When Toronto dug its first subway, the long lines of streetcars on Yonge were proof of a ready-made ridership.

More recently, though, subway boosters have needed to weigh potential demand when making the case for the expensive form of transit. Which is why the city planning department's new and higher Scarborough ridership projection last year was so pivotal, and so controversial.

An old ridership projection pegged peak one-direction usage at 9,500 passengers per hour, barely enough to justify a subway extension. The new one – which appeared as the transit debates rose to their crescendo – boosted peak ridership to 14,000, almost beyond the capacity of light rail.

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In a stroke, the case for a subway was much stronger.

Amid political squabbles, good projections can help cut through the debate and offer the closest thing to an impartial assessment of a subway line's worth. But if they're wrong, they can help lumber a city with an expensive white elephant such as the under-used Sheppard subway.

The problems on Sheppard – where ridership is about one-third the original projection, forcing heavy subsidies – speak to the dilemma with forecasting. Planners looking to the future have to make assumptions that could, with the benefit of hindsight, prove unwise.

In the case of the Scarborough extension, the bulk of the nearly 50-per-cent increase in projected ridership is based on two decisions that raise questions. Planners assumed a train frequency that does not appear budgeted for and they assumed that transit projects that today are unfunded lines on the map will be completed.

But these assumptions are not cast in stone. Although pro-subway politicians like to declare the project irrevocable, the planners who produced the Scarborough projection are the first to stress that their work is preliminary. Even though all three levels of government have committed big dollars to the project, much more analysis needs to be done and a more accurate ridership figure has yet to be determined.

Councillor Josh Matlow, who continues to advocate for a light-rail line in Scarborough, views the latest number with skepticism, He still recalls how frustrated he was at council trying to determine the basis and validity for the increased ridership figure that emerged at such a pivotal moment.

"Right now it's still clear that there's different numbers that are competing with each other," he said recently. "It's not like we just didn't happen to have the information. I clearly asked for the information… that information never came to the floor of council… and council decided nonetheless just to move forward, regardless."

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With the debate about Scarborough continuing to reverberate through the mayoral election – as recently as late June, Premier Kathleen Wynne had a chance in a press conference to state definitively that the province's funding for transit in that part of Toronto would be for a subway only and chose not to do so – The Globe took a close look at the math.

More trains

Although subway boosters have argued for years in favour of more underground transit in Scarborough, the numbers undermined their case.

But there were signs of hope in 2013, when the transit debate heated up again and city planning staff produced new data showing peak ridership of 14,000 per direction per hour by 2031. This represented a huge rise over the previous projection, done in 2006, which pegged peak ridership by 2031 at 9,500 people an hour, easily within the capacity of an LRT.

Mike Wehkind, program manager with the Transportation Section of the city's Planning Department, said that the "lion's share" of the jump was because the model they were using to project ridership assumed an increased frequency of trains in the subway extension.

The model back in 2006 assumed that half the Bloor-Danforth trains would go only as far as Kennedy and then turn back, with the remainder carrying on to the final station. The new model – based on current TTC service levels – assumes every train will continue on to the end of the line.

It's far from clear, though, how often the trains would run if the extension gets built. A city report in 2013 suggested TTC budgeting for the project assumed only enough new vehicles to run half the trains to the final station. The TTC did not respond to a detailed question about train frequency.

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The exact portion of the increased ridership due to greater train frequency would be impossible without more research, Mr. Wehkind said. "It certainly is an important part of it, you know. I just don't know if it's 60 per cent or 50 per cent or 40 per cent, or 35 per cent, for that matter."

Based on those rough estimates, running only half the trains through to the end of the line could theoretically drop ridership to between 11,300 and approximately 12,400 per hour at its peak.

The process sparked concern from widely read blogger and local transit expert Steve Munro, who said that, while he had no reason to believe the planners had "cooked the numbers," he wondered if there might have been willful blindness.

"Dare I say that when you run a model and it produces the results you want, you stop working."

A changing landscape

Another reason for the increased ridership figure is it takes into account proposed and ongoing transit projects, making the assumption they would all come to fruition.

In the summer of 2013, that looked like a reasonably solid idea. The Liberals were being propped up by an NDP that appeared unwilling to force an election. Ms. Wynne, a former transportation minister, had become Premier and was promising a serious discussion on funding transit expansion.

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Fast forward to now and the picture looks much murkier. The conversation on funding dwindled into silence. Shortly before the election, the Liberals unveiled a plan to fund $15-billion worth of transit expansion in the Greater Toronto and Hamilton Area, but earmarked only about half the money needed. A major expansion in suburban commuter rail could cost as much as $12-billion, leaving little for other projects if different sources of money are not found. And those projects – including ones that could affect Scarborough ridership – will be among a longer list jockeying for funding.

Eric Miller, director of University of Toronto's Transportation Research Institute, said that it is normal to start a projection with what he called a full build-out scenario. This model includes everything you might possibly build. After this, he explained, you start adding and removing elements from the model to see what results this causes.

"We often get kind of locked into 'the scenario for the future' and then spend a lot of time debating it, where we really should be looking at, you know, what are the differences if we do different things?" Prof. Miller said. "And it's those differences that I think are important. The absolute forecasts we know are going to be wrong. Just the question [is], how wrong?"

He said that a problem in government is that they often lack resources to produce and analyze multiple variations on a model. Mr. Wehkind, at the city's planning department, confirmed that this work is only just beginning. It will be next year before this more detailed analysis is tabled.

Ed Levy, whose book Rapid Transit in Toronto detailed a century of ambitious plans that too often didn't come true, called it "foolhardy" to include in the model projects that remain very much up in the air.

"Certainly not when you're trying to seek the commitment of billions of dollars, for a project that is of questionable benefit, that's for sure," he said.

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If the broader transit landscape changes substantially, the current projection for ridership of a Scarborough subway extension would invariably have to be adapted. And another wild card is mayoral candidate John Tory throwing his support behind the provincial plan for increased suburban commuter rail, with an unknown effect on Scarborough subway demand.

More than numbers?

Although planners stress that early projections are works-in-progress, politicians have a tendency to run with the number if they like what they hear.

This happened after Toronto Transit Commission CEO Andy Byford repeatedly described the projection during last year's debates as being "on the cusp," justifying either type of transit. With a projection that offered some solace to both subway and LRT camps, more subjective factors – among them value for money, impact on motorists, city-building and Scarborough alienation – became the dominant narratives in the debate at city hall.

In recent interviews, two of the biggest subway supporters on council played down the importance of ridership, suggesting that momentum and doing the right thing in Scarborough are more important.

"All Toronto residents should have access to a good healthy vibrant transit system," said Councillor Glenn de Baeremaeker, a subway booster through whose ward the extension would run. "If it went as low as 9,000 people per peak hour, I would still say you build the system, just like you did when you built it up to North York [in the 1960s]."

And fellow councillor Karen Stintz, who helped orchestrate the move away from light rail, said the numbers were just one component of an important city-building project that cannot be derailed.

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"I'm only concerned about the divisive debate that we'll have if we reopen this issue. That concerns me more than anything," said Ms. Stintz, whose changing position on transit was widely seen to be a stepping stone for her mayoral candidacy. "From my perspective, there's no going back."

In the planning departments of the city and TTC, though, work will continue.

The 14,000-passenger figure for a Scarborough subway extension will be further refined through an environmental assessment. If the data being used in the model change, so will the result. For staff at the TTC and the city, the projection is considered a good first stab.

"What is actually going to be happening by 2031? I don't know. I think then it would probably fall somewhere within here," said Bernard Farrol, senior planner with the TTC, gesturing to the projections for 9,500 and 14,000 riders.

Later in the interview he elaborated, speaking about the larger of the two figures.

"We would be in the ballpark," he said. "How big is that ballpark? I'm not going to say that. But, would it be double that? I doubt. Would it be half that? I doubt."