From the Exodus International FAQ:
What's your "success rate" in changing gays into straights?
What you are really asking is whether there is realistic hope for change for men and women who do not want their sexual orientation to be homosexual. And the answer to that is yes!
I'm glad they haven't changed this, in the years since I first read it. Gave me a bit of a chill at the time... talk about spin.
Exodus International FAQ, continuing:
"In 1 Corinthians 6:9–11, Paul gives a list of all kinds of sinners that will not inherit the kingdom of God, including those that practice homosexuality. But he goes on to say, "and that is what some of you were. But you were washed, you were sanctified, you were justified in the name of the Lord Jesus Christ and by the Spirit of our God." Some Corinthian Christians had formerly been homosexuals, but now were counted among the saints. Now, that's good news indeed!
No one is saying that change is easy. It requires strong motivation, hard work, and perseverance. But we find hundreds of former homosexuals who have found a large degree of change--attaining abstinence from homosexual behaviors, lessening of homosexual temptations, strengthening their sense of masculine or feminine identity, correcting distorted styles of relating with members of the same and opposite gender. Some former homosexuals marry and some don't, but marriage is not the measuring stick; spiritual growth and obedience are.
On the statistical side, careful reviews of research studies on sexual orientation change suggest that real change is indeed possible. Studies suggesting change rates in the range of 30-50% are not unusual, although "success rates" vary considerably and the measurement of change is problematic. For details and review of several studies, see the link below.
A link to several studies is provided... but frankly, I'd heard enough, even the first time I read it. Then again, I was an unhappy atheist, not a desperate Christian. Maybe this does sound like a reasonable answer, if read from the right perspective.