How do Tom Simpson and Piney Woods bring out the best in other characters?
Tom and Piney bring out the best in three of the outcasts, because Piney and Tom are innocent and completely clueless. Tom believes that Oakhurst is a good man, because Oakhurst gave back to Tom all of the money that he lost while betting against Oakhurst. Tom also doesn't know that Mother Shipton and Duchess are prostitutes. In fact, he thinks that Oakhurst and Duchess are married.
Basically, Tom and Piney initially think the best of each of the outcasts, and Tom and Piney treat them as such. It has probably been a long time since anybody looked at Duchess and Mother Shipton without disdain or as a sexual object. Because Tom and Piney are seeing the best in the group, the group does not want to disappoint those initial impressions; therefore, the three outcasts have the very best brought out of them, because they like being seen like that again.