in my experience mic placement is heavily dependant on which sport you're recording.
with that said, the general idea is to be in a position to record as much of the action as possible, and to use whatever techniques and access are necessary to get there.
Almost all sports employ plant mics based around the part of the playing surface where the action is most likely to occur.
An example would be basketball, where in the NBA the arenas will use contact mics and lavs attached to both goals (for the Mavs, there are COS-11s placed inside the breakaway hinge of the basekets - these catch everything from dunks to shoe squeaks for the broadcast). Baseball also uses plant mics inside of the actual bases. American football does something similar in that they lav up the center's back and use that during the start of each play, so the center is essentially a plant mic that moves around the field with the action. Hockey tends to use pzm mics attached the glass at multiple points, and the mixer will fade them in and out as the action approaches them. I believe that tenns and table tennis use plant mics at the edges of the net aimed out at either side.
In addition to plant mics, most sports employ multiple shotgun mics for additional coverage.
Again, placement is sport specific, but for example baseball tends to have a shotgun in the first base dugout aimed at the batters box, two behind the batter aimed at the box as well (one high one low), and another aimed at the pitcher, all permanently mounted and without operators. For hockey and basketball at the AAC in Dallas, there are two MKH60s under the center hang aimed at opposite ends of the ice/court that catch broad coverage for when the action is at one side of the playing surface or the other. Basketball also has roving boom operators covering action. American football famously employs parabolic mics with operators along the sidelines, and I assume that soccer is similar. In many sports, the roving cameras also have shotgun mics attached that can get mixed in with the camera cut. Golf does this, and has a crew of roving shotgun operators as well.
the last part of the equation is crowd mics
The AAC in Dallas has four schoeps CMC6 with omni heads hung 100' above the crowd for wide crowd coverage, and they use the other plant mics to supplement the crowd sounds. Cowboys Stadium does something similar. I'm not sure what other arenas do, but the general idea is to get coverage of the wide perspecive with an omni pickup.
In the end, the real answer is that you need tons of plant mics and mounted shotguns in coverage areas, and then you should supplement that with roving shotguns and wide mounted crowd mics. dozens of channels of coverage are not unheard of in big events.