Welcome to Nikonians! Are you shooting games in daylight, evening, or night games under the lights? For games in daylight conditions, the 70-300mm f/4.5-5.6G ED IF AF-S VR or even the 55-300mm f/4.5-5.6G ED IF AF-S will provide the additional reach you are looking for while allowing a shutter speed fast enough to freeze the movement of your subject. For evening games or night games under the lights, your maximum shutter speed is limited by the ambient light level, the ISO capability of your camera, and the maximum aperture of your lens. The D40 maximum ISO is Hi (ISO 3200) though ISO 1600 is significantly cleaner and all of the variable aperture zooms are f/5.6 at the long end. If you are shooting in low light, your choices are limited to the fast zooms and primes. Unfortunatly the fast zooms and prime telephoto lenses are expensive, large and heavy. If your budget is tight you might want to consider the Tamron 70-200mm f/2.8 Di LD which should be fast enough though you won't gain any range. If you provide the shutter speed, aperture, and ISO settings of a well exposed image in low light at your field, we can extrapolate the aperature you will need to freeze the action. Good Luck and Enjoy your Nikons!