Pay discount points on a mortgage, and you take a gamble. Plenty of borrowers lost that wager in recent years, according to a pair of economists.

Yan Chang and Abdullah Yavas set out to describe consumers' behavior, not to give advice about whether one should pay discount points. Even so, their research can be boiled down to this: Think hard before you pay discount points, and if you do, don't hesitate to refinance.

Their research paper, "Do Borrowers Make Rational Choices on Points and Refinancing?" is a chapter of Chang's doctoral thesis at Penn State University. Chang is a senior economist at mortgage-financing giant Freddie Mac. The study was done independently of her employer, and she speaks for herself. Yavas, an economist and professor of business administration at Penn State, was her thesis adviser.

Chang and Yavas concluded that borrowers tend to pay too many points because they overestimate how long they'll keep the mortgage. Furthermore, people who pay discount points tend to wait too long to refinance.

Paying discount points is a way of reducing the mortgage's interest rate. One discount point is 1 percent of the loan amount. On a 30-year, fixed-rate mortgage, 1 point typically reduces the rate by one-quarter of 1 percent. If you can borrow $200,000 at 6.25 percent with zero points, you could borrow the same amount at 6 percent by paying 1 point, or $2,000. That would save $32.33 a month. It would take 62 months to break even -- for the accumulated monthly savings to total the $2,000 paid upfront.

Chang and Yavas looked at 3,899 mortgages that were originated between January 1996 and December 2003. About one-eighth of those borrowers paid discount points.

Of those who paid points, two-thirds had paid off the mortgage by June 2005, either because they sold the house, refinanced or defaulted on the loan. Of those people, 1.4 percent had benefited by paying points.

The other one-third of the points payers still had the original mortgage in June 2005, the cutoff date. Of those people, 16 percent already had benefited from paying points by June 2005, and the percentage probably grew higher as time passed.

To summarize: At least two-thirds of the points payers made the wrong bet. Most of the non-points payers made the right call.

That might sound like a slam-dunk case against paying points. It's not, because mortgage rates were falling and home values were rising during much of the study period, creating many opportunities to refinance.

"Personally, I think that it is a caveat of this study that it covers a period typified by historically low mortgage rates and increasing house prices, which offers borrowers more incentive to refinance than times of rising interest rates, where more borrowers might reap the full benefits of mortgage points," Chang said in an e-mail interview.

Would the result have been different in a period of rising rates?

"That we simply do not know," Yavas said in an e-mail interview while on sabbatical in Turkey.

Bob Moulton, president of Long Island-based Americana Mortgage, said the results probably would have been different in a time of rising rates because a greater percentage of people would have held onto their mortgages past the break-even point.