amfoto1 Loc: San Jose, Calif. USA

It's mostly about the lenses. Both Canon and Nikon offer them.

But the camera is important, too. Do you have the original 18MP 7D (2009) or the current 20MP 7D Mark II (2014)? I've used both extensively and find the newer model has noticeably better high ISO shooting performance. You may need to bump up ISO too, though how much will depend upon stage lighting. For sports, the 7D and 7DII both have high performance autofocus. Like Canon's 1D-series, the 7D-series use a discrete chip to handle AF... where most other cameras and all other Canon models "share" AF duties using the same processor that's handling images. (Note: 7D-series also have dual image processors, like 1D-series. 5DS models also use dual processors to handle the extra large image files possible with their 50MP sensor. AFAIK, all other Canon use a single processor.)

Canon f/2.8 zooms might work for your purposes. Or fast primes such as 85mm f/1.8, 135mm f/2, 200mm f/2, 300mm f/2.8. Most large aperture lenses also include high performance autofocus (Exception: The ultra large aperture f/1.2 lenses use a slower AF designed for high precision rather than speed, since these lenses can potentially render very shallow depth of field and accuracy is more important than sheer focus speed... the same is true of macro lenses.)

Stage lighting actually often is brighter than people think. It might be difficult to shoot using any of the auto exposure settings, though, because there may be a lot of dark areas around the spot lit ones, fooling the camera.

In sports you want to be able to use faster shutter speeds to freeze rapid movement. I image luge runs tend to be surrounded by a lot of snow, which can fool cameras into under-exposure. So in both cases, you may need to experiment with manual exposures.

Stage lighting also might call for setting a Custom White Balance. Outdoors shooting luge Auto White Balance might be fine... unless shooting a shaded area, where it may be better done with a Custom WB, too. Certainly if shooting at night by artificial light or with mix of artificial and daylight during the day, a Custom WB may be needed.

Speaking of which, some types of lighting can present problems. Likely stage lighting is halogen or tungsten... no problem. But fluorescent or sodium vapor that might be used at a sports venue can be tricky. Those types of lighting actually cycle on and off very rapidly, faster than the eye notices (120 times per second). This can really mess with camera exposures. Canon 7D Mark II and some other models have a "Flicker Free" mode to deal with this. It tries to time the shutter release to match the peak output of the lighting and does a pretty good job. Without it, half or 2/3 of exposures made in this type lighting can be under-exposed beyond what's possible to recover. With Flicker Free, probably 90% or better are acceptably exposed (though some color balance adjustment might still be needed).

Sorry, but I don't use one, so know enough about the D5300 to say how it compares.

SquareRoot Loc: southeast Missouri

70 mph & low light sounds like what I wanted to deal with
for baseball after dark. I bought a used 70-200 Nikon f/2.8 on eBay.
Here are some results.

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TriX Loc: Raleigh, NC

And it did a very nice job for you - a perfect lens for exactly this application. Congrats on a nice series.

SteveR Loc: Michigan

SquareRoot....What camera were you using at what ISO. Also, some of these ballfields have excellent lighting at night. Was that the case?

SquareRoot Loc: southeast Missouri

Thanks for affirming my choice. I am complimented. I've been pleased.
At my age and physical condition, the lens is about all I can handle, ha!
I like to use a variety of angles, which I am allowed to do at our 'home'
ballpark, and to resort to a tripod or monopod would take some of the fun
out of it for me.

SquareRoot Loc: southeast Missouri

I use my Nikon D500, usually at 1/3200. Shutter priority with the camera deciding the ISO.
It used 25600, 20000, 16000, and 1100. The last pic was a bit before sundown, the others
a couple of hours later. The ballpark has new turf, but I won't brag about the lights -- I'm
guessing they are at least 20 years old. My 70-300 f/4.5-5.6 wouldn't do the job for me after
twilight with my Nikon D5200. So bought the 70-200 f/2.8 and like it.

Eddy Vortex

Shooting from 10 rows back? Remember that there's nothing wrong with getting a few rows of the audience in the shot.

balancr Loc: VA

Love the D700 image.

mjskates

I have the Canon 7d with the 18mp. I do have a Canon 50mm lens as well as the kit lenses for both cameras. I won't be buying any new cameras but I will try to work with lenses, and love the idea of renting them for the occasion. The hard part is that I don't have much practice time... actually, none because I can only "sneak" pictures during the actual performance, not even during rehearsals. :( So I will try to play with the suggestions offered and hopefully come out with some great pics!

SteveR Loc: Michigan

The D500 is a gamechanger. You wouldn't need an f1.8 with it.