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Telling stories with the help of data.

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DC Metro

If you rely on Metrorail for your evening commute, you may see savvy riders waiting outside the gates shortly before 7:00 pm. Then, like clockwork, they swipe into the station at the top of the hour. These thrifty riders clearly aim to qualify for Metrorail’s cheaper off-peak fares that kick in at 7:00 pm.

While evaluating Metrorail data, I wanted to quantify this financially-sensitive behavior – How many Metrorail riders are delaying the start of their trip for off-peak pricing?

In the process, I found that some riders, depending on their itinerary, were more likely to wait than others. Interestingly, these varying behavioral responses appear to stem from different incentives created by the pricing structure.

This report explains why some riders traveling particular, seemingly arbitrary, distances have relatively more to gain by waiting for off-peak fares. 


Ridership Patterns

Fares of WMATA’s Metrorail are divided into peak and off-peak periods. On weekdays, peak fares are in effect from opening to 9:30 am, and again from 3-7 pm; off-peak fares are charged all other times. Peak period riders benefit from extra trains and shorter wait-times between departing trains. For these advantages, peak period riders pay more than riders traveling during off-peak periods.

Since most riders must get to work by a particular time, the morning commute often does not offer riders much wiggle room. But when traveling home from work, commuters tend to be more flexible with trip start times.

I chose to focus on WMATA data for times when riders could most feasibly delay their travel times to receive off-peak rather than peak prices. Does the data support that some riders, after weighing the opportunity cost of time, are making a rational economic decision to adjust their travel time and save money?

Metrorail data confirms that some riders entering stations on weekdays around 7 pm – on the cusp of the peak/off-peak fare change – delay their entry to qualify for off-peak fares.

Looking at weekday ridership at the most frequented Metrorail stations, the graph below suggests that some riders are delaying their travel times to receive the less expensive off-peak prices. This is evidenced by the “bump” at 7 pm, which runs counter to the natural pattern of declining ridership over this period.

Exhibit 1

Source: WMATA origin/destination-level ridership data from April - May 2015, aggregated to six minute intervals. [Behind the Visual]

Source: WMATA origin/destination-level ridership data from April - May 2015, aggregated to six minute intervals. [Behind the Visual]

Taken at face value, this bump is what we’d expect as riders respond to the pricing incentive. It’s only when digging a bit deeper that a curious pattern emerges.

Exhibit 2a shows the average number of riders who exited select stations after beginning their trips at any of the nine entry-stations displayed on Exhibit 1 at either [6:54–6:59 pm] or [7:00–7:05 pm].

On Exhibit 2a:

  • The blue line predicts the “normal” generally-declining trend of Metrorail riders, assuming there was no fare change at 7 pm (i.e. assuming Metrorail’s existing peak to off-peak fare structure did not exist);
  •  The black lines represent trends at the top nine exit-stations where rider tendencies most contradict the “normal” behavior represented by the blue line. Data from these exit-stations indicates that riders are clearly delaying travel to secure off-peak fares; 
  • Notably, however, the grey lines represent trends at exit-stations where riders are not waiting for lower off-peak fares.

Exhibit 2a

Source: WMATA origin/destination-level ridership data from April - May 2015, aggregated to six minute intervals. [Behind the Visual]

Source: WMATA origin/destination-level ridership data from April - May 2015, aggregated to six minute intervals. [Behind the Visual]


Personal Explanations: Travel Time Needs

Looking again at Exhibit 2a, it’s possible delayed travel to ‘black-lined’ exits is not related to off-peak fares, but simply indicates that riders going to these exits need to travel later. For example, they could hold jobs that require them to work later than riders traveling to other stations.

However, if we extend Exhibit 2a to include the subsequent time interval [see Exhibit 2b], the ridership spike to ‘black-lined’ exits appears limited to the first period of off-peak fares.

Exhibit 2b

Source: WMATA origin/destination-level ridership data from April - May 2015, aggregated to six minute intervals. [Behind the Visual]

Source: WMATA origin/destination-level ridership data from April - May 2015, aggregated to six minute intervals. [Behind the Visual]

Further, throughout the 45-minute period surrounding this singular uptick, regression results suggest there is no difference in the trend of ridership to grey-lined vs. black-lined exit-stations. So we cannot explain away the ridership uptick to particular exit-stations as a difference in riders’ travel-time requirements.


Personal Explanations: Income

Income differences between riders are another potential explanation for the varying ridership responses to off-peak fares. Maybe riders associated with lower incomes are prone to delay travel for off-peak pricing.

Using Metrorail survey data I estimated the average income of riders by exit-stations.

A quick check reveals the average income of riders delaying travel for off-peak fares compared to riders insensitive to the fare change is nearly identical ($108,286 and $108,514 respectively). 

While this doesn’t rule out riders’ incomes as a factor, it’s enough to suggest there is likely another motivation causing riders exiting at certain stations to be more sensitive to off-peak fares.

Now let’s look more closely at the Metrorail fare structure.


Metrorail Fares: A Brief Refresher

According to WMATA and regardless of where your trip takes you, off-peak fares were designed to be “generally a 25% reduction from peak fares.

But in actuality the percentage discount between peak and off-peak Metrorail fares varies quite a bit - depending on the specific distance of a rider’s trip. This may be the reason that riders’ behaviors vary depending on their exit-stations.

As context, let’s consider the details and history of Metrorail’s current fare structure.

Metrorail relies on distance-based fares. For trips at or less than three miles, a flat fare is applied. After three miles, an incremental fee is added for each subsequent mile of travel. While the off-peak base fare is only 19% less than the peak base fare (as displayed in Exhibit 3), the difference between incremental off-peak and peak fees is larger.

Exhibit 3

By this metric, riders traveling three or less miles receive a 19% discount by waiting for off-peak fares. For longer trips, with incremental fees in play, the total off-peak trip discount will move towards but never surpass 25% [Exhibit 4a].

Exhibit 4a

Still, this variation in percent discount, between 19% and 25%, seems small and unlikely to cause rider responses to vary significantly.

But due to the existence of well-intentioned off-peak “fare caps”, off-peak discounts for trips of certain distances are significantly greater than 25%.


Metrorail Fares: Discovering Off-Peak Discount Spikes 

Metrorail’s off-peak fares originally followed a simple three-tiered structure. But in 2012, off-peak fares switched to a fee-per-mile pricing calculation. When this change was enacted, and to avoid imposing excessive price increases for Metrorail riders, WMATA instituted “fare caps”. (see How are Metrorail Fares Calculated?)

One fare cap ensures that off-peak fares are limited to no more than 47% of what the same trips cost in 2010. As Exhibit 5a shows, the 47% fare cap is triggered for trips of just under seven and ten miles in length (right before 2010 off-peak fares jumped tiers). A “max fare cap”, providing that the top allowable off-peak fare charged for any Metrorail trip is limited to $3.60, comes into effect before a third 47% limit is reached.

Exhibit 5a

Exhibit 5b displays Metrorail’s current peak fare pricing superimposed on off-peak pricing. Because the peak structure was never strictly tier-based, there is no 47% fare cap on current peak fares. There is a max fare cap on peak fares of $5.90. Comparing Metrorail’s max fare caps for off-peak and peak travel with respect to distance traveled, the off-peak max cap comes into effect before the peak max fare cap.

In summary, Exhibit 5b clearly shows that the difference between peak and off-peak fares increases when off-peak fare caps are triggered.

Exhibit 5b

For a moment, let’s refer back to Exhibit 4a. At face value, Metrorail discounts range from 19-25% for off-peak travel.

Now, consider the actual percentage discounts applicable to off-peak travel when off-peak fare caps are triggered. As displayed in Exhibit 4b, actual current off-peak Metrorail fares in these cases can exceed 25% discounts from peak pricing. And in some cases, for trips of longer lengths, off-peak fares are almost 40% less than peak fares. 

Exhibit 4b

Source: WMATA origin/destination-level ridership data from April - May 2015, aggregated to six minute intervals; WMATA History of Fare Increases. [Behind the Visual]

Source: WMATA origin/destination-level ridership data from April - May 2015, aggregated to six minute intervals; WMATA History of Fare Increases. [Behind the Visual]

So why are riders traveling to ‘black-lined’ exit-stations [Exhibit 2a & 2b] significantly more likely to delay starting their Metrorail trip until off-peak pricing is in effect?

Without fail, all fifteen ‘black-lined’ exit-stations are at a distance, from multiple entry-stations in question [Exhibit 1], subject to larger than expected discounts.

In support of visual evidence displayed on Exhibit 4b, consider the regression analysis which finds both percent discount and income to be significant predictors of one’s likelihood to wait for off-peak fares.


Conclusion

If we look again at ridership patterns at the most frequented entry stations - this time dividing riders by off-peak discount levels - the trend is apparent. As potential savings grow, more riders delay travel for off-peak fares and the ridership uptick at 7 pm steepens.

Exhibit 6

Source: WMATA origin/destination-level ridership data from April - May 2015, aggregated to six minute intervals; WMATA History of Fare Increases. [Behind the Visual]

Source: WMATA origin/destination-level ridership data from April - May 2015, aggregated to six minute intervals; WMATA History of Fare Increases. [Behind the Visual]

Large percentage discounts incentivizing Metro riders to delay travel are the unintended consequences of policies aimed to cap off-peak fares. And through this, we see how carefully attuned riders are to their environment.

Small tweaks in the fare structure have large behavioral effects.

Interestingly, while riders are internalizing their own percent discount, they are likely unaware that the rider next to them may be confronting a drastically different pricing incentive. The mileage for specific trips is not readily available to Metro riders. And even if it was, the special mileages subject to abnormally large discounts aren’t common knowledge.

So when your lease is up, is it worth moving to a Metro station where the mileage between home and office falls in a sweet spot (just under seven or ten miles), leaving you with a short commute and more affordable off-peak fare?

Maybe not, but regardless you can use this calculator to know if you are — or can be — one of the lucky few.

Download: Interactive Off-Peak Savings Calculator


Thanks to Justin Antos and Michael Eichler of WMATA for providing data and insight along the way.