I have a question regarding the value between business and proof coins based on mintage numbers. If business strike mintage is very high, does that negatively affect the proof's value? Obviously the number of proofs minted also plays a role in value, as well as other factors, but is there a correlation between the two?
I haven't completed a statistical analysis but my guess is no. My thoughts are that proof values are based on a combination of the proof's mintage, proof's grading, and the average collectors desire for the proof 's.
There is NO relationship of value between business strike and proof as both represent different manufacturing techniques AND both have totally separate mintages which makes them different coins with different pricing structures. Sometimes, the designs are even different which accounts for the different business strike and proof varieties that exist today. Different designs make them different coins with no pricing relationships. For example, the 1972 Type 2 IKE, which has the Proof Reverse, shares absolutely no relationship in price to either a 1971-S Proof of 1972-S Proof IKE. The same is true of the WAM Lincoln Cents (Proof Reverse) and the Type B Reverse Washington Quarters (another Proof Reverse).
If I understand you correctly, and unless speaking of most modern coins, concern yourself more with survival numbers as it is more important than mintage. Generally speaking, PRs are PRs and have little to do with BS coins. One notable exception is the 95PR Morgan which, because no Philly BS coin was issued that year, carries a substantial premium over other Morgan PRs and is quite popular because of it.