How Many Residents Ride IndyGo?

Very Few Ride Very Often

Introduction

At a meeting of the Indianapolis City-County Council’s Municipal Corporations Committee the CEO of the Indianapolis Public Transportation Corporation (“IndyGo”) was asked how many Indianapolis residents ride IndyGo buses.  IndyGo conducts on-board surveys from which she could have inferred that more than 24 out of 25 Circle City residents either never ride IndyGo or ride it on less than one day a month.  Perhaps because that answer would have been inconsistent with IndyGo’s “transit is essential” campaign, however, she denied having even a rough idea of how many residents take the bus.  This post will therefore go through the exercise of inferring what she refused to.

In the process we will describe what was probably an error in an estimate on which our previous post based its statement that “less than 2% of Marion County residents take the bus even once a year.”  This will not only illustrate a type of statistics problem that might profitably be considered in high-school math classes but also show why students should learn to be wary of conclusions based on reported “studies.”  We will also see that the subsidy cost imposed upon residents far exceeds any likely benefit.

“Twenty-Six Thousand Folks Do Use Transit”

Our previous post’s statement was based on a statement quoted in a news report about a 2017 IUPUI Polis Center study.  The report quoted study co-author Matt Nowlin as saying, “Twenty-six thousand folks do use transit and half of them use it to get to work every day.”  That 26,000 figure would have meant that only 2.7% of Indianapolis’s 969,466 residents ever took IndyGo buses, so our estimate of less than 2% seemed reasonable in light of IndyGo ridership’s having since fallen from 9,193,293 to 5,152,520. 

But there were two problems with our estimate.  The first is that we read “at least once a year” into Mr. Nowlin’s “do use transit,” whereas he hadn’t really said that.  By that 26,000 figure he could have meant to include even people who hadn’t ridden IndyGo since the 2012 Super Bowl activities.  This would have implied that fewer than 26,000 take IndyGo at least once a year.  The other problem is that his estimate was probably based on a math error.  Although correcting that error doesn’t much change our conclusion that in Indianapolis transit actually is not essential, we will discuss it in detail because it’s a good example of how in statistics even the simplest of concepts can cause confusion. 

Frequency Data

To that end we will make an estimate from scratch based on the above-depicted data recently presented to IndyGo’s board of directors.  To express Fig. 1’s categories in terms of the number of days per year on which rides were taken we’ll multiply the first seven categories’ numbers of days per week by 48.2 weeks per year (to allow for vacations and sick days), convert the one- and two-days-per-month frequencies to twelve and twenty-four days per year, and take “less than once a month” to mean anything less than twelve days per year.

We’ll then convert the resultant number of days on which riders take the bus to the number of rides they take.  This will require that we guess how many rides the average rider takes on a day when he rides the bus.  We note in this connection that 50.9% of respondents to a previous survey said they would also be making the same trip in reverse on the same day.  And IndyGo’s board was told that 88% of one-way trips require only a single bus: the average number of bus rides in a one-way trip is at least 1.12.  Those two quantities may be dependent, but if they aren’t they imply that riders average at least (1.509 × 1.12 ≈) 1.69 rides on days when they ride.  Moreover, some riders who aren’t taking the same trip in reverse still take at least one more bus ride on the same day.  So we’ll guess the average is a little over 1.69.  Specifically, we’ll assume that riders average 1.75 rides on days when they take the bus.

We have to make another guess, too.  Note that the “first time riding” category tells us nothing about how frequently the respondent would be taking the bus; someone who’s riding for the first time could be a new resident who will be taking the bus every day, just as someone who’s been riding every day at the time of the survey may be about to move away and never ride again.  And a significant number of survey respondents who fell into the “first time riding” category may well have been visitors instead of residents.  Given that only 1% of respondents fell in this category, though, we probably won’t go too far wrong by simply ignoring it and so normalizing the other categories’ percentages that they add up to 100%.

The Naïve Estimate

Cell G14 in the spreadsheet below displays the resultant estimate: that only about 23,000 residents ever ride IndyGo.  The values in Columns G and E represent the normalized percentages p in the various categories and the numbers d of days per year on which those categories’ passengers ride, while Column F’s values are the results of multiplying d by our assumed r = 1.75 rides per day to obtain respective categories’ ride frequencies f. 

The formula bar at the top shows that we calculated the average ride frequency F = 396 rides per year as the scalar product f • p of the categories’ frequencies and (normalized) percentages.  (As Cell E2 shows, that average-frequency value F is based on taking “less than once a month” to mean four days per year, but it turns out that nearly the same F value would have resulted from any Cell E2 value less than twelve days per year.)  We obtained Cell G14’s resultant number of different riders by dividing the average frequency F into 2016’s total number N of bus rides taken.  As Cell G15 indicates, this seems to say that only about 2.4% of Marion County’s 969,466 residents rode the bus that year. 

Now, we’ve made some guesses about quantities such as how many rides people usually take on the days when they ride.  If we set the guesses aside, though, the foregoing spreadsheet calculation might at first seem to be exactly the right approach to estimating how many residents ever take the bus in a given year.  After all, the number F of rides taken by the average rider is by definition the total number N of rides divided by the total number R of riders: F = N ÷ R.  And weighting frequencies f by the percentages p of riders who ride at those frequencies would seem to be the right way to calculate that average frequency F.  So our calculation R = N ÷ (f • p) would seem to follow by simple algebra.  And, since Mr. Nowlin’s 26,000-rider estimate is fairly close to Cell G14’s 23,196, it would seem to be reasonable.

The Probable Error

But that reasoning is based on the tacit assumption that the percentages p are percentages of residents who ever take the bus, and that’s probably not what those percentage values actually mean.  Those data came from a survey that was taken on board the buses.  So instead of, for example, the Cell G9 entry’s meaning that 29% of riders take the bus five days per week, it probably means that 29% of the rides are taken by riders who ride five days per week. 

A simple example will illustrate the distinction.  Suppose that 50% of the residents who ever take the bus ride one day per week and that the remaining 50% ride four days per week.  Among those who ever ride, the average frequency would then be 2.5 days per week.  If survey respondents are chosen randomly from among the riders in the seats, though, about 80% of them will respond that they ride four days per week even though only 50% of the total rider population actually does.  Without compensation for that bias, the resultant average-frequency estimate would be 3.4 days per week instead of 2.5, seeming to make the logged number of rides imply a smaller number of riders than it actually does.

Frequency Compensation

To make a more-accurate estimate of how many residents ever ride we’d therefore need to compensate for ride frequency.  Specifically, we’d need to divide the response percentages by the corresponding frequencies and then so scale the results that they add up to 100%.  In our hypothetical this would mean dividing 20% and 80% by 1 and 4, respectively, to get 20% and 20%, which normalization converts to the correct 50% and 50%. 

Now, it could be that such compensation was actually used in producing Mr. Nowlin’s estimate.  As we will see later, though, that doesn’t seem likely.  In what follows we will therefore assume that the survey takers saw their job as profiling the average cohort of riders in the seats, not as profiling all the people who ever take the bus, so we will perform the type of compensation we did in our hypothetical. 

The formula bar at the top of Sheet 2 contains the Excel formula for performing such compensation, i.e., for converting the percentages p of the people on the buses to the percentages q of the people who ever take the bus.  Column H displays the results.  Row 14 shows that thus compensating for the on-board bias increases the number of riders from 23,196 to 46,148, so Mr. Nowlin’s estimate was probably low.  As Rows 18 and 19 show, though, this compensation does not increase the estimated percentage who ride at least three days per week, and it actually reduces the estimated percentage of riders who ride at least five days per week.

Something else that performing such compensation tells us is that basing estimates on data from an on-board-survey makes the estimated number who ever ride at all more uncertain than the estimated number who ride frequently.  Unlike Cell G15’s uncompensated estimate of the percentage who ever ride the bus at all, Cell H15’s compensated estimate of that quantity is quite sensitive to the value we use for the “less than once a month” category.  If instead of Cell E2’s four days per year we had assumed only one day per year for that category, our estimate would have been 8.9% instead of 4.8%, whereas assuming eleven days per year would have made that estimate 3.9%.  In contrast to that all-rider estimate, on the other hand, Cells H16:H19’s compensated frequent-rider estimates, like the corresponding uncompensated values in Cells G16:G19, would be found to be virtually independent of Cell E2’s value.  

Again, we can’t be sure that Mr. Nowlin’s estimate resulted from failing to compensate for frequency.  But we think it probably did.  Rather than the more-recent survey whose data Fig. 1 depicts, his estimate was probably based on an earlier on-board survey, and that survey found fewer frequent riders and more infrequent riders than the more-recent one.  If Mr. Nowlin had compensated the survey results for frequency we’d therefore have expected a rider-population estimate higher than the frequency-compensated estimate we found above.  The fact that on the contrary it was lower suggests that he didn’t perform the compensation and that our previous post’s estimate based on his was therefore low.

The Update

So to answer the question that IndyGo’s CEO ducked we’ll take Sheet 2’s approach but update its calculations to reflect IndyGo’s ridership decrease from 9,193,293 in 2016 to 5,152,520 in 2022: 

As a result of this update Cell H15’s value for the fraction of residents who ride the bus at all falls from 4.8% to 2.7%: although that particular calculation’s sensitivity to assumptions makes it relatively uncertain, it still suggests that our previous post underestimated the number of those who ride even once a year.  But the more-certain estimate in Cell H16’s tells us that something like 49 out of 50 Indianapolis residents either didn’t ride at all last year or rode on less than one day a month.  True, that value depended on our guess that passengers average 1.75 rides on bus-riding days.  But even if we assume the theoretical minimum (i.e., even if we assume that every rider rides only once on any day he rides), we would still conclude that more than 29 out of 30 residents ride less than one day a month. 

In other words, transit in Indianapolis is hardly “essential.” 

Math-Education Topics

Obviously, the error we explored above is minor in the context of deciding whether “transit is essential.”  But we went through the exercise because it illustrates that when it comes to statistics even studies issued by our institutions of higher learning are vulnerable to elementary errors. 

That fact may be relevant to a debate that arises from time to time about the high-school math curriculum.  In a 1986 fantasy movie called Peggy Sue Got Married a fortyish woman faints and wakes up to find herself back in high school, where she tells her math teacher, “I happen to know that in the future I will not have the slightest use for algebra, and I speak from experience.”  The experience of most real-world adults is probably the same.  Some critics have therefore argued that the high-school mathematics curriculum should be shifted to statistics from its current focus on algebra and other calculus prerequisites.  The rationale is that most adults never use calculus but do encounter statistics quite often, in things like news reports (and political discussions of issues like transit subsidies).

Now, we haven’t found that rationale entirely convincing.  For one thing, statistics itself requires calculus if it’s to be studied in much depth.  Moreover, a significant minority of adults do use algebra, geometry, and/or calculus from time to time.  So dispensing with the current math sequence doesn’t seem wise. 

But within the existing curriculum there may be room to discuss some of the simpler statistical pitfalls, such as improper uses of averages.  More generally, students who “will not have the slightest use for algebra” can still profit from learning how vigilant they need to be if they’re not to be misled by the math they see in news reports. 

A casual reader might have failed to notice, for example, that the news report of Mr. Nowlin’s 26,000-rider estimate didn’t actually say that the study he co-authored produced the quoted estimate.  It turns out there’s a good reason for that omission.  All the study did was describe in terms of age, race, employment level, ride frequency, and trip purpose five groups into which survey respondents had been divided by canned cluster-analysis software applied to vectors whose elements were those respondents’ races, employment levels, household languages, and neighborhood bus-service levels.  Despite the study’s “Who Rides the Bus?” title its grouping of respondents didn’t answer that question noticeably better than the survey it was based on did. 

More to the point, the study didn’t provide Mr. Nowlin’s 26,000 figure—or any other estimate of how many residents ride.  As support for the estimate the study, that is, it was little more than window-dressing.  A healthy skepticism of study citations may be beneficial.

The Larger Question

Although the low percentage of residents who ride IndyGo is indeed eye-opening, a more-important question is probably whether taxpayers’ IndyGo-subsidy expenditures are worthwhile.  The proposition that they are is highly questionable in light of the fact that the vast majority of residents are paying for a service they never use.  But for the moment let’s set aside those expenditures’ value to taxpayers generally and concentrate initially on just the riders.

As evidenced by the average fare, even the value that riders themselves place on those rides is only about a dollar,¹ whereas IndyGo’s CFO recently said that providing those rides this year will cost about $23 per ride.  Although even that figure is probably an understatement—dividing the overall budget of $263.1 million by, say, 6.5 million rides comes to over $40 per ride—it still works out to more than $5 per passenger-mile, probably more than twice what cabs cost and well over an order of magnitude greater than our average transportation cost.  If we paid that much for all Indianapolis transportation its cost would exceed Indianapolis’s entire aggregate personal income; there’d be nothing left for food, clothing, or shelter.

Whereas IndyGo provides less than than 80,000 passenger-miles per day, Indianapolis streets conduct about 20 million vehicle-miles per day in non-Interstate traffic alone.  That probably translates to about 25 million daily passenger-miles per day.  So IndyGo provides less than a third of a percent of Indianapolis human transportation.  Yet according to Table 2 of the latest available IndyGo financial report, IndyGo received over $150 million in subsidies.  Even if we ignore the portion residents paid through state sales and federal gas taxes and consider only what they paid through local property, income, and excise taxes the local subsidy exceeded $110 million.  That’s two-thirds as much as the entire Indianapolis Department of Public Works’ $164 million transportation budget for last year—to subsidize less than one-third of a percent of Indianapolis human transportation.

Transit-Oriented Development

Proponents attempt to justify such outlandish expenditures by arguing that a subsidized bus system attracts “transit-oriented development” and thereby increases the tax base.  This seems to be such an article of faith among urban planners and transit-subsidy proponents that it’s rarely questioned.  But it should be.

Consider what transportation expert Randal O’Toole found when he investigated “transit-oriented development” in Portland, Oregon, which is a perennial darling of transit planners:

Because the demand for living in small apartments on noisy streets is limited, Portland and other cities have had to subsidize such developments. When Portland opened its first light-rail line in 1986, it zoned everything near light-rail stations for high-density development. Ten years later, planners reported to the Portland city council that not a single such development had been built. To encourage such development, the city decided to use a variety of subsidies, the most important of which was tax-increment financing, to dense developments along the transit lines.

And, pressed in a Municipal Corporations Committee meeting for evidence in support of IndyGo’s claim that its Red Line alone is responsible for over half a trillion dollars of development along that route, IndyGo’s CEO could only produce opinions of booster organizations like Indy Chamber. 

The Indy Chamber representative did claim that a store had cited the BRT as an “integral reason of why they’re locating there,” but he provided no evidence that the store wouldn’t have located somewhere in Indianapolis anyway.  And to the extent that subsidized-bus stops do attract development he provided no evidence that IndyGo doesn’t thereby reduce development in districts that don’t have stops.  Nor did he attempt to prove that city buses attract more people into Marion County than transit taxes drive to the doughnut counties.  Or explain why development along the Red Line needs to be subsidized by tax-increment financing if the Red Line is what’s mainly attracting it. 

Of course, we’re dealing with a counterfactual; no one knows what development would look like in the Red Line’s absence.  But we do have good reasons to suspect that the Red Line isn’t a substantial net positive for Indianapolis development.  By counting, say, Saturday-morning traffic at a point on the Red Line’s College Avenue stretch we might find a traffic frequency on the order of ten cars per minute.  In contrast, IndyGo and Federal Transit Administration records show that in the entire month of April the Red Line provided only 88,932 rides and that the average trip length on the 13.1-mile Red Line is 3.6 miles.  During the Red Line’s 20-hour operational day, in other words, less than a single bus passenger per minute (88,932 passengers/month ÷ 30 days/month ÷ 20 hours/day ÷ 60 minutes/hour × 3.6 miles ÷ 13.1 miles ≈ 0.7 passenger/minute) passes a Red Line location that probably sees over ten times that many cars.  

Given this lopsided ratio and the fact that the Red Line’s appropriation of a travel lane from College Avenue has reduced car traffic on that street, it’s quite likely that the Red Line has reduced rather than increased College Avenue businesses’ market exposure.  That would be true even without the street closures that Red Line repairs have necessitated.

This isn’t to say that no business owner has based any location decision on the Red Line’s presence.  No doubt some have indeed been duped by IndyGo propaganda.  In the long run, though, businesses’ success depends on realities, not propaganda-driven illusions.  And, again, it’s entirely likely that any development the Red Line does attract to its corridor would have occurred somewhere else in the city anyway. 

Conclusion

Even if we take the on-board-survey bias into account, we conclude that only a tiny fraction of Indianapolis residents ride IndyGo even once a month.  And there’s just no hard evidence that “transit oriented development” provides residents enough benefit to justify IndyGo’s outrageous cost.

1. True, that statement ignores what’s sometimes referred to as “consumer surplus”: some riders would be willing to pay more than they have to.  Given IndyGo’s refusal to increase fares for over a decade despite inflation, however, we are entitled to speculate that the average consumer surplus is not great.