I never use Safety Shift. It's just too unpredictable.
An evenly lit gym like in the above photos is a great example of the type of lighting where M excels and any form of auto exposure (Tv, Av or M) often will cause more problems than it's worth.
The problem with auto exposure in this type of situation is that the camera's reflective metering system is going to react to the tonalities of the players' jerseys. When a dark jersey is what's predominently being metered, the camera will tend to over expose. When a white or light colored jersey is more of the image area or the central point being measured, the camera will want to under expose. And, because the lighting is relatively even, there's really no good reason to have to deal with this variation while shooting, via Exposure Compensation or AE Lock or other methods of overriding the metering system. If you don't deal with it, you'll end up having to adjust each image differently in post-processing.
It's so much easier just to switch to M and lock in your exposure settings.
Now in order to set up M there are a number of different possible methods, all of which will work.
You could just take a short series of test shots and sneak up on a "good exposure" a little at a time. You'll need to know what your histogram is telling you, don't rely on the playback image because it's not properly calibrated, nore is it reliable since it's being viewed under different light sources each time you use it.
Some people just "spot meter off their hand", then dial in some known value. This works because the tonality of your hand doesn't change. Once you figure out the adjustment value (+1 stop might work for a caucasian person... but figure it out for yourself), you just have to make sure to orient your hand much as the subject your are shooting. For example, in the gym shots shown above you are shooting the subjects from the side, so you want to meter your hand held upright at arms length. This measures the light falling onto your hand in the same way you are photographing the light falling onto the subjects.
A separate, handheld incidence meter is another good method.... though of course you have to go out and buy a meter. This measures light falling onto the subject, rather than what's being reflected off of it. So it's not influenced by subject tonalities such as the dark and light colored jerseys. Again it's important to orient the meter correctly, for example holding it vertically in a case like this, where you are going to be shooting the subjects from the side. You don't want to hold the meter out horizontally, where it would measure the illumination falling on top of their head (unless for some reason you are shooting down from above).
If you get there early and can do so, walk around to different locations you might be shooting from and take meter readings, to see if there is any variation in the lighting. If so, make a mental note of it and be prepared to adjust your exposure slightly, if and when you move to the new location. There also might be brighter or darker areas shooting from one location... and if you know about them you can quickly dial your manual exposures up or down a click or two to compensate, while following the action in and out of those areas.
Yet another method is to use a neutral gray target such as a Lastolite EZ Balance
and spot meter off that with your camera. Once again, be sure to orient the target same as your subjects.
An added bonus of this type of target is that besides arriving at a correct exposure, it also can be used to take an image that's used to set a Custom White Balance, which IMHO the above photos might have benefited from. AWB doesn't work particularly well in many types of artificial lighting. And there is often too much variation in light color to rely on the presets or try to do a manually set color temp. You can try to correct in post-production, but why go to the trouble when it's so easy to set a Custom WB? Color temp and tint are one of the few things that all editing softwares pick up and use faithfully, even from RAW files. Só it's always a bonus if you can get it right, from the start.
By the way, if you want to bias color temp for some reason, there are so-called Warm Card targets that an be used, so that the camera will consistently render an image with a slight tint, much as we used filters to achieve a certain "look" with film in the past, but soooo much easier with digital. (Note: The set of cards linked includes both warming and cooling targets, as well as fluorescent correct, a neutral gray card, and a color checker.) If you take and keep reference photos of these targets in the location, you can later use those for exposure and WB control in post-production, too... via a simple eyedropper sampling tool.
Setting up and locking in exposure at the start of the game isn't the end of it. During an event it's important to periodically check your exposures via the histogram. If, for example, that evenly lit gym has some skylights, the lighting will gradually change during the day, as the sun moves. Lighting also can change as lamps warm up over time. So be sure to call up an image and check your results every so often. You might need to tweak your settings a little. Another reason to check the histogram every so often, while shooting fast moving action Ive found my settings got bumped and are ending up incorrect more than I'd care to admit. 
You also might want to vary some of your exposure factors during the course of the event for other reasons.... such as to use larger or smaller apertures to get different depth of field effects. Or perhaps drag the shutter a bit for some deliberate action blur or panned shots.... so every image doesn't end up looking like every other image. I go for my "meat and potatos" shots first. Then, when I'm sure I have plenty of those in the can, I like to experiment a bit, try to get some different techniques, change lenses, move around and shoot from different locations, etc.
Anyway, give M a try, the next time you are in such an ideal location to use it. I think you'll like it.
There are plenty of other times when the various auto exposure modes are useful or even necessary. So they won't be "neglected".
