We have never met Mr. Trump, let alone examined him, so it would be inappropriate of us to offer a formal assessment of his level of narcissism. And in all fairness, today’s constant media attention makes a sizable ego a virtual job requirement for public office. Still, the Trump phenomenon raises the question of what kinds of leaders narcissists make. Fortunately, a recent body of research has suggested some answers.

In a 2013 article in Psychological Science, we and our colleagues approached this question by studying the 42 United States presidents up to and including George W. Bush. (The primary data were collected before Barack Obama’s presidency.) First we took a data set compiled by the psychologists Steven Rubenzer and Thomas Faschingbauer, who for an earlier study asked experts on each president to complete personality surveys on the subjects of their expertise. Then, using standard formulas from the research literature on personality, we produced estimates of each president’s narcissism level. Finally, we correlated these personality ratings with data from surveys of presidential performance obtained from independent panels of historians.

We found that narcissism, specifically “grandiose narcissism” — an amalgam of flamboyance, immodesty and dominance — was associated with greater overall presidential success. (This relation was small to moderate in magnitude.) The two highest scorers on grandiose narcissism were Lyndon B. Johnson and Theodore Roosevelt, the two lowest James Monroe and Millard Fillmore.