Think of it this way: If the vaccine is, say, 30% effective, then a single person vaccinating themselves will bring their risk down by 30%. But if there are N p

Think of it this way: If the vaccine is, say, 30% effective, then a single person vaccinating themselves will bring their risk down by 30%. But if there are N people between that person and patient zero, and all those people are vaccinated, the risk is brought down by 1-0.7^N. For the virus to propagate through a chain of 3 vaccinated people that comes out to 66%, an effect more than twice as effective as that of just the person getting the vaccine themselves. (It's more complicated than that, especially since getting the flu isn't binary, but it should give an indication of how the effects scale.)