The name of the game is science denial for the anti-vaccine activist. They have their work cut out for them. Concocting a worldview where a health measure that prevents between 2 and 3 million deaths every year is a bad thing takes a lot of work.

Thankfully, sometimes all we need to do is give them enough metaphorical rope to hang themselves.

Here's an example!

Earlier this year, a study was published to the Bulletin of the World Health Organization on the progress towards the elimination of measles in China.

Sayer Ji, infamous for misrepresentation of scientific articles, in a blog post about the study, says:

China has one of the most vaccination compliant populations in the world. In fact, measles vaccine is mandatory. So why have they had over 700 measles outbreaks from 2009 and 2012 alone? The obvious answer is the the measles vaccines are simply NOT effective.While the study's conclusion states unequivocally that:

In 2013, most of the resurgence seen in measles cases was the result of the susceptibility of unvaccinated or incompletely vaccinated children...Which directly contradicts the central claim of Ji's blog post. This is typical of Ji. He consistently references scientific studies in an attempt to lend credibility to his argument despite the fact that the contents utterly refute his argument. He relies on the laziness and lack of education among his readers. If any of them simply read the study, they'd notice that it says the opposite of what he claims.

His biggest mistake was using the word "effective" which, in the study of vaccines, has a rigorous mathematical meaning. The efficacy of a vaccine is defined as:

E = 1 - (V / U)

Where U and V are the "attack rates" in the unvaccinated and vaccinated population, respectively. We calculate these attack rates by dividing the number of sick people divided by the population size. So the first question is, who got sick? The cited study shows 53% of measles sufferers were unvaccinated, while 47% were fully vaccinated.

The anti-vaccine activist might say, "but those percentages are almost the same! It looks like the vaccine hardly made a difference. You've got almost a 50% chance of getting sick either way, right?"

Wrong. And we just need one more piece of information to prove it.

According to the title of Ji's own blog post, "99% are vaccinated." Now we can calculate attack rates:

V = 0.47 / 0.99 = 0.475

U = 0.53 / 0.01 = 53

U = 0.53 / 0.01 = 53

Which means the efficacy of the measles vaccine in China is:

E = 1 - (0.475 / 53) = 0.991

Or, 99.1% effective, consistent with efficacy noted on the CDC website.

So why is the anti-vaccine activist wrong to suppose you've got a 50% chance of getting sick either way? I like to think of it from the point of view of the measles virus. If I spread randomly from person to person, it will be hard for me to find that one unvaccinated person in a crowd of 100 people. If I do manage to find that person more than 1% of the time, I've done better than chance. That means it was easier for me to infect this person than the other 99 vaccinated people.

It only takes grade school math to expose the likes of Sayer Ji.