Some 135,000 fans gathered in the Indianapolis Motor Speedway for the Indy 500 over the 2021 Memorial Day Weekend. A Washington University in St. Louis mathematician, who helped write a scientific formula and a paper regarding the risk analysis of fans attending sporting events, has a simple, evidence-driven answer to two questions about that race crowd: How many were vaccinated? How many were safe from COVID-19 transmission?

Not enough.


This has little to do with whether fans were masked, socially distanced, even scream-free to the point where potentially infectious droplets weren’t moisturizing the air much like the ever-present milk that is chugged in Victory Lane by the Indy 500 winner.

Rather, this is a mathematical, computational risk analysis, says John E. McCarthy. And he knows: He was part of a team of scientists consulted earlier in May by PGA Championship officials (more on that later) and consulted over the past pandemic year-plus by more than 30 teams, leagues, states and cities across the country and the four major U.S. professional sports.

“If vaccines or negative COVID-19 tests are required for attendees, 100% attendance is safe,” said McCarthy, the Spencer T. Olin Professor of Mathematics in Arts & Sciences and chair of the Department of Mathematics and Statistics. “Without requiring vaccinations or testing, it’s not.

“There should be a pass system, like the Coronapas in Denmark: Either a person is vaccinated or has been tested in the previous 72 hours. With such a pass system, we could go back to nearly normal life” at outdoor and even indoor live events, McCarthy continued. “If they don’t, I think it’s crazy to fully open.”

McCarthy wrote the model, published Jan. 28, 2021, in the journal PLOS ONE, along with Barry D. Dewitt at Carnegie Mellon University, Bob A. Dumas at Omnium LLC and Myles T. McCarthy at the University of Illinois at Urbana-Champaign.

The model estimates the relative infection risks. Such risks and infection numbers have been dropping through the first quarter of 2021 during a nationwide vaccination movement, yet still a sizable portion of U.S. adults remain unvaccinated. But the NHL and NBA have been allowing fans back through their turnstiles for the playoffs, with some 15,000+ attending New York Knicks games, where McCarthy pointed out they used the state’s Excelsior pass system.

NFL and many college football officials have pledged to return to 100% attendance come fall, meaning as many as 100,000 people will be gathering in extremely close proximity, eating and drinking (mask-free) and likely screaming for their beloved teams.

Inter Miami FC fans cheer on their Major League Soccer club earlier in spring 2021 in DRV PNK Stadium in Fort Lauderdale, Florida. (Photo: Shutterstock)

Is America ready? Not yet, according to the numbers already vaccinated.

Vaccinated fans in the stands have “two shields” working in their favor: “They have their own vaccination, and they have a very low chance of being exposed to infection from those around them,” McCarthy said. “So, we’re not going to get a super spreader event.”

Still, risk remains. Take the Brickyard race, for example: Heading into Indy 500 weekend, barely 1 in 3 Indiana residents were vaccinated. Roughly half of all U.S. adults are vaccinated.

“Fifty percent vaccination, that’s not a good idea,” McCarthy said.

“This summer, a baseball game with half the people unvaccinated would be even more dangerous than 50% attendance last summer,” McCarthy added. The model for the risk analysis includes consideration for masking, social distancing, every-day protocols enacted early in the pandemic. “They likely would not be wearing masks as routinely [nowadays]. The people who are vaccinated, they’re going to be exposed to a lot of unvaccinated people. You have one shield [in the form of the vaccine], which is not perfect. The two shields together, with the people around you being vaccinated or tested, is pretty close to perfect.

“I think it is irresponsible to open large events to 100% occupancy without either testing or vaccinating. Especially now with both of those being easy.”

You can’t give a single overall risk score, however. “The risk depends on the infection rate in the community, which fluctuates,” McCarthy said. “As the rate goes up and down, the risk goes up and down. Whatever the given day, you can factor in our model the number of people vaccinated and hence relative risk … so you can come up with a risk plan on any given day. But it’s going to change from day to day.

“As the number of vaccinations in a community goes up, the overall infection rate goes down, so even unvaccinated people pose less of a risk.”

Until the numbers of vaccinated people considerably outweigh the unvaccinated, and the rates of infection, hospitalizations and deaths dwindle to minuscule numbers, there still will be human factors involved: masking, distancing, hygiene to prevent potential infection and guarding against droplet spread.

The PGA Championship that concluded May 23 — with Phil Mickelson becoming, at 50, its oldest winner ever — posed additional challenges for McCarthy and team when consulted by organizers: Fans would ride a far distance from their parking lots in commuter buses and pop into numerous hospitality tents. To combat those issues, Omnium and the team advised officials to monitor density, require distancing in seating and ensure optimal air flow.

Speaking of air flow, indoor events such as the NBA or NHL playoffs are less of a risk in an arena with a modern, quality ventilation system, he noted.

“The devil,” McCarthy said, “indeed is in the details.”

Human behavior again being one of those details. Near the end of this year’s PGA Championship, a throng of prescreened fans crowded around Mickelson. In one famed photograph, there are 160-plus people within 10 yards of the victor — of the one-third whose faces can be made out, only five masks are visible.

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