How much do points affect the interest rate?

When I consider paying points to get a mortgage, how can I determine what the effect of paying discount points will be on my loan's interest rate?

There is no single answer to that, because it's not a linear relationship. In general, each point will lower your interest rate by between 0.125% and 0.25%, but the exact trade-off depends on the mortgage lender. It can also depend upon the type of mortgage you selected (fixed or ARM) and the term of the loan. Even the lockin you select can affect it.

For the most part, lenders have a range of pricing options which range from "rebate pricing" (where you get a higher-than-market interest rate but cash back at closing), up to about four points you can pay out-of-pocket. The maximum interest rate change from "par" -- that is, a zero point interest rate -- is probably no more than about 1% or thereabouts.