It is common to suspect that leaders, whether in business or politics, are an unimpressive bunch, who don’t measure up to the heroes of the past. In fiction, of course, 'the idiot at the top" really is an idiot, like Chauncey Gardiner, the simpleton played by Peter Sellers in the 1979 movie "Being There", with his inane comments about his garden taken as great wisdom for society to live by.

But in real life, the balance between "simple" and "brilliant" leaders is often seen differently by the lenses of history. In American history, as in business, things aren't always what they seem on the surface. Consider these US presidents, and their reputations at the time of their governing, versus what history has learnt of them:

Some of the most successful American presidents, derided at the time as rising above their training and competence, were in fact deeply gifted.

1. Harry Truman is now considered one of the greatest American presidents – for rehabilitating Europe with the Marshall plan, desegregating the US army, and putting the foundations of US prosperity and success in place for the post World War II era.

Yet Truman was notorious as the president who "had greatness thrust upon him" when Franklin Roosevelt died. Only a high school graduate, and a failed haberdasher and farmer before entering public service, he was considered ill-prepared for the presidency.

His strength of will was noted quickly, and his decisiveness. But it was only in his last years that his breadth of historical knowledge became known. As Dean Acheson, Truman’s brilliant (and Harvard and Yale educated) Secretary of State said in an interview shortly before his death: "Mr. Truman read every book in the Independence (Missouri) library, which had about 3,500 to 5,000 volumes, including three encyclopedias, and he read them all the way through. He [got] a lot more out of that effort, which he took out of farming when he did it, than he would listening to all of this [junk] that goes on at Yale and Harvard."

2. Dwight Eisenhower was selected to command Allied Forces in World War II in Europe over dozens of more senior generals –he seemingly came out of nowhere. His success was often attributed to his political skills. As president, his inarticulate press conferences were a national joke, and he was considered of mundane intelligence.

Years later, historians documented how Ike was actually one of the premier intellects in the US Army in the 1930’s, first in his class at the Army War College. Furthermore, as senior aide to Douglas MacArthur, he demonstrated his ability as a gifted speechwriter.

Eisenhower’s stumbling presidential press conferences are now viewed by many historians as the staged performances of a supremely confident man, attempting to deflect media inquisitiveness on delicate topics of state.

3. Ronald Reagan was widely considered the least intellectually able modern president. The former actor was famously characterized as "an amiable dunce" who couldn't keep his facts straight. Even after the Soviet Empire collapsed without a shot being fired, critics assumed he had "followed the script" of key advisors in his decades-long crusade against "the Evil Empire".

But in 2001, Reagan, in His Own Hand was published, a collection of hundreds of radio talks given by Reagan in the late 1970’s. He wrote about two-thirds of these himself, and the drafts are reproduced in his own handwriting. Reagan, it turns out, was far more immersed in books and ideas than even his supporters realized.

Contrast these with three brilliant, well educated presidents who were not nearly as successful.

1. Woodrow Wilson was former president of Princeton University, and a brilliant and idealist man. Yet he overreached in his relations with the US Senate and was unable to get it to ratify membership in the League of Nations, the post-World War I predecessor to the United Nations.

2. Herbert Hoover was a great engineer and humanitarian. A staunch free market advocate, he was helpless in the face of the Great Depression, and was beaten for reelection by Franklin Roosevelt, an ordinary intellect with a higher tolerance for trying different approaches to repairing the economy, rather than waiting for it to heal itself.

3. Jimmy Carter served as one of the US Navy’s first nuclear submarine officers, had a successful business career and was one of the first pro-civil rights governors of a southern state. Yet Carter was another engineer and humanitarian who was ineffective in the White House. He was a micromanager, famous for scheduling the White House tennis court’s personally, and his spiritual humility masked an intellectual arrogance, which made it difficult for him to influence Congress, or the American people.

What are some principles for assessing the effective intellect of leaders? Here are four guidelines:

1. EQ is Critical – "Emotional Intelligence", the concept popularized by Daniel Goleman in the book of that name several years ago, is more important than raw intellect for a leader. EQ includes factors such as self-awareness, altruism, personal motivation, and empathy.

2. IQ is Valuable, if it Doesn't Get in the Way - A first rate intellect can be a great leader (like Jack Welch or Bill Gates), if he is able to discipline himself in making and executing decisions.

3. Don’t Overrate Articulateness – In business or government, articulating an exiting vision is not as important as following through. Truman, with his reedy voice and wooden speaking style, was just as effective as the charismatic Roosevelt, and more so than several later presidents whose magnetic personalities were not matched by dogged implementation.

4. Don’t Overrate Credentials - Success in past endeavors is the single most reliable indicator for success in the future. But as described above, Truman and Eisenhower had great experience, without formal credentials.

Formal credentials are valuable, as long as the bearer of them has also conquered real adversity. If they haven’t, they face the danger of equating success with climbing an organization pyramid. But at the upper reaches of government or business, there is no longer a pyramid to climb. The challenge becomes creating new steps, or a new endeavor altogether.