Amateur Sports Integrity Act - Athletic Performance-Enhancing Drugs Research and Detection Act - Requires the Director of the National Institute of Standards and Technology to establish a program to support research into the use of performance-enhancing substances by athletes, and methods of detecting their use.Requires the Director to: (1) consider research proposals involving performance-enhancing substances banned from use by competitors in events sanctioned by organizations such as the International Olympic Committee, the U.S. Olympic Committee, the National Collegiate Athletic Association, the National Football League, the National Basketball Association, and Major League Baseball.Requires the Director in carrying out such program to: (1) fund research on the detection of naturally-occurring steroids, such as testosterone, and other testosterone precursors (e.g., androstendione), and other substances, such as human growth hormone and erythropoietin for which no tests are available but for which there is evidence of abuse or abuse potential; (2) fund research that focuses on population studies to ensure that tests are accurate for men, women, all relevant age, and major ethnic groups; and (3) not fund research on drugs of abuse, such as cocaine, benzodiazepines, barbiturates, phencyclidine, marijuana, morphine/codeine, and methamphetamine/amphetamine.Requires the Director to develop a grant program to fund educational substance abuse prevention and intervention programs related to the use of such banned performance-enhancing substances by high school and college student athletes.Amends the Ted Stevens Olympic and Amateur Sports Act to make it unlawful for a governmental entity to sponsor, operate, advertise, promote, license, or authorize by law or compact, or for a person, to sponsor, operate, advertise, or promote, a lottery, sweepstakes, or other betting, gambling, or wagering scheme based on a competitive game at the Summer or Winter Olympics, a competitive game in which high school or college athletes participate, or a performance of high school or college athletes in a competitive game.