I understand what both you and kalel33 say, but have to agree with kalel33.
In general kids sports at night are not easy. The pro sports stadium and play fields are well lit or at least much better lit than the local park. Young kids usually get the worst field with the poorest lighting. And young kids are not as predictable as the trained pros, they can run in all directions.
Now the more technical part. For sports, you need shutter speed 1/500 or faster. You may be able to use 1/100 for slower actions or with panning. It is true that using higher ISO will let you increase shutter speed so that you may be able to get by with a slower lens, but at the cost of slower AF and noise. Slower lenses will hunt for focus in low light even at higher ISO, not as responsive as a fast bright lens. Nikon D700 is one of the best in high ISO with low noise (alongside its bigger bros D3 and D3s), so you may be able to get by at ISO 6400. But you can do much better with a fast lens (and crop if you need a tighter FOV). An entry level D-SLR with a smaller sensor will likely have a lot more noise.
Let me show you a couple of my own photos to illustrate what I mean. Here are 2 night soccer photos of my kid's team in a local park, with poor lighting. The shots are bad but I was the only parent who could still take the photos at that time. The other parents (quite a number) with D-SLRs and the regular tele lenses have packed their cameras away an hour before my shots. They only got some shots of their practice and missed the shots of the game.
(I have not processed these photos, they are straight out of the camera)
I use the Canon 5D Mark II (which is close to the Nikon D3/D700 in terms of high ISO performance) and the EF 70-200mm f/2.8L IS. Even wide open at f/2.8, I have to use ISO 3200 to get adequate speed for the action shot. This lens is more than 2 stops faster than the Tamron. So even ISO 6400 will not likely make it in this situation using the Tamron. And at ISO 3200, I can start to see some noise showing up (personally I have not used higher than ISO 3200 for my action shots). At regular print size, it may look okay. But definitely these are not the photos for wall size prints.
So my suggestion is to get the fastest lens you can afford for low light actions. If you like the versatility of a zoom lens, then get one with f/2.8. Most people will spend more money on the lenses than the camera bodies. I spend less than 1/3 of my D-SLR budget on the camera bodies (5D MkII and 30D). Photos always look better with better and more light (with a larger aperture lens) than to crank up the sensitivity of the sensor.
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