe & Mail’s blog titled “How Toronto’s transit plan takes taxpayers for a ride”. The article decries the high cost of the Eglinton LRT and in particular the high effective subsidy per rider of the capital cost of burying much of the line.

The basic premise, the questions behind the article are sound, but the methodology is not. This leads to a substantial overstatement of the per passenger subsidy for the capital construction.

At the outset, I must emphasize that my intent is not to attack Richard Gilbert himself, but rather to comment on the pitfalls involved in making comparisons between different systems, and in the use of generic formulas in planning. In many of the critiques I have written over the years, the hardest part has been to delve into the underlying assumptions and methodologies (themselves often hidden away in background papers). These may “prove” something, if only that an author found the number he wanted to find and looked no further.

Gilbert writes:

According to Metrolinx, the provincial agency charged with implementing the transit improvements, the Eglinton line is to cost $4.9-billion (an amount under review). It is forecast to carry 5,400 passengers per hour in the peak direction in 2031, eleven years after it is scheduled to begin operation. This peak rate is usually associated with an annual total of some 17 million rides. The annualized capital cost of the line is about $300-million per year ($4.9-billion amortized over 35 years at 5 per cent). Thus the capital cost per ride will be an extraordinary $17.50 ($300-million divided by 17 million). This will be the effective subsidy per ride if the fares to be paid roughly cover the operating costs.

Central to this calculation is the translation of a peak point/hour demand of 5,400 to an annual ridership of 17-million. The Eglinton route, like many transit lines in Toronto, is not a commuter line feeding unidirectional demand into one point like a GO train. It is a route (actually several bus routes) serving an overlapping set of demands. Many riders on the line do not contribute to the peak point count — a peak measured westbound to Yonge in the AM peak will not include any riders using the west end of the line, nor will it include any counter-peak traffic. Many riders will not contribute to the peak hour counts — the ratio of off-peak riding on the TTC is much higher than on GO Transit even where all-day service is provided.

Any claim that a single peak point’s ridership can be translated to an annual figure will be inaccurate because it ignores the characteristics of the line as a whole.

A good example of a single line with multiple overlapping demand patterns is 504 King. In practice it is made up of at least four major sets of demands:

Parkdale to Dundas West via Roncesvalles

Parkdale and Liberty Village to Downtown

Riverdale and King East to Downtown

Riverdale to Broadview Station

Some of these have counter-peak flows (notably Liberty Village) contributing to the all-day ridership without affecting the peak point.

To get a sense of the range of values that might be “reasonable” for this sort of back-of-the-envelope analysis, I turned to Metrolinx demand projections and TTC ridership data.

[As a general rule, I am a strong advocate of envelopes as the best place to test hypotheses. If you can’t do a decent estimate, preferably mostly in your head, as a first cut, then you should take up another line of work. The important points are having rules-of-thumb that are accurate most of the time, being able to catch the exceptions, and choosing the right envelopes.]

Metrolinx Demand Data

As a backgrounder to The Big Move, Metrolinx produced a set of demand estimates for their network. Although I do not agree with some of the results from their model (mostly because of assumptions regarding service levels and capacities that would actually be provided), the numbers are useful examples of the anticipated behaviour of major transit routes following substantial expansion of Toronto’s network.

Peak Annual Ratios Metrolinx

The first set of lines in this table are “Express Rail” routes where frequent two-way all-day service would be operated. The first three columns of figures are taken from the Metrolinx demand backgrounder (see Appendix C starting on page 26):

Peak hour boardings (number of riders on the line during the height of the rush hour)

Peak point peak hour ridership (number of riders at the peak point and direction in the peak hour)

Annual riders (note that this column is in millions)

The next three columns give ratios between:

Peak riders and peak point riders. If a line is serving only one demand (e.g. commuting in to a terminal point like Union), then the ratio of peak riders and peak point riders will be very low — almost all peak riders pass through the peak point in the peak direction. If a line has a diverse demand (local demand hubs along a route and/or counterpeak flow), then the ratio of peak riders to peak point riders will be higher (many of the peak riders don’t go through the peak point, at least not in the peak direction).

Annual riders and peak hour riders. If the nature of routes are that most ridership has a common pattern (mainly peak, or a “standard” amount of off-peak demand), then the ratio between annual and peak hour riders will be similar for these lines. If many of these ratios are identical, then the annual figures are simply a projection up from the peak hour numbers, not a modelled value in its own right. If a route has a higher ratio of annual to peak hour riders, then it has good off-peak and/or counter-peak demand.

Annual riders and peak point riders. This ratio will reflect the relationship between peak hour and peak point ridership. Again, if these numbers have the same value for many routes, then this would show that they were obtained using a standard conversion factor, not from an actual simulation.

For the Express Rail lines, the ratio of peak riders to peak point riders varies from 1.08 (Richmond Hill) to 2.33 (Lakeshore West). This shows that almost all of the projected demand from Richmond Hill is going to the same place and will pass through the peak point, and that there is almost no counterpeak flow. By contrast, Lakeshore West has riders with a more diverse set of origins, destinations and directions of travel, and so its total peak hour riding is over twice the peak point demand.

The ratios of annual riding to peak hour riding are quite consistent in the range of 1625:1. The slight variation will be due to rounding in the ridership numbers. This shows that the annual figures are derived by factoring up the peak hour figures using a standard formula.

For the all-day services to Georgetown and Bradford, the calculations show similar results, but with a lower factor used for conversion between peak and annual riding of about 1370:1.

When we turn to Metrolinx estimates of demand on the TTC subway network (remember that these are numbers presuming a full build-out of The Big Move and are for year 2031), we see very different results.

The ratio of peak hour to peak point riders varies from a low of 1.53 (Spadina subway) to 4.27 (Bloor-Danforth subway). The two major subways have good diversity of travel patterns and so they have many more peak riders on the line as a whole than at their peak points. Interestingly the Downtown Relief Line comes third in the list at a respectable 3.26 showing a strong modelled demand that is not oriented to one node or time period. The very close values for most lines raise suspicion of whether these are actual annual ridership numbers or values projected from the peak hour.

The ratios between annual and peak demands are fairly consistent for three lines (BD, Sheppard, DRL, with Spadina close by) while the Yonge-University line is an outlier. This is particularly evident in the high ratio of annual demand to peak point demand of almost 20k:1.

When we turn to Metrolinx projections for the Transit City routes, we see that the annual ridership has been calculated with a factor of about 2045:1, quite similar to what we see on most of the subway lines. Whether this produces reasonable results will depend on:

Whether each of the lines has the same pattern of demand (overall riding versus peak point and direction, and time of day usage effects).

Whether each of the lines matches the general behaviour of the subway system for which a similar factor appears to have been used.

Finally, we come to the figure Richard Gilbert used in his article. He claims that 5,400 peak point riders translates to 17-million annual riders. This is a ratio of 3148:1, considerably below the value for urban routes and more indicative of the projections for “Express Rail” regional corridors.

TTC Routes

As a cross-check on the Metrolinx numbers, I turned to TTC data (to the extent this is possible).

Peak Annual Ratios TTC

The data available for TTC routes is not the same as in the Metrolinx projections, and so a different tactic for analysis was required. The first three numeric columns of this table contain:

Peak vehicles per hour calculated by dividing the headway (in seconds) into 3600.

Peak capacity calculated as the number of vehicles (with some rounding) times 74 (CLRVs), 104 (ALRVs) and 54 (buses). On the assumption that the design capacity of the service matches the peak hour demand, I have used this as a surrogate for an actual peak count. On routes where the peak is very short, this will overstate the demand, but on busy routes, the peak tends to be smeared out and the design capacity is probably a good indicator of peak demand on the vehicles (as opposed to latent demand on the street). (The King corridor is a special case because of service design including many trippers. The capacity is built up from the component services.)

Daily riders. These numbers are taken from the TTC’s report on route performance and they are a few years out of date, but for the sake of this discussion, they will do. In all cases, these are real numbers, not estimates factored up from peak values.

The ratio between daily ridership and peak capacity varies from 17.5 on St. Clair to 39.2 on Dundas. It is hard to assign a meaning to any specific value, but in general the range of numbers will reflect various factors:

A low ratio indicates that more riding, proportionately, occurs in the peak for such routes and/or that peak service is comparatively generous relative to demand. It should be noted that the high capacity for King is not provided over the entire route, and so this ratio is not really stated on the same basis as with other lines.

Routes with multiple overlapping demands will show a higher ratio of overall riding to peak point capacity. St. Clair is at a disadvantage here because its service does not extend east of Yonge Street and it has fewer opportunities for distinct local demand centres.

The Spadina route has been omitted because the TTC only reports combined ridership for Spadina and Harbourfront and, therefore, I cannot calculate ratios just for the busier Spadina segment.

The daily ridership is factored up to an annual value by multiplying by 300. This effectively presumes that each weekday counts for “1” while weekend days and holidays count for about “0.5”. In turn, this gives ratios of annual ridership to peak point capacity (and imputed peak demand).

For the routes I included, these values range from a low of 5,254 (St. Clair) to a high of 11,757 (Dundas). None of these numbers “means” anything in an absolute sense. They are useful only to show the difference between the patterns of ridership and service levels on various routes. All of these values are much higher than the factor used by Gilbert in his estimate of annual ridership on the Eglinton LRT route.

Indeed, the factors for the Eglinton buses are about 6800:1 (west) and 11200:1 (east). Splitting the difference, a ratio of 9000:1 would not be out of order, and this would triple the projected annual ridership. In turn, the capital subsidy per rider would be cut in one-third. If the Eglinton LRT attracts even more riding that does not pass through the peak point and hour, then the ratio would go up, and the cost per rider will drop even more.

It is worth noting that the ridership on the two Eglinton bus routes combined is about 18m per year, higher than the number Gilbert uses in his article. This implies that ridership years in the future would actually fall, something that is difficult to believe.

All of this yields a rather full “back of the envelope”, and there are several assumptions/estimates along the way. However, my envelopes tend to be quite reliable after years of practice. If someone wants to challenge the methodology or come up with a better estimate, please do so, but be sure to include all of the steps including any claims about demand that may have been derived through “fudge factors” rather than real planning.

How Expensive is Too Expensive?

Gilbert’s other major argument is that the Eglinton line is overpriced with a cost of about $250m per kilometre. This is considerably higher than the cost for other projects with some degree of tunnelling such as the Canada Line in Vancouver ($110m/km), Seattle (also $110m/km with tunnelling) and generic surface LRT systems ($35m/km).

The Canada Line comes up often as a point of comparison, but a few things are worth noting about its design and construction:

The tunnelled portion was built cut-and-cover, not with deep-bored tunnel, at a considerable saving. This also placed the stations closer to the surface and reduced their construction cost.

The Canada Line tunnels are smaller than the Eglinton LRT tunnels, as are the stations themself.

Soil conditions in Vancouver were considerably simpler than what Metrolinx/TTC will face in Toronto with a tunnel that crosses an undulating terrain including underground streams.

Also, the amount of underground work on Eglinton is somewhat larger than the commonly cited figure (11 of 19km) because the stations at Don Mills and Kennedy (including their approaches) will be underground. $250m/km is comparable to the cost for the Spadina extension from Downsview to Vaughan Centre which is all to be in bored tunnels.

I agree that we must avoid high-cost underground construction wherever possible, and that was, of course, the reason for my long-time advocacy for surface LRT where it makes more sense than a full-blown subway. Even if some parts of an LRT line must go underground, the technology can run on the surface and should do so wherever possible.

Wasting money on transit is not the exclusive preserve of LRT advocates.

Updated May 17 at 11:00 pm: Richard Gilbert replies, and I respond to his comments.

Dear Steve,

Thanks for going to so much trouble to question my annual ridership estimate. I must admit to simplifying the matter, and I should have at least acknowledged current ridership on the four bus routes that serve the portion of Eglinton where the LRT is to run. I also simplified my account in ways that work in the other direction (many rides on the Eglinton LRT will be partial, congestion at Yonge-Eglinton will be a deterrent to expansion, ridership of LRT routes is usually, but not always, lower than predicted, etc.). Nevertheless, all in all, I’d be happy to accept a convincing higher estimate of ridership. However, if you are truly suggesting 51 million riders by 2031 without substantial at- and near-station development we’re going to have to continue to disagree.

Steve: I’m not sure where the ridership number will settle, and part of the problem is that even the starting point, 5,400 per hour at peak, obviously presumes a considerable increase over current riding and with it some change in land use. I agree that this will have to occur to reach those numbers.

Metrolinx projections are extremely frustrating because it is impossible to determine which factors drive the change from today’s demand in various corridors to the 2031 values. A related issue is that they model a fully-built network when we all know we’ll be lucky to see half of “The Big Move”, and not necessarily the parts we really need. There is no sensitivity analysis to the removal of selected parts of the network to see how the remainder would behave and, by extension, just how critical some segments might be. For example, which of many routes that could drain loading away from the Yonge line are actually the most attractive to riders (current and future) and therefore have the best effect on that criterion?

Unlike your criticism of my ridership estimate, I don’t find your defense of the high cost of the Eglinton LRT the slightest bit convincing, and I’m not sure you do either. If you could apply your remarkable analytical skills to a more in-depth analysis of this matter we would likely all benefit.

Steve: I was trying less to defend the cost of Eglinton (which would get into a discussion of construction prices in Toronto generally) than to point out that claims for some other cities, notably Vancouver, do not take into account differences in circumstances from one project to another.

Another fault of my piece, which I readily admit to, was pointed out by a correspondent from the CD Howe Institute: I did not admit that $17.50 could be worth much less as years pass. This, or course, depends on whether we have inflation or deflation. I’m inclined to think we will have more inflation, to relieve government debts, but sustained economic depression could well bring us deflation. Thus, this was another simplification.

The headline the Globe gave to my piece, which I did not object to at the time, I see in retrospect as changing the article’s messages. My primary intention was to blow a horn yet again that I have been blowing for several years: that we need more development at higher-order transit nodes, and thus new ones should be planned with this in mind. My secondary intention — also frequently advocated — was to draw attention to the absurdly high unit cost of the Transit City proposals, particularly the Eglinton line. My headline for the piece focused on how to reduce the capital subsidy.

I’ve lived in Toronto for 44 years and have not owned a car for the last 41 of them. I may not use the TTC as much as you because I live more centrally and bicycle a lot. But I do use it several times a week and I’m becoming truly offended and alarmed about the deterioration in everyday service. In this context, extravagant capital spending is especially repugnant and I would like to do what I can to prevent it.

Best wishes,

Richard

If we are going to attack the $250m/km cost on Eglinton, we must also attack the 8.6km, $2.4b Spadina project ($279m/km). The North Yonge project is for a 6.8km extension at a cost of $2.4b (2008). That’s $353m/km before escalation. Projects like this eat up huge amounts of capital (not to mention the political effort to raise the money one way or another) when there are many competing uses in transit and elsewhere.

I wish that Metrolinx would break down the components of the Eglinton cost so that we knew how much is due to tunnels (and stations), how much to surface construction, how much to fleet and maintenance facilities. With a single combined figure, it’s not easy to say whether we are getting hosed for individual components. I suspect at this point that they don’t want to get into detailed estimates for fear of giving bidders on each component a sense of the budget they are aiming for.

I agree with you that we need to find less extravagant ways of building transit, and we also need to turn attention to the day-to-day service which is the “store window” for transit, the thing that attracts or drives away business.