Popularity hounds that they are, American presidents pay close attention to two sets of polls. The first is the presidential approval rating taken regularly in polls of ordinary Americans. The second is the perennial presidential ranking survey, where historians and political scientists are asked to judge presidential “greatness.”

“Legacy”-minded presidents might learn some strange lessons from these scholarly surveys. For instance, Harry Truman, who launched our first major undeclared war, routinely beats his successor Dwight Eisenhower, who kept the peace during hair-trigger tensions with the Soviets. Similarly, the odious Woodrow Wilson, who brought the United States into the pointless carnage of World War I, is a top 10 favorite for historians, while Warren Harding, who followed Wilson with peaceful “normalcy” — is nearly always dead last.

I’ve long thought there was something perverse in the way scholarly surveys seem to award bonus points for being a “warrior president.” (Was the Teapot Dome scandal really worse than 117,000 dead doughboys?)

Last week, economists David Henderson and Zachary Gouchenour released a study, “War and Presidential Greatness,” that provides empirical support for my simmering suspicion. It’s a sober, scholarly paper that comes to an absolutely horrifying conclusion: “military deaths as a percentage of population is a major determinant of greatness in the eyes of historians.”

War: Huh, yeah! What is it good for? Boosting your presidential ranking, apparently.

Henderson and Gouchenour investigated “the connection between presidents’ greatness rankings and the intensity of the wars that those presidents carried on. Using multiple regression analysis, we compare the effect of war intensity with other explanations offered by previous researchers,” such as intellectual prowess, GDP growth and involvement in major scandal. They found “a strong positive correlation between the number of Americans killed during a president’s time in office and the president’s rating.”

Presidents have long recognized the “wartime bonus” doled out by historians. Henderson and Gouchenour quote Teddy Roosevelt: “if Lincoln had lived in times of peace, no one would know his name now.” (TR would later come to envy Woodrow Wilson because Wilson got to fight the European war TR himself had pushed for.)

In 1996, the legacy-obsessed Bill Clinton spent hours with adviser Dick Morris mulling over what Clinton could do to end up in the top echelon of presidential “greats.” “I envy Kennedy having an enemy,” Clinton said at one point, imagining how much easier it must have been for the president to get his way by raising the specter of communist domination: “The question now is how to persuade people they could do things when they are not immediately threatened.”

Luckily, Clinton decided to keep his wars small and pointless, rather than large and bloody.

Let’s hope that the lure of “presidential greatness” doesn’t tempt Barack Obama into rash action with Iran. After all, he’s already benefiting from grade inflation. In July 2010, just 18 months into his term, a Siena Research Institute survey of 238 academics ranked Barack Obama as the 15th best president we’ve ever had.

One lesson to draw from their findings, Henderson and Gouchenour suggest, is that “we should stop celebrating, and try to persuade historians to stop celebrating, presidents who made unnecessary wars. One way to do so is to remember the unseen: the war that didn’t happen, the war that was avoided, and the peace and prosperity that resulted.”

It’s also worth reminding presidents that, as Wilson, Truman, and George W. Bush discovered, unnecessary wars make presidents unpopular. While historians may eventually award extra credit for spending American blood and treasure, ordinary Americans generally don’t. Here again, they come out looking smarter than the intellectuals.