In an earlier posting, I talked about the Forest Hill bus and the methodology used to identify candidate routes for service cuts.  The rule is simple:  if the number of passengers lost per dollar saved is less than .23, then the service goes on the list for evaluation of cutbacks.  The same process is used in reverse for new services:  if they will attract .23 riders per dollar expended, then they are implemented on the system.

What is the magic about .23?  At least if it were something like .42 we might attribute this to some long and complex process involving much Deep Thought.

To discover the meaning of .23, we need to delve into the history of the TTC Service Standards.

Up until 1998, the TTC evaluated its routes in a different way from today.  They calculated the supposed cost and revenue for each line in ways similar to present methods, but the criterion for unacceptable performance was different.  In 1997, the standard was that no service receive more than five times the average subsidy per rider.  Back in those days, the average subsidy per rider was 24 cents, and the cost recovery rate was in the high 70s percent.  Five times the maximum subsidy was $1.20.

It is worth noting that only four routes failed to make this standard:  139 Huntingwood, 10 Van Horne, 115 Silver Hills and 121 Front-Esplanade.  Our old friend the Forest Hill bus sat at a quite respectable 61 cents per rider or just under three times the maximum permitted subsidy.

By 1998, the scheme had changed and the riders per dollar figure came into being at, wait for it, the magic level of .23.  If we invert this figure, the dollars per rider value is $4.35.  This is a very generous figure compared with the old $1.20 maximum, but that was on the all-day average, not out at the margins for a new service.

Looking at Forest Hill we find that it has gone from a decently performing route in 1997 to a poor performing route in 1998.  The line carried 580 passengers per day, up slightly from 540 in 1997.  However, the revenue allocated to the route dropped from $420 (76 cents each) to $340 (59 cents each).  The operating cost went from $750 per day (rush hour only service) in 1997 to $1,000 per day because mid-day service was added in February 1998.

The analysis of Poor Performing Routes that appears in the 1999 Service Plan (published in August 1998) claims that cutting peak service on Forest Hill would have an impact of .10 riders per dollar saved.  We already know that peak service on the route costs about $750 (from the previous year’s report), and that most of the riders are in the peak period, say 500 of them.  If we are going to save $750, you can see that we have to keep most of the existing riders on the system.  At .10 rider per dollar, we will lose only 75 of them.  (It’s a bit more complex, but you get the idea.)

The crucial point here is the assumption made about how many riders will be lost to the TTC.  This information is not published in the Service Plan.  Note that a route can show up on this list simply because we assume that we can cut service without chasing many riders away, and this calculation is hidden from scrutiny.

If, for example, we assumed that cutting the Forest Hill bus would lose half its riding, we would lose 250 riders to save $750 (gross, because we also lose their fares) or a riders per dollar value of .33, well above the criterion.

Let’s go back to the 2005 Service Plan and its evaluation of the route.  Ridership has grown to 750 at a revenue per head of 69 cents (still not at the level assigned back in 1997).  Costs are up to $1,300 per day, and the revenue/cost ratio is 41 percent.  We can work backwards from the 80 percent system average to figure out that the minimum recovery under the old scheme would have been 40 percent.  Forest Hill is near the line, but not over it.

Meanwhile, analysis of possible elimination of service gives a riders per dollar value of .17 peak and .14 midday.  We know that most of the riders are in the peak, and so we will use a value of .16 here.  This means that the TTC assumes that they would lose around 200 of the 750 riders if they eliminated the service.  That’s an improvement from the 1998 analysis that assumed almost no riders would be lost, but still we had to work backwards to the assumptions.

Now let’s return to tha magic number .23 riders per dollar.  The idea is that we can spend a dollar to get .23 new rider or, equivalently, spend $4.35 to get a new rider.  However, this number has not changed since it was introduced back in 1998 despite a claim in the 1999 Service Plan that the number is updated every year.  A small matter of inflation intervenes.

It costs a lot more today to add more hours of service or buses to a route, but you still get the same number of new riders.  The dollars spent goes up, but the riding counts don’t, and you need far more riders today to “justify” adding new services or to save existing ones from the chopping block.  If the TTC’s operating costs have gone up by 30 percent, then the riders per dollar value (an inverse function) should go down by 30 percent from .23 to .16. 

Such an adjustment would have a significant affect on many routes now deemed to be “Poor Performers”.  Forest Hill, as I said earlier, would be marginally acceptable rather than well below the line.  I suspect that some proposed service improvements, rejected because they didn’t make the .23 criterion, might have slipped through using .16.  We will never know.  The TTC doesn’t include this information in their Service Plan report.

Finally, one other subtle factor is the effect of moving from the old two-thirds cost recovery level to the new 80 percent level.  If we were looking at a Maximum Permissable Subsidy of five times the system average, here is what happens:

Assume revenue per rider is 80 cents (just for the sake of it).  This means that the cost per rider is 100 cents and the subsidy is 20 cents.  Five times the subsidy is 100 cents and therefore the maximum permitted cost per rider is 180 cents (80 cents revenue plus 100 cents subsidy).

However, if the cost recovery ratio is only two-thirds, then for that 80 cent ride, we have a cost per rider of 120 cents.  The subsidy per rider is 40 cents, the maximum subsidy is 200 cents, and the maximum cost per rider is 280 cents.

It is ironic that as the farebox recovery rate goes up, any formula based on a multiple of the subsidy will actually lower the total amount of money our formula lets us spend per rider and hence the amount of service we can give them.

This exercise is not going to save the real dogs of the system from further review, but it shows how we can be caught up in the magic of a formula without understanding how it actually works.