fireflyblob
I won't show you the statistics. I don't have them. It is my opinion after 40 years of flying.
Why is it the best? Entering on the 45 at pattern altitude allows you to see and be seen by those in the pattern, descending into the pattern means you will have a greater chance of descending upon another plane. Those on the crosswind will have a chance of seeing you, you will have a chance of seeing them and those on the downwind. Once in the pattern, good luck to you all.
AND if you all agree to join on the 45 then you will all be looking there for the incoming traffic instead of fooling around with all the other methods. Standardization, try it, you will like it.
When in Rome, its time to go home. I understand the Romans helped build some of the roads in England. But I really don't think the roads in the US lead to rome, now do they?