Here's how these 11 ranked:
Three in the top 10 excellent category (Washington, Lincoln, Cleveland)
Three above average (Jackson, Taylor, Fillmore)
Three average (Harrison, McKinley, Truman)
Two poor or bottom 10 (Van Buren, A. Johnson)
Moral: Our random odds are actually better with presidents who didn't graduate from college.
Since Harrison only served one month, it is unfair to put him anywhere but average.
If you choose to include the current bozo occupying the White House, that would make the score: academics - 2, America - 0.