I've done some experimentation with BLE range sensing and I've found that it is not very accurate. It is based on RSSI - a received signal strength indication - and the received signal strength is affected by a lot of things apart from distance. For example, putting a BLE device into your pocket so that some of the RF energy is absorbed by your body causes a similar decrease in RSSI as moving it 10 meters away in free space. Also the radiation pattern from a device is not even in all directions, so 3 meters in one direction may give the same rssi as 8 meters in another, etc.
One way that this is got around in beacon type applications is in taking several readings over time and taking an average. This is not ideal in your case as you need fairly instant results.
One of the ways in which low-energy is achieved in BLE is by not communicating very often. I.e. a peripheral device may communicate with a central device only once a second or so. This is what gives keyring type devices that can be on for a year. You get to choose these intervals when you design a system so in your case you can probably have a shorter interval and turn the devices off when no one is playing.
BLE works as a hub-and-spoke type network where devices are either a central or a peripheral. A peripheral can establish a link to only one central (but broadcast packets from a peripheral may be received and ranged by any central). Ranging is from each peripheral to the central.
You don't need a dual mode chip in a BLE system, you can have an entirely BLE implementation. Common embedded BLE chipsets (Nordic Semiconductor, TI, CSR) can all operate in central or peripheral mode.
I'd be tempted to use a simpler ranging system between your wristbands and your ball. Maybe iR, ultrasonic or other radio techonolgy would do the job. You could interface this to a BLE device and use that to communicate scores, who has the ball to a smart phone