Big event logistics and Taylor Swift

Or … the case for a stadium-specific train station in Foxboro instead of a sea of parking.

Football stadiums are big, but where do they “belong”?

Football stadiums are generally unlike other types of stadiums. With a few notable exceptions, baseball parks and hockey/basketball arenas are located in relatively urban areas. While they are sometimes surrounded by parking lots (ahem, Chicago) there is usually (but not always, looking especially at you, LA) relatively good transit access. Baseball stadiums generally seat around 40,000 people and are used for 80 to 90 games per year (plus other events), arenas seat fewer than 20,000 but a basketball-football-event arena may be used more than 150 times per year.

Football stadiums are much larger (generally 60,000 to 90,000) but far less frequently used. Aside from 10 or 11 football games, even a large city may only attract a few acts which can fill a 70,000 seat stadium: the Taylor Swifts and Bruce Springsteens and Beyonces of the world. MetLife Stadium in New York has just 23 large events aside from football this year, meaning it sits idle more than 300 days of the year, and it is likely the most heavily-used stadium in the country. There are only a few stadium-level acts touring at any time (it’s a lot easier to fill a 20,000 seat arena compared with a 80,000 seat stadium) and outdoor events can really only take place between May and October in most places. A large stadium will be a ghost town most of the time, not a great land use if you’re trying to build a vibrant area around it.

A ballpark or arena may see upwards of 4 million visitors per year, spread over 100 dates or more. Football stadiums may barely crack one million, concentrated into a couple of dozen dates. These two factors mean that these large stadiums are often sited differently than smaller arenas in the US. But when nearly 100,000 people descend on one location, it’s not easy to accommodate them. Football stadiums can leverage existing downtown infrastructure (transit and parking) but this can lead to or exacerbate to poor surrounding land use. Or they can be built in another existing, American amenity: the suburbs.

A quick aside: American like our stadiums like we like our highways: big. Of the 11 stadiums with a capacity over 100,000, eight are in the US (all college football, two of the other three are cricket, the third is in North Korea so who knows how big it actually is). NFL stadiums are usually a bit smaller, with more premium seating. Still, they’re big, Americans drive cars a lot, and football fans like to stand outside their cars and eat food and drink beer before the game so with few exceptions, at least some outdoor parking is present.

As Ray Delahanty recently pointed out, it’s tricky to get good land use with that size of an arena if it’s placed near a downtown. I’d go further: in the United States, football stadiums are so big and so car-focused and lightly used they don’t belong downtown at all. There are large stadiums in non-US cities which manage to avoid parking seas, although in general they are located in cities where the majority of people don’t drive (don’t worry, they still drink before the game). Of stadiums larger than Soldier Field, the smallest NFL stadium (62,000 seats), 70 of 153 are in the US, including 29 NFL stadiums and plenty of other college stadiums. (Other countries with at least 3 on this list: UK with 7, Germany and China with 5, Brazil with 4, Japan, Mexico, India and Spain with 3, often with access to multiple metro lines or near a major railroad station.) So midsize metro areas and college towns in the US have larger stadiums than the national stadiums in most countries.

Because of these factors (big, America, cars), football stadiums have developed with a lot of parking. The actual football field of play covers 57600 square feet, or about 1.3 acres (wider soccer fields are about 77,000 square feet). The stadium surrounding the field might take up around half a million square feet, or 10 times more. The parking around a football stadium? It takes 10 million square feet (in some cases, more), about 230 acres, which is worth point out is more than about a square kilometer, or nearly 20 times as much space as the stadium and 200 times as much as the field itself.

Many stadiums are indeed surrounded by this sort of sea of parking. Professional American football stadiums tend to fall into two broad categories: those in the suburbs and those downtown. (Larger college stadiums are often much less parking-dependent: many fans come from the adjacent campus and weekend games utilize campus employee parking which otherwise sits empty). Suburban stadiums are generally parking seas: in nearly all cases they utilize stadium-specific parking. (The two exceptions are in Green Bay, when neighborhood streets, yards and lawns soak up much of the parking demand, and Santa Clara, where nearby office parks can be used for weekend events.)

Urban stadiums are rarely islands in the middle of parking seas. For the most case, they rely on existing parking facilities in the downtown neighborhoods they border. There are two glaring exceptions, both of which somewhat paradoxically date back to the early 1900s:

  • Denver’s Mile High Stadium (or whatever it is called now) is urban-ish. It’s a bit more than a mile from Union Station and the edge of Downtown, too far to take advantage of Downtown parking garages, although there are some closer transit connections. It was originally built on land that existed because it was an early-20th century landfill.
  • The South Philadelphia Sports Complex, which dates to filled river delta area in the 1920s. The original purpose of the land was to build a large arena for the Army-Navy game larger than the ballparks which football fields were typically squeezed into at the time. This led to perhaps the most robust stadium-only transit service in history. Since neither team was local (the game taking place roughly in between Annapolis and West Point), the Pennsylvania Railroad ran dozens of special trains to a temporary station built on a rail yard adjacent to the stadium, handling tens of thousands of cadets, midshipmen and other attendees. The extension of the Broad Street subway line wouldn’t be built until the 1970s.
Grif Teller’s “Mass Transportation” depicting the Army-Navy game trains.

No modern stadium has been built near a city center with a full 10-million-acre parking ocean. Even here the economics don’t work to have massive parking lots only used a few days per year. It makes much more sense to utilize nearby parking garages which are usually empty on Sundays and that’s what generally occurs. There is some space for tailgaters, but most event-goers use parking garages. An added benefit: downtown areas are designed (for better or worse) to accommodate a lot of people arriving by car at the same time, and usually has a decent transit system which can bring in a fair number of event-goers as well. It’s interesting that there are a number of cities with NFL stadiums and no appreciable rail service: Las Vegas, Jacksonville, Charlotte, New Orleans, Detroit, Indianapolis, Nashville and Cincinnati, and only Atlanta really has a heavy rail-served downtown stadium

Moving a lot of people to one location is … hard, actually?

While these stadiums are at the center of urban bus networks, bringing tens of thousands of people to one place on buses is difficult (for instance, loading 20,000+ people onto buses for the Boston Marathon requires closing several blocks of streets to stage buses and to load them in two lanes at a time, a large queueing area, and all this for a single origin-destination pair, so there is no need to direct people anywhere than to “get on any bus”). And even if these smaller cities took advantage of their bus systems, they would be quickly overwhelmed. Nashville’s system only operates 150 buses at peak times, and only carried 11,000 people all day on Sundays before the pandemic. (Indianapolis, Jacksonville and Cincinnati operate on a similar scale, and several other cities’ transit systems aren’t much larger.) Even if buses were used at scale, it would require a huge fleet. At 50 people per bus (meaning selling almost exactly 100% of the seats on a bus, not an easy task), transporting 20,000 people would require 400 buses, plus dispatch staff, crowd control and route planning. This would dwarf the bus fleets of smaller cities, and since the buses would only provide a single round trip, it would require a full shift of bus and driver pay to move a single load of people, not a particularly efficient use of resources.

Picking up a lot of people in one place and moving them to another happens to a task at which mainline commuter trains excel. A 10-car train can carry upwards of 2000 people (more if packed with standees), so even if one third of attendees came by transit (unlikely for a football game, but more likely for, say, a concert for a singer popular with teens and 20-somethings) it would only take 10 trains to transport everyone. Trains could also transport event-goers to park-and-ride lots unused at off-peak times. 10 trains might only require 50 staff, an order of magnitude less than buses to move the same number of people.

Football stadiums are not designed with transit in mind are three football stadiums for which commuter rail is the only high capacity transit connection (others—Baltimore, Seattle, Santa Clara, Chicago’s current stadium—have rail lines nearby but more heavily utilize other forms of transit): the Meadowlands in New Jersey, Foxboro outside of Boston and the proposed Arlington Park stadium outside of Chicago. Not surprisingly, these are the three most extensive commuter rail networks, and in each case, the rail connection is made far outside the city. Each city provides an interesting example of how commuter rail service does, or does not, provide transit access to large events.

Chicago (Arlington Park)

Chicago doesn’t have a football stadium served by commuter rail, yet, but it may not far in the future. The Bears are planning to move from the smallest-in-the-league, 100-year-old Soldier Field on the periphery of Downtown to a larger, more modern suburban stadium on the site of an old racetrack. It’s hard to fault them for this: a new stadium downtown or anywhere near transit would require a large site that would only be used a few times per year. (I guess adjacent to the United Center or Comiskey would work?) Arlington Park is about 20 million square feet (nearly a square mile, three times the size of Suffolk Downs in East Boston) and adjacent to a three-track commuter railroad, which can support frequent service and a 30 minute ride into the city (it also runs on a diagonal through the Northwest side of Chicago, with a number of stations allowing bus and L connections).

Unlike some agencies, Metra is actually pretty good at running extra service to meet extra demand, and would likely be able to stage as many trains as were necessary to move people from this new arena to the city, and also to satellite commuter parking lots along the line. The third track of the railroad would allow the agency to stage as many trains as necessary to handle crowds while maintaining regular service. The station has two adjacent storage tracks, and a new development could allow for an expanded station to manage higher loads. The Bears’ plans don’t call for a sea of parking, but rather a mixed-use development next to a train station. Would I call it a perfect location? I might not go that far, but it’s a decent place for a 75,000-seat football arena.

New York (New Jersey Meadowlands)

Both the Jets and Giants play in the Meadowlands, build on reclaimed land in the swamps in New Jersey. The shared use of of the stadium means that it gets somewhat more frequent use than it otherwise would (a low bar; it still lies dormant more than 300 days each year), and with many non-drivers in the area a rail spur was eventually built to take people to and from the stadium. (It only cost $185 million—equivalent to $265 million today—for 2.3 miles. Really. It may serve 500,000 people per year, or about 1500 per day on average. And it may not even be the biggest boondoggle in the Meadowlands.) Other than events, there is no use of the line, which only serves the sports arena and the American Dream shopping mall, which opened after a 25-year, on-and-off construction period and may be all but stillborn, hemorrhaging money now that it has finally opened its doors (i.e., boondoggle). For football games, it works fine, with between 6000 and 10,000 people arriving and departing by train. For larger events, like line has been overwhelmed since the stated capacity of the line is just 8000 to 10,000 per hour.

This speaks to a bottleneck somewhere along the line:

  • Perhaps it is an undersized station, with just three tracks (the rail station at Belmont Park on Long Island was originally built with eight tracks, although only two are now in regular operation). 8000 to 10,000 people per hour means that the rail line only supports a full train every 12 to 15 minutes, which hardly seems like the capacity of the line. With three tracks, the Meadowlands station should be able to turn a train in 15 to 20 minutes on each track (and that’s generous, since trains are only loading or unloading at any given time passenger traffic flows in one direction) meaning that the station should support 9 to 12 trains per hour.
  • Maybe line capacity? The upper bound of the station may stretch the capacity of a two-track railroad with diesel trains and an intermediate stop and existing service; the 18-track terminal at Hoboken would be able to swallow the traffic at the other end of the line. The Pascack Valley, Bergen and Main Lines, which share a trunk route into Hoboken, only amount to three trains per hour at off-peak times (when nearly all concerts and events end, either on a weekend or late in the evening). These lines support 12 trains per hour through Secaucus and into Hoboken at peak hour, meaning that 9 stadium trains plus the normal service would be reasonable. That should allow 18,000 people per hour to be moved.
  • My guess is that it’s simply the number of trains on the line for high-use events, and inexperience of the agency. With a cycle time to Hoboken and back of more than an hour, NJT would have needed more than a dozen trains on the line to fill the theoretical capacity of the line and station, so rather than having trains stacked up on the line ready to pull into the station, they were relying on six trains to make the round trip and come back for more. This is certainly better for crew utilization, but not so great for the passenger experience.

The 2014 Superbowl, where fans were highly encouraged to take transit, was a stress test the railroad seems to have failed somewhat spectacularly. It took three hours to clear 35,000 people from the stadium; 12,000 per hour is actually higher than the stated capacity (likely as people pushed onto trains) although some very helpful Internet people suggested just running buses without pointing out that they would have needed about 700 of them. If I had to guess, the issue was a lack of trains and crews:

Boston (Foxboro[ugh])

Which brings us to Foxboro, the third stadium near a commuter rail line. Sort of. There hasn’t been regular passenger service on the Framingham Secondary since 1933. 40 years later, the stadium itself was built, on a shoestring $7 million budget on donated land. At the center of this land deal: parking. The league stipulated that teams play in 60,000-seat stadiums. The itinerant Patriots had used a number of smaller venues: Fenway Park, and three small college stadiums (Harvard, BU and BC) and unlike the Bears, which moved from Wrigley to a “temporary” home at Soldier Field (they’re now looking to move half a century later), there was no large-enough structure in the area.

The owner of a local racetrack offered the land for the stadium but kept the adjacent parking lots which would now generate cash for both horse races and football games. The site happened to be adjacent to a rail line, and from early on some event service was provided. Service, however, is minimal, since the rail line isn’t designed for much more than a few freight trains. In general there is one train from Boston and one from Providence (the Boston train usually sells out) which meet at the platform. There’s no room for anything more. Aside from the poor local infrastructure, the railroad could support direct service from Boston, Providence and Worcester, theoretically linking the stadium to the three largest cities in New England, provided there was room to store more than two trains.

In the past 50 years, Foxboro’s sea of parking has grown, as the complex owner Bob Kraft has since developed a large shopping mall adjacent to the stadium (more of a lifestyle center than the atrocity that is the American Dream in Jersey). This is not a good setup for traffic as Foxboro is accessed by Route 1, a four-lane highway with traffic signals, and traffic is notoriously bad after games (one review calls it a “great stadium with terrible traffic,” a microcosm of Boston, depending on your definition of “great”). Lots of advice to beat the traffic is to take the train, although it means no tailgating and capacity is limited.

Most everyone else has to drive. There are two ways to distribute a lot of vehicles parked in one place. One is to surround the parking lots with highways and ramps (either in the suburbs or downtown). Another is to disperse parking near the stadium, allowing it to filter through nearby neighborhoods (Green Bay does this, but no one in Green Bay complains about Lambeau Field, which is probably against several state laws). Foxboro is located in the corner of a far-flung suburb a quarter the size of the stadium’s capacity. Decisions are made by an open town meeting. The stadium is located on a local four-lane roadway with traffic lights before it spills onto nearby highways. Traffic jams are legendary.

In 2019 the MBTA started, then aborted with the pandemic, and now restarted, a yearlong pilot to bring regular service to Foxboro, partially subsidized by Patriots ownership. Parking is provided for free, which may help apparent ridership, but there’s really little other reason for most riders to go to Foxboro instead of another nearby station, especially since rush hour service from nearby Mansfield is a faster trip by 20 minutes. (Before the pandemic, other lots would be full, but even with ridership bouncing back, parking scarcity is not as much of an issue.) With nothing but parking lots for a mile in any direction, there is about as much need for transit service to the site as there is to a mall Jersey. High ridership, for now is little more than an American Dream.

A station for Foxboro (and Tay Tay and … the World Cup?)

Which is not to say there shouldn’t be a station there. It should, if the 12 million (half square mile) of land were ever developed as something other than parking lots. It may be the largest developable plot of fully-impacted land in the region. And it happens to be next to a railroad. So while the current pilot may not be successful, if the surrounding area were home to 5,000 housing units it would make far more: Windsor Gardens, but on steroids, an anchor a the end of the line. I’m sure the citizens of Foxboro, who enjoy the largesse of the stadium’s tax revenue while keeping the traffic on Route 1 on the periphery of town, would throw a fit, but in Boston right now, nearly any housing is good housing. Transit-oriented? Even better. (In the very long run, a shuttle train to a connecting service on the higher-speed Providence Line might make more sense.)

In the short run, however, the line is wholly inadequate for handling crowds: it consists of one long platform which can handle, at most, two trains, and the slow, single-track lines in either direction make it nearly impossible to store or stage additional equipment near the stadium. So once a train is sold out, it’s sold out. For Patriots games, there’s not too much demand past what is provided. But when a different demographic comes to town, the situation can get dicier.

Enter Taylor Swift. The only ticket hotter than a T Swift ticket to Foxboro was a ticket on a train to get there. Rather than the SUV-driving, tailgating, suburban type, Swifties seemed happy to snag a seat on Commuter Rail from Boston, such that the first batch of tickets sold out almost instantaneously, and when more were added, they went in 90 seconds. (The Swifties who did get onboard seemed to enjoy themselves!)

The lack of any terminal facilities in Foxboro means that there is no way to leverage the existing rail line to bring crowds to the site and reduce the need for parking, parking which could be repurposed for something other than a parking lot only used a few times per year. There is plenty of room for an event rail terminal not significantly different (although at a smaller scale, sketch here) from what the Pennsy ran for the Army-Navy game, in essence, a few tracks facing in each direction allowing trains to park and unload passengers before the game and then swallowing them up afterwards. It need not be fancy, just ramps to platforms to allow accessible boarding for trains waiting for the crowds. This would allow multiple trains for football games (there is more demand than current supply) and for an event like a Taylor Swift concert, as many trains as needed to transport the requisite masses. Full trains make money. If the Cape Flyer makes a profit on an $40, 160-mile, 5 hour roundtrip with a couple hundred passengers, 1800 people on a $20, 60 mile roundtrip should be a cash cow. But the real value is in repurposing the land around the stadium from parking to something more beneficial to the region.

It’s hard right now to make an argument that the current Foxboro Stadium land use needs regular transit service. In a region with a housing shortage and relatively few large sites adjacent to rail lines, the half square mile of parking could be put to far better use if it weren’t needed and there was enough transit service to allow people to get to the stadium without driving (even if it just meant parking at an existing Commuter Rail lot elsewhere and taking a train). Should the public pay for this? Certainly not. But if improved rail service were funded by Bob Kraft, it would be a good investment which could leverage the value of the acreage around the stadium to be something other than parking cars for a few days each year.

In the shorter term, Foxboro will host at least 6 games of the 2026 World Cup. These fans will be much closer in demographic to a T Swift concert (international, interested in soccer, less interesting in tailgating) and many will be staying in hotels in Boston (and probably Providence, too). If the T can’t figure out how to manage moving more than 3000 people to and from the stadium on trains, they’ll have to have a fleet of buses, and all of the logistics that go with that. So if there is a good time to build a stadium terminal which can handle larger crowds that time is now.

Queuing theory, inefficient Search Algorithms (or … where’s my bag at the Boston Marathon?)

I’ve run the Boston Marathon five times now, and during three of those, I’ve waited for my bag in a cold rain at the end of the race. While this is certainly preferable to the alternative, the marathon’s bag pick-up illustrates how systems can experience bottlenecks even if the overall system has plenty of capacity.

Boston is a unique race in many ways, but because it requires qualification for most runners, it is perhaps the most “densely-populated” marathon in the world: rather than spreading finishers across a four hour window (2 to 6+ hours), most are concentrated in the qualifying window (under 5 hours, depending on age, with most runners under 4). It certainly isn’t the largest race: New York, London, Paris, Berlin and Chicago all clock in around 50,000 runners, while Boston has settled in at a maximum size of 30,000.

The reason that Boston is smaller is that unlike those other races, it starts in a small town, takes over the high school for the athletes village, and the first few miles are on a two-lane wide road with no shoulders, meaning that even spread across four distinct waves, there are only so many people who can be bused to the start of the race, lined up, and started. (Chicago, by contrast, starts and ends in the Loop, Berlin, London and Paris are served by massive transit systems and New York uses an armada of buses to move people a couple of miles from the ferry to the start, which happens to be on to a major highway). On race morning, the parking lot behind the Hopkinton CVS is a sea of port-o-johns; New York uses the 160-acre Fort Wadsworth, Chicago starts in the middle of Grant Park.

(Aside: as I stood in line for the line for mobile urinals—a Nobel-worthy invention in the field of race waste management—people next to me worried we’d miss the start. “Nonsense,” I said, doing some quick math. “There are 80 urinals. There are about 250 people ahead of us in line. If each person takes 1 minute, we’ll be done peeing in 4 minutes.” We were. Logistically, each urinal holds about 400 liters and men can pee 10 to 20 ml/sec per the Internet, so these urinals will not fill up during the 90 minute pre-race pee period. Let’s move on.)

The roads in Boston eventually widen, although most of the course is less than four lanes wide. When you take this relatively narrow course (parts of London are narrow as well), and add, unlike the other races, the seeding of qualified runners, it means that the field never spreads out. Marathon finish times mostly resemble a bell curve (although with some eccentricities, discussed momentarily). The “average” marathon has a median time of about 4:30 with a standard deviation of about an hour. Boston has a median of about 3:45, with a standard deviation of only about 40 minutes. (Standard deviation data can be found here; European races tend to be a bit faster than American races on the whole per the study linked below.)

Why is it not an exact bell curve? Because many runners attempt to—and generally succeed in running—specific times. [2:59:56 marathoner this year raises hand.] Here is a very interesting business school paper on reference-dependent preferences which included the results from several thousand marathons and shows the distribution of marathon finish times.

Distribution of Marathon Finishing Times (n 9,789,093) 

The n in this study is 9,789,043, so 100,000 finishers is just about 1% of the race, and other than a peak right around 4 hours, most of the race is under 0.8% per minute. Boston, on the other hand, has a solid hour with more than 0.8% of the race finishing, with a peak minute of 1.4% or 372 runners (in 2023) and several other minutes around 1.2%, or about 320 runners per minute. And that peak reference-dependent preference is a full hour earlier.

In other words, in a typical marathon, 40% of the runners finish in the peak hour (between about 3:35 and 4:35). In Boston, 60% of runners finish in the peak hour (between 2:55 and 3:55). 40% of runners finish across just 38 minutes, a rate more than 50% higher than typical.

Add to this: Boston’s runners are very well-seeded, so the heavy waves tend to start and finish together. In nearly every large race, runners are sorted into waves to start, with each wave starting every 25 to 35 minutes (rather than having one huge field stage and take 30+ minutes to clear the start). In larger races, the wave start means that although there is a peak between 3:55 and 4:00, that peak finishers are spread across multiple start waves. Most runners near the peak in those races do not have a qualifying race time, and are seeded based on interpolated times from other races.

Meanwhile, in Boston, the first three waves of runners almost all have qualifying times based on a recent marathon and are seeded quite well. Boston has less of a reference-dependent preference signature other than at the 3:00 mark, which happens to be the qualifying time for men under 35 and a significant goal for many runners. In fact, the largest single race for people qualifying for the Boston Marathon is usually the previous year’s Boston Marathon (the only exceptions are when the weather is uncooperatively warm). So in other races, at the peak times, runners are spread across multiple waves (not finishing all together), while in Boston most runners coming in at peak times started together (and in some cases ran the whole race within earshot).

Note: I could go and scrape start and finish data with gun times to go into this further, but for now, just trust me on “Boston has a lot of runners finishing together.”

Data from here. A few notes: the BQ standard was decreased by 5 minutes for the 2013 and 2020 races. 2004 and 2012 were run with temperatures in the 80s; 2012 allowed deferrals. 2013 was cut short because of the bombings, but at that point nearly all potential qualifiers had finished; 2014’s field was larger and consisted of many people who hadn’t finished in 2013; most were not qualfiers. 2016 and 2021 were relatively warm years. With 13,700 BQs run, 2023 Boston is the largest number of Boston Qualifying times ever run in a single race. This will likely mean that, after two years where all qualified runners gained entry to the race, there will be a cutoff in 2024.

This all means that at peak finishing times, there are not only 1000 people finishing per minute, but for much of the race, those people all started together. And what does this mean for bag pick-up? Here’s how bag drop works:

  • Before the 2013 attack, Boston had bag drop at the start: you gave a volunteer your bag and it showed up in Boston on a bus a few hours later. (See DC Rainmaker’s blog post, back before he started reviewing every device.)
  • After 2013, a bag drop policy was instituted at the start: you left your bag there and took a disposable bag to the start (and for cold years, wore extra clothing, transferring throw-away items from the Goodwills in Boston to Hopkinton).
  • Setting up a bag drop system for 20,000 or more bags requires erecting the infrastructure in Back Bay the day of the race; at first, this was tents and rows of bins with bags, the system has now morphed into one where you drop your bag at a school bus where it is stored through a window specified by your number range, allowing the storage units to be rolled away after the race (this, on its own, is a very good idea, here’s an image which shows how the easy part—the drop-off—works).

However, the system is still quite space-limited. Most every other big marathon ends in a park, or open area. Boston ends on a main street in the middle of a city. So there is not much room for queuing or storage for the bag drop. Which means that each bus stores approximately 1000 runners’ bags. Which is fine when they are dropped off: runners arrive over the course of about an hour per wave, with some early birds and some late arrivals, meaning about 15 drop-offs per minute, and drop-offs do not have to be sorted to the right person, only put into the right “bin” (a window of a school bus and on the inside, I assume, a numbered seat).

The buses are lined up by wave (red, white, blue, yellow) and then bags are ordered within each wave (1-1000, 1001-2000, etc). It is easy for race volunteers to look at a runner’s bib color and send them in the right direction to drop off their bag. They do, and go off to run their race.

On the pickup end, however, metrics are reversed. 1000 runners may show up over three minutes, and I’d guess as many as 600 of them may all need to get their gear from the same bus. Simply throwing random bags to runners would require, at times, more than three bags per second to be thrown at participants. But unlike drop-off, pickup requires sorting through as many as 25 bags (assuming a bus has 30 seats and bags are sorted into these seats). Without perfect ordering, volunteers search through the pile of bags until they retrieve the correct one. This may take 10 to 20 seconds or more, and even with five or ten volunteers on the bus (there really isn’t space for more), it means only 15 to 60 participants receive their bag each minute. If we assume the geometric mean here of 30 runners served per minute, it would take 30 minutes to serve all the bags in a bus, resulting in long queues.

As this occurs, a wave of long queues forms. Once the high rate of finishers starts around 2:50 from the start, the buses have long lines which form a slow-moving wave from bus to bus. After waiting for my bag in the 4000s for a long period of time in the cold rain (as I have in 2015 and 2018) I shuffled past the bus ahead of me with the 3000s. Aside from a few stragglers, it had no queue, the volunteers there had retrieved all of the bags and were catching their breath. Meanwhile, the queue behind me at the 4000s bus was ebbing, while the queue at the 5000s bus behind us had grown. But elsewhere, three-quarters of the buses, for the white, blue and yellow waves, wouldn’t see their first runners for, in some cases, an hour or more.

In introductory computer science courses, students are often taught about efficient search algorithms. Let me stop here and state that I am completely unqualified to write in depth about the efficiency of search algorithms. But mostly, it is very inefficient to search through an entire unordered list each time you want to find an item. It’s better to either sort the list (and then search through it) or sort the search term in a way that only searches part of the list. (That said, this is, let’s just say, a simplification, people write dissertations about this.)

Essentially, searching an unordered list is what the pile of bags search is. One solution would be to build a better sorting apparatus: I have participated in the American Birkebeiner ski race every year since 2006, and even produce the most popular (read: only) podcast about the race. Drop bags there are sorted and lined up, by number, in a parking lot, and distributed to finishers. This would work in Boston, if only there were several acres of parking lots in the Back Bay which could be used to stage the bags. Fortunately, urban renewal mostly steered clear of Boylston Street (the Pru was built mostly on old rail yards) and we lack the luxury of this open space. The school bus solution allows the apparatus to be set up on the streets, while providing cover from the weather for the bags (and volunteers), but does not lend itself to sorting beyond these bins.

If finishers were better distributed amongst the two dozen (or so) buses as they crossed the line, the sorting problem would be less of an issue. If 240 of 300 people crossing the finish line each minute had dropped a bag and they were evenly distributed amongst the buses, it would mean 10 people per bus per minute, and if five volunteers were on each bus, it would allow 30 seconds per bag for each user without long queues forming. The issue is that with this inefficient search algorithm—which is necessitated by the location of the bag pickup—has concentrated finishers. Hundreds of finishers wind up at a single bus at any time, and there are only so many volunteers who fit on this bus. When these “servers” can’t keep up with the demand of the “customers” (to use queuing theory terminology), the queue grows exponentially until, at some point, the wave of runners ebbs, and the speed at which customers are served exceeds the additions to the queue, and the lines dissipate. Of course, by this time, a similar wave has moved to the next bus down the line.

The author’s 2023 drop bag. Note that this bag (or at least, the 2022 version) can hold a 30-rack of beer (not pictured). No word on whether anyone has ever dropped off a 30-rack.

There is, I believe, a solution to this problem: sort the customers before they get to the bags. The main issue with this setup comes from a concentrated wave of people overwhelming a single service point. If the people were dispersed to more servers, it would allow more efficient use of the volunteers, rather than having one bus overrun while others lie idle. There is a simple way to do this: sort first by the last digit of the bib, and then by bib color and number. This would decrease the concentration of the customers by an order of magnitude, distributing them across the buses, rather than having them queue up in one place where there aren’t enough volunteers to handle them.

Here’s how such a system could work. When the BAA gives out drop bags, runners affix a sticker with their number and wave color. For instance, it might say:

4 8 7 6 or 1 8 7 6 5

This allows a rough sort by color and then number, but color is simply a function of the number, so it does not spread out the customers. Here’s a proposed redesign:

4 8 7 6 or 1 8 7 6 5

What I’ve shown here is that the numbers could have the final number highlighted to help inform people of the new sorting method, allowing the runners to be sorted first by the final number of their bib, and then ordered by their number. This would reduce the concentration by a factor of 10.

Directions about the changes could be given to runners with their drop bag sticker, as well as at the bag drop-off in the morning. Instead of signs pointing to different colors, they would instead point to numbers: 0 to 3 to the left, 4 to 6 to the right, 7 to 9 straight ahead. The start would be less tricky: before the race, people are generally more mentally aware than after running 26.2 miles. Once overcoming this small hurdle, runners would proceed to their number, then to the bus assigned to their color (each bus would likely have two waves assigned) and then the correct range. It would introduce an extra sorting step at the start, but would pay dividends later on.

The finish would introduce more complexity: runners and volunteers would have to direct people based on the last number of their race bib. This would be mitigated in a couple of ways. First, racers would have already experienced the system before the race. Second, volunteers already have to sort barely-cogent runners stumbling their way along Boylston Street by color, so they would instead sort “right/straight/left” by bib number. Once on the right street, runners would be able to find their correct bus by last digit and then color and join a much shorter and congested queue. Rather than 15 to 30 minute queues for bags, most runners would be served in just a few moments.

It might also allow the race organization to cut down on number of volunteers required for the system. Rather than moving volunteers between buses as demand changes, each bus would have even demand during the entire bib pick-up procedure. This would reduce “deadhead” time when volunteers are required to move between buses as they are needed elsewhere, by allowing them to maintain a single duty station during the entirety of the bag pickup process. There would still be 300 or more finishers per minute, but they would be spread across 10 pickup locations at any given time, not concentrated at a single site.

Since this is sometimes a transportation-related site, there is a lesson here in the transportation planning realm: A system which seems efficient may have an unforeseen bottleneck which creates a single point of failure, meaning that a small portion of the system is oversubscribed while the rest is underutilized. A wide highway might encounter a lane drop or even a situation where traffic has to sort into different lanes, resulting in a long backup. A rail line may have plenty of capacity along most of the line but a busy station with long dwell times or a single switch may curtail capacity along the rest of the line. For the Boston Marathon bag pick-up, the well-intentioned decision to simplify the drop bag system results in a bottleneck of hundreds of cold runners huddling under thermal sheets, all too often in cold rain. Simply by changing some procedures, this may have a fix which would benefit everyone involved.