I am trying to decide which camera to buy. Have looked into both the Nikon Coolpix P100 and 1 J1, and feel that the 1J1 is more adaptable, and has many features that I'd like to enjoy. But, I'm concerned about how "close" I can zoom into a shot. For example, will the 30-110mm lens allow me to take a close-up of my son playing center field, if I'm sitting on the third base line?
The easiest way to explain this is with examples. Lucky for you, many of these exist online already. The trick though, is that most of the online examples will show you the 35mm equivalent focal lengths. Instead of showing a 30-110mm lens on the Nikon 1 J1, they usually show lenses on a full frame 35mm size sensor camera, such as a Nikon D800. So you will need to do a bit of math to use these same online examples if you are considering the Nikon 1 J1. The math comes into play for the crop factor. The crop factor is the digital sensor's size compared to a full frame 35mm sensor size. The Nikon 1 J1 has a crop factor of 2.7(read on for more).
Here is an example. 30mm on the Nikon 1 J1, is similar in field of view as a 81mm lens on a 35mm or full frame format camera. I got to this by taking 30mm x 2.7. So overall the 30-110mm is equivalent to the field of view of a 80-297mm lens on a full frame camera.
With that said, now you can take the information you now know, to see what type of zoom or view you will have on the standard focal length examples below:
Remember, this lens will have the same view as an 81-297mm lens would in the example links above!
Also, see these other great questions for more information on this topic:
Important to note as well, the Nikon Coolpix P100 typically already has it's specs stated in 35mm format equivalent form. It is a 26-678mm lens in 35mm equiv. So the P100 has a much much larger range then the 30-110mm lens you were looking at.
Overall, a 110mm lens on the Nikon 1 J1 is a great deal of zoom. That should easily suffice for personal use at a baseball field. The limiting factor will likely be light, as low light sports photography is very demanding of equipment in multiple ways. It isn't by any means a bad idea to get this lens for your intended purposes, but just be aware that a full size DSLR with a professional lens will be able to achieve better in this situation.
You will be able to zoom in almost twice as close with the P100 than the 1 J1 with the 30-110mm lens. If your son plays most of his games in bright daylight you will probably be happier paying around $300 for the P100 if that is the primary use for the camera. On the other hand, if your son plays a lot of night games the 1 J1 may perform better enough in the low light to allow you to crop the resulting image and still wind up with a higher quality photo. The 30-110mm lens along with the 1 J1 and the included 10-30mm kit lens will leave you more room to grow as a photographer and be much more adaptable to other types of photography. Of course the cost is significantly higher at around $500.
The Coolpix P100 has an zoom range that yields an equivalent field of view (FoV) of 28-560mm on a 35mm camera.
On the Nikon 1 J1 the 30-110 will yield a FoV equivalent to 81-297mm on a 35mm camera. This places the 30-110 squarely within the range of popular consumer grade telephoto zoom lenses.
On the surface it would appear that the P100 wins hands down, right? Not so fast, my friend!
Nikon claims the J 1J has the world's fastest auto focus (AF) system. This would lead one to assume that means it is faster than the Nikon P100. If, by the time the camera can focus and fire the shutter, the moment has already passed the extra zoom of the P100 isn't worth as much. Focus speed on both cameras will be affected by the brightness of the scene. In lower light both will take longer to focus than in bright sunlight.
The P100 has a 1/2.3" sensor that is sized at just under 1/4 the total area of the 1 J1's 1" sensor. Since they are both about 10MP, this means the pixel wells on the 1 J1 are about twice the width (and 4x the area) of the pixel wells on the P100. This allows the 1 J1 to perform much better in low light than the P100. The 1 J1 should also generate less image noise than the 1 J1 in similar shooting situations.
As with any lens like the one on the P100 that has a zoom ratio of 20x, there are a lot of design compromises that have to be made that will affect image quality and maximum aperture. This is much less the case for the 3.7x zoom ration of the 30-110mm lens.
Aperture is important because it affects how much light is allowed into the camera and that affects the minimum shutter speed, especially in low light such as a sports field in late afternoon or at night. In this regard there isn't a lot of difference between the two options in your question. The part of the P100's focal length range that is equivalent to the 30-110mm lens on the 1 J1 is around 14mm-51mm. Although the P100 is at f/2.8 at 4.6mm (equivalent to 10mm on the 1 J1), by 14mm it is probably around the same as the f/3.8 of the 30-110 at 30mm. On the long end, which is what you would be most concerned with at your son's baseball game, the P100 is a little faster than the 30-110 at maximum focal length (f/5.0 vs. f/5.6).
All of these factors will affect the way the images you take at a baseball game with either choice will appear. You will definitely have more reach with the P100 than the 1 J1 + 30-110mm lens. But you might also have a noisier, more distorted image that was not taken until after the moment you wanted to capture had passed.