Estimates in a July 2005 Energy Information Administration report – In twenty years, when the ANWR production of oil would reach its theoretical maximum, gas prices would be affected by only around one cent per gallon or 50 cents per barrel (this was assuming a $27 barrel of oil, but oil prices have since increased, which could possibly make the potential impact greater).
Counter-arguments
Any reduction in oil prices is a good reduction. It is not necessary that such a reduction be dramatic.
Increasing domestic reserves for national security purposes is more to the point than attempting to decrease prices. It is more a way of hedging against vulnerabilities in foreign supply (Middle East chaos…), than it is a way to decrease costs.