Attic venting started and was incorporated in building codes because of cold climate ice damming. It has very little benefit in hot climates, with large volume venting the heat load might be reduced 10%, while losing 10-20% is a/c ductwork losses.
The best way to improve thermal efficiency in the attic is do go with a fully sealed attic with spray foam on the underside of roof, making the roof the thermal barrier not the attic floor.
The attic becomes part of the condition envelope and any a/c losses through ducts are retained in the envelope along with leakage pathways through attic into house.
If you want to know how to properly insulate and improve the efficiency of you house there is no better place than
Building Science they know what the are doing. This is the specific research report on unvented attics:
RR-0301 and here is a very detailed article on attic venting:
Understanding attic ventilation
In a 100 years no houses will have vented attics, it would be like having a dirt floor now.