|Alcohol and drug abuse are far more likely to result in violent behavior than mental illness by itself. In the National Institute of Mental Health's E.C.A. study, for example, people with no mental disorder who abused alcohol or drugs were nearly seven times as likely as those without substance abuse to commit violent acts.
It's possible that preventing people with schizophrenia, bipolar disorder and other serious mental illnesses from getting guns might decrease the risk of mass killings. Even the Supreme Court, which in 2008 strongly affirmed a broad right to bear arms, at the same time endorsed prohibitions on gun ownership 'by felons and the mentally ill.'
But mass killings are very rare events, and because people with mental illness contribute so little to overall violence, these measures would have little impact on everyday firearm-related killings.