camcorders... First we need to identify those with a wired remote. Generally, LANC camcorders are in the realm of the upper end of prosumer and pro gear. At the low end of the range, the Sony HDR-FX7 and HDR-FX1000 come to mind. There are some of the newer flash memory based units, but for this post we don't really need them. This wired remote can control a couple of camcorder items - usually zoom and focus. No pan or tilt (left/right; up/down). For that, we need a separate remote controlled head that can deal with that motion - and the controller that can deal with that.
Then there's the matter of the recording media. If is is located in the camcorder, that means getting to it and replacing it when the media fills. In the case of miniDV tape, a 60 minute rated tape can store up to 63 minutes of high quality, low compression high definition video in digital HDV format. An external recorder is possible - connect to the camcorder's firewire port and record for a few hours. In your case, when the game is done, the ladders are brought out to get to the tall camcorders for the media swap. While the current field of flash memory camcorders can record for many hours, assuming a high capacity memory card, the ladders still need to be setup for climbing and media replacement.
The remote controlled camera heads available from Sony, Canon and a few others eliminate this remote media access issue by sending their video over cabling to a computer with big hard, fast, drives that stores the captured video. In a studio environment, the video person accesses the video from a computer on their desk that is connected to the same network the storage computer connects to. There is no "media swap" requirement because the remote heads have no storage.
Because of their design, the remote head pan/tilt/zoom control is built-in to a single controller. The cameras have a cable bundle that includes power, video and PTZ control. The cable bundle form the camera plugs into a controller. The controller plus into a couple of different boxes, including a video switcher. The design allows the user to select a camera, view its video on a monitor and the PTZ controls can be used properly for the camera sending the video being displayed. The other cameras will continue sending their video and get that recorded, but the use of the PTZ controller does not impact them until switcher selects the next camera.
Usually, these remote heads have no mic, so you'll need to consider how you'll deal with audio. At college level and above basketball games that are recorded, there are anywhere from 6-20 mics installed throughout the venue connected via XLR cable to an audio mixing board. The mixing board is connected to the video recording subsystem... and all the electronics are what allow you to see what is on TV or in a recording... Studio cameras that look like camcorders may be used for ad-hoc interviews. But a camera operator has them shoulder mounted - or use of a SteadyCam vest system with articulated, counterbalanced arm and a sled for counter balancing the camera can be used. You see them more at football games at the end of the game when everyone runs onto the field connected with big cables (occasionally wireless). The remote PTZ video head is on the uprights somewhere. We won't get in to the remote PTZ Skycam that runs along the cables over the stadium.
If you watch college or pro basketball games, the remote PTZ video head is usually mounted to the top of the backboard... but the bottom line for all this is... no camcorders.