None! As long as it's heading in the right direction at the right time. Once something is moving at escape velocity it can go anywhere else, unless it is captured by something bigger.

​

In this case, escape velocity from the Moon is 2.38km/sec and the orbital velocity of the Moon is 3.68km/sec. So, at most the baseball would be travelling at 6.06km/sec relative to the Earth if it was just at lunar escape velocity. Since that is less than the Earth's escape velocity of 11.19km/sec, it would be captured by the Earth as it moved away from the Moon. At that point, depending on the fine details of the orbits it could either orbit the Earth, crash into the Earth or be re-captured by the Moon.

That is, of course, an excellent point. What we do have is estimates from a few different methods (mass distribution, perturbation analysis, discovery curve, etc) and they are converging on <1000 NEOs larger than 1km. Here's a nice, though slightly outdated, graphic: https://www.nasa.gov/mission_pages/WISE/multimedia/gallery/neowise/pia14734.html

And a recent paper giving an estimate of 940+-10. https://www.sciencedirect.com/science/article/abs/pii/S0019103521001342

&#x200B;

Edit: Article link

I'm not a rocket engineer, but I did work for several years as an astronomer at a now defunct observatory (pre-SST LINEAR) that was working on NEO research. Good news! We've well cataloged almost all of the NEOs large enough to cause an extinction level impact and are doing a good job of cataloging this that would "merely" cause widespread devastation. However, for objects that could cause local or regional destruction, we really need something like this in orbit. It's like insurance, you hope to never need it but you'll be glad if you do.

Edit: Missing "almost"