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What if the Covid-19 vaccine only works half the time?

Even a mediocre Covid-19 vaccine could help end the pandemic.

A person receives an injection from a health worker wearing surgical gloves.
A health worker gets a vaccine as part of a drill to prepare for the arrival of a Covid-19 vaccine at a health clinic in Depok, West Java, Indonesia.
Jefta Images/Barcroft Media via Getty Images

In the not-so-distant future — we’ll probably know who won the 2020 election, but memories of the weirdest Thanksgiving ever will not have faded — you may be faced with an incredibly important choice. Should you get the Covid-19 vaccine?

It’s been less than a year since the discovery of SARS-CoV-2, the virus that causes the new disease, and we have not just one, but multiple vaccine candidates that may in time truly shut the door on the pandemic.

Though nothing is certain, it’s very likely that some vaccine will be approved soon — and widely available by the end of 2021.

Which leads us to ask an important question: What if that vaccine is not very good?

The paradox of the mediocre vaccine

What do I mean by not very good? 50 percent efficacy. Food and Drug Administration commissioner Stephen Hahn has pledged that the FDA will not grant approval for a vaccine that has less than 50 percent efficacy, so this seems like a reasonable floor.

To give a sense of what vaccine efficacy really means, let’s imagine ourselves in the board rooms and meeting spaces at vaccine manufacturers Pfizer, Moderna, and their ilk as they wait for the results to come in. Each of these companies is running large, randomized clinical trials of 30,000 to 60,000 individuals who have not yet contracted Covid-19 in areas where the virus is prevalent. Half get the vaccine; half get a placebo shot. The companies then wait to see who gets sick.

The best-case scenario for the manufacturer? Zero cases in the vaccinated group and something well north of zero cases in the placebo group. With, say, 150 cases in the placebo group and zero in the vaccine group, they would be able to claim that their vaccine was nearly 100 percent effective. (To be clear, no vaccine has ever been 100 percent effective.)

If there are 150 cases in the placebo group and 75 cases in the vaccine group, now they could say that their vaccine is 50 percent effective. Not as impressive, clearly, but something is still happening. Both Pfizer and Moderna planned on presenting early results after 150 infections had occurred in their study population.

But here’s the problem. The less effective a vaccine is, the more of us need to get it to end the pandemic.

The math is pretty straightforward. Let’s say that, on average, an individual infected with Covid-19 infects two more people (the now familiar R0). Unchecked, that leads to a huge growth in infections.

To end the spread, we need to make sure that each infected person infects less than one additional person. That can be achieved through mask-wearing, social distancing, canceling large gatherings, you know the drill. But it’s not ideal — we want to lift all the restrictions. We need one out of every two people to be immune.

And there’s two ways to become immune — through infection or vaccination. (Caveat: The mechanics and durability of Covid-19 immunity are still being studied).

If there is a 100 percent effective vaccine, and one out of every two people need to be immune, it means that 50 percent of the population would need to be vaccinated to end the pandemic.

But what if we had a 50 percent effective vaccine? In that case, one out of every two people who is vaccinated won’t be protected. To end the pandemic under this scenario, 100 percent of the population would need to be vaccinated.

The worse the vaccine is, the more people need to get it to get us out of this mess. The less effective a vaccine is, the less likely people will choose to get it.

A new survey in JAMA Network Open evaluating factors predictive of whether people would accept the vaccine found that vaccine efficacy was the No. 1 determinant. People were, on average, 16 percent more likely to accept a vaccine with 90 percent efficacy compared to one with 50 percent efficacy.

Get the vaccine anyway

It’s tempting to look at the math of a mediocre vaccine and give up, but a mediocre vaccine can still end the pandemic — just not on its own.

The key is the R0. My example assumed that the average infected person infects two more people, but it doesn’t have to be that way. In fact, due to the policies enacted to stem the tide of the virus, the effective R-value (often called Rt) is probably lower than 2 — maybe around 1.2.

If that’s the case, you’d only need to get a 50 percent effective vaccine to 33 percent of the population to end the pandemic, provided we all continue to wear masks until it’s over.

A chart showing the percent of the population you need to vaccinate with a 50 percent effective vaccine with an R0 ranging from 1 to 2.
A chart showing the percent of the population you need to vaccinate with a 50 percent effective vaccine with an R0 ranging from 1 to 2.
F. Perry Wilson

Most polls suggest that around 70 percent of Americans will get a Covid-19 vaccine when it is available. A 50 percent effective vaccine may have different efficacy in different groups — if a vaccine is highly effective in young people but ineffective in older people, it would complicate matters quite a bit, as this new perspective in the journal Science notes.

What about side effects?

Efficacy is not the only thing to think about when you are lining up to receive a vaccine. The side effects are critical, too.

Researchers categorize adverse events as serious or not depending on how severely they affect the patient. Redness and swelling at the injection site? Not serious. Anaphylaxis that lands you in the hospital? Serious.

There’s no need to be too worried about non-serious adverse events. Every vaccine will have them: fevers, injection site reactions, malaise. It’s the serious adverse events that we need to worry about, and fortunately these are usually rare.

Of course, it is that rareness that leads to uncertainty. Let’s say I’m Moderna and I enroll 30,000 people in a vaccine trial and not a single one develops anaphylaxis, a life-threatening allergic reaction. You might think that implies that the anaphylaxis rate for this vaccine is zero percent, or at least less than 1 in 30,0000. You’d be wrong.

The vicissitudes of chance become clearer if we make the numbers smaller. Imagine this trial only enrolled 10 patients, and, again, none developed anaphylaxis. It would be wrong for me to conclude that anaphylaxis can never happen with this vaccine.

All I can say with absolute certainty is that the anaphylaxis rate is less than 100 percent. But it could be 99 percent. I may have just been lucky enough to enroll 10 people who don’t get anaphylaxis from my vaccine.

We need some way to estimate a plausible side-effect risk, given the observed data. This can be done with some simple statistics.

We can ask what is the plausible range for the anaphylaxis rate given that I saw it zero times out of 10. We’ll define plausible by saying that, whatever the real rate is, I would have a greater than 2.5 percent chance of not seeing it at all in my 10 patient sample (this is a standard rate of plausibility for this type of thing). The answer: 0 to 31 percent.

In other words, if the true anaphylaxis rate is 50 percent, it would be unusual to enroll 10 people and not see a single case. But if the true anaphylaxis rate is 30 percent, I’d have a shot to pitch a no-hitter (I’d get data like mine around 2.5 percent of the time).

That’s a huge range, but fortunately the ongoing vaccine trials enrolled many more than 10 people. How certain can we be about side effects? For serious adverse events that don’t occur at all in the trial, we can be confident that the true rate is less than one in 10,000. That is a really small number, but not necessarily reassuring when we’re talking about vaccinating 350 million Americans (or nearly 8 billion people).

Given that, you may think it’s appropriate to take a wait-and-see approach. Though there is a bit of moral hazard (if we all act this way, we’ll never learn anything and the pandemic will march on), it’s not an untenable position.

In fact, since it’s extremely unlikely that mass vaccination will be available to everyone at the same time, those at highest risk of Covid-19 (including health care workers like me) will be prioritized, take on the unknown risks, and be followed closely for side effects. By the time the vaccine is ready for everyone, we should know much more.

Me versus us

This pandemic has brought to light a particular weakness in American society: a seemingly irreconcilable tension between a perception of individual liberty and collective sacrifice. Nowhere has this been clearer than in the case of face masks, which carry zero risk, provide modest individual protection, and have a strong societal benefit.

Mediocre vaccines are more like face masks than miracles. The real benefit of getting vaccinated may be less to the individual and more to society. Sure, a 50 percent effective vaccine buys you some peace of mind. You’ve cut your risk of infection in half, and (since vaccine effectiveness counts all infections the same, regardless of how severe they are) even if you become infected you may get less sick. But in the end, if all we have is a mediocre vaccine, the goal needs to shift from providing individual protection to ending the pandemic.

That means we need to start convincing people to get vaccinated now. We need to prepare the public for a less-than-ideal scenario — a mediocre vaccine — and show why it is important to get vaccinated anyway. A mediocre vaccine won’t necessarily save you, but if enough of us get it, it can save us.

F. Perry Wilson, MD MSCE (@methodsmanmd) is an associate professor of medicine at the Yale School of Medicine and director of Yale’s Clinical and Translational Research Accelerator. He writes a weekly column on and is the creator of the free online course “Understanding Medical Research: Your Facebook Friend is Wrong.”

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