The idea is that the moon's gravity changes the trajectory of asteroids whose path would otherwise cause them to strike the Earth. But that works both ways: the moon's gravity is every bit as likely to change the trajectory of other objects which would have missed
the Earth, curving them into a collision. It's a wash: if the collection of potential objects is random, then there are just as many nudged into
a collision as out of one. All the moon does is complicate the math.
Given the high relative speeds of interplanetary objects, there are very few that could initially miss the face of the moon by such a tiny margin (maybe only a few miles) that they are nevertheless pulled down by its gravity into striking its surface. The calculation of the protection offered by the moon, then, is simplified to simple geometry: how big is it? So the coverage of the moon's "protective shield" is limited to only a little more than its apparent disc, which is some 3.67 million square miles. The disc of the Earth is about 49.3 million square miles. The moon is catching, therefore, about 7% of the asteroids that would hit the Earth that are coming from a direction that takes them down the moon-Earth axis
. Again, assuming a random selection of trajectories, that would be a tiny fraction of all the potential hits.
moon blocking asteroids - Imgur