HOUSTON—When March rolls around, few will have a tougher time filling out NCAA basketball tournament brackets than Steve Trauber, Citigroup Inc.’s top energy banker.

Over the past decade, the banker and his wife, Leticia Trauber, have groomed some of Houston’s most talented young basketball players, sponsoring a regional travel team that won two national championships. As those players now start their freshman year at colleges around the country, including basketball powerhouses Duke University, the University of Kansas and...