Probably the very best lens for Basketball (and likely also your competitive dance) is the EF 70-200mm f/2.8L IS USM II
BUT... this probably violates your "that won't break the bank" category.
Here's an interesting video by Scott Kelby on shooting sports. Scott used to shoot Nikon. Now he shoots Canon. But the points are still valid.
https://www.youtube.com/watch?v=wQ4KsGYDzgU
The challenge is that with consumer grade zooms, the lens is a "variable focal ratio" lens and usually it's an f/3.5-5.6 range or even f/4-5.6 range. Lower values in the focal ratio mean that the lens delivers more light to the camera. But the low values in those ranges only work when you are zoomed out to the lowest possible focal ratio. As you zoom in, the focal ratio increases (meaning you start to lose light) and hits the high end of the range usually by the time you are only half-way through the zoom range. E.g. if you are using a 55-250mm lens, then the lens is probably already at f/5.6 by the time you make it to 150mm focal length.
The Canon EF 70-200mm f/2.8L IS USM II provides the lowest possible focal ratio for a zoom and it's not a variable focal ratio lens -- meaning it can provide f/2.8 (more light than even the best scenario for a consumer grade zoom) and it can provide that throughout the entire zoom range. But the downside is that this lens is about $2k. Low focal ratio zooms are always expensive.
Your photos are likely blurry because you are shooting at lower shutter speeds due to the lack of light. If you inspect your images, you may find your camera (if allowed to automatically choose it's settings) is using the minimum aperture it can get away with (probably f/5.6) and whatever shutter speed is required.
An f/2.8 lens literally collects FOUR times more light. This means your shutter speed could be four times faster than whatever you are getting now.
There is a middle ground... Canon also makes an EF 70-200mm f/4L IS USM. That lens is about $1150 considerably less than the $2k f/2.8 version. But f/4 is only 1 stop faster than f/5.6. That means the lens collects twice as much light and can use a shutter speed which is twice as fast.
This f/4 compromise may or may not be enough for you. If unsure, considering renting these lenses before you buy. A number of outfits will rent lenses. My nearest "real" camera store (not a big box store that happens to sell camera gear, along with TVs, washing machines, and video games -- but a store in business exclusively to sell camera gear) does rent lenses. There are also a few online companies that will rent lenses. LensRentals.com and BorrowLenses.com both rent gear. I think B&H Photo and Adorama may also have rental departments.
Tim Campbell
5D III, 5D IV, 60Da
