Zach Binney is a sports epidemiologist and assistant professor at Oxford College of Emory University. Angela L. Rasmussen is a research scientist at the University of Saskatchewan’s Vaccine and Infectious Disease Organization.

Nine fully vaccinated members of the New York Yankees — including one player and eight other staff — tested positive for the virus that causes covid-19 last week. To many, this may suggest the vaccines, which are extremely effective, don’t work as well as advertised. In fact, the Yankees outbreak is a case study showing how well the vaccines are working.

Let’s first note that data from tens of thousands of people enrolled in clinical trials — and hundreds of millions of other partially or fully vaccinated people — have shown that the vaccines administered in the United States are safe and effective. All the cases on the Yankees came from its traveling party — the group of players and other personnel who go to road games, about 50 to 60 people. That’s not enough to overrule the existing data.

But even if we focus just on those 50 to 60 people, does this outbreak cast doubt on vaccines? No. Of the nine cases, at least seven showed no symptoms. The only one who has so far was the first case to appear, third-base coach Phil Nevin. It is possible we will find out the vaccine “failed” only once — in Nevin — allowing him to build up a high enough viral load to spread it to eight others, all of whose vaccinated bodies likely fought it off quickly before they could develop symptoms or transmit it.

That is the vaccines working as designed. While they don’t eliminate the possibility of becoming infected, they virtually eliminate the risk of severe disease and death by preparing your immune system to fight the virus so it can respond more quickly and strongly. Cases that would have been hospitalizations become colds, and symptomatic cases become asymptomatic. Most infections are avoided entirely. The vaccine works like a strong head wind from the outfield, turning homers into doubles and doubles into harmless fly outs. These effects may be the result of a more powerful immune response in vaccinated individuals, which is also thought to reduce viral loads and thus further spread of the virus.

What about the Yankees’ rate of spread? Is nine infections out of 50 to 60 people high? To fully answer that question, we would need to know how many would have become infected without the vaccine, which would require a detailed epidemiological investigation of contact patterns within the team.

But we can look at similar outbreaks to assess the risk in unvaccinated teams. Last July, 18 players and two coaches on the Miami Marlins tested positive. Shortly after, the St. Louis Cardinals saw its own outbreak among 18 people (10 players and eight staff). These would have represented at least 30 to 40 percent of a typical traveling party in 2020. In the National Football League, the Tennessee Titans had 24 cases (13 players, 11 staff) in October, while the Baltimore Ravens had more than 12 cases in December. These both represented about 20 percent of players; the percentages for staff are more difficult to estimate.

All of these outbreaks occurred under tighter covid-19 protocols than what the Yankees were under, including greatly limited shared indoor time and strict masking requirements. Vaccinated Yankees were allowed to spend unmasked time together indoors in hotels and clubhouses. Coaches and staff, who represent eight of the nine cases, were in tight indoor quarters during a rain delay just before the outbreak began. This is a perfect environment for the virus to spread, much like the Skagit County, Washington, choir practice outbreak in March 2020 that sickened about 86 percent of the 61 attendees.

Without vaccines, then, one could reasonably guess that at least 40 percent of the roughly 60-person Yankees traveling party, or 24 people, would have been infected. The fact that only nine were infected suggests that vaccination prevented 15 cases out of 24 possible, or 63 percent. That would be almost exactly the reported efficacy against infection (66.3 percent) of the Johnson & Johnson vaccine, which most Yankees received. In other words, the vaccine would have been operating as expected.

Finally, the Yankees are a unique case because they are tested regularly. Outside of pro sports, many “breakthrough infections” that occur in fully vaccinated individuals — while most likely still quite rare — are undercounted because those people are often asymptomatic and don’t get tested. We saw a small outbreak of mild disease on the Yankees because we were looking for it. There may be others elsewhere that we don’t see. But when we look at the arguably more important data on severe cases, such as hospitalizations and deaths, we have seen dramatic improvements in areas with substantial vaccination.

It is likely the vaccine worked as expected on the Yankees: It prevented many more cases, only allowed the virus to spread from one person and reduced disease severity. This is what is needed to return us to normal. Willie Mays never played finer defense.

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