BTW, I question the contributor who reckons greatest risk of collision is in the circuit: with everyone going the same direction, with the same intention and on the same frequency, all these factors reduce collision risk.
We don't need to guess... Statistics talks. Most collisions do happen in the traffic pattern, with a significant number on final approach.
Why that is so is an interesting question IMHO, bearing in mind the factors you mention... One interpretation is that the main collision avoidance mechanism is the big sky concept, and where that does not apply (=traffic pattern) the risk of collisions goes up tremendously, despite same direction frequency intention etc.
This is a pretty interesting publication on the subject:
http://www.aopa.org/asf/publications/sa15.pdf