They say you can tell a lot about a person by the company they keep. The presidency is no different: when it comes to a commander-in-chief, you can tell a lot from the aides they keep close.

Barack Obama’s closest staffers were often intensely competitive, earnest, studious types who struggled to understand why the world didn’t admire their idealism and talent as much as they did. George W Bush, at least in his first term, surrounded himself with trigger-happy street fighters who confused patriotism with their own paranoia and prejudice.

In the case of Donald Trump, the company he keeps is surprisingly consistent: a singular type with a shared set of character traits. They are, to a man, cocky, unqualified and kooky. You might call this the CUK theory of the Trump presidency, in honor of one of their archetypes: Steve Bannon.

All the president’s men – at least, the CUKs – are a constant presence, in spite of the huge turnover among them. There was Bannon, now there’s Bolton. There was Scaramucci, now there’s Giuliani. It matters not. Trump cycles through his CUKs happily and frequently because he needs to keep one or more close through all his volatility.

Sign up to receive the latest US opinion pieces every weekday

Let’s start with Bannon: the man who believed he was reshaping global politics. Never mind all that help from Russia and Facebook, Bannon was riding the crest of a wave of his own making. Nobody had discovered white male resentment before: not Richard Nixon, not Pat Buchanan, not even Bill Clinton.

Bannon thinks he’s so good at this stuff that he was considering running for president himself in 2020. He also told Vanity Fair that getting fired from the White House was an upgrade: inside the West Wing he had influence, but outside he had real power. Cocky? Check.

How unqualified was Bannon at his purported job of chief political strategist? Exhibit A is Roy Moore in Alabama, a candidate accused of child abuse, whose doomed campaign was Bannon’s great last stand. If you can’t see the limits of white male resentment in the state that built its politics on those foundations, then you have forever lost your credentials as a political strategist. Status: unqualified.

Kookiness was Bannon’s calling card, his cri de coeur. You could plunge into the conspiracy-filled world of his media creation, Breitbart, to explore all the crazy theories he thrived on. Or you could read about the guy who ate green ketamine before he showed up to work, because he makes more sense.

So many pundits took Bannon’s kooky ideas as some kind of mark of genius, because of 70,000 votes in three swing states and the quirks of the electoral college. But to recap, Bannon was inspired by a French occultist and Italian racialist to assert that western civilization was locked in “a new dark age” as part of an existential battle with Islam. Which just goes to show that reading books doesn’t necessarily make you less kooky.

Where does John Bolton, the latest in a long line of Trump’s national security advisers, sit on the CUK scale? If Bannon is a perfect 10, Bolton is a nine.

People who worked with him in the Bush administration say he’s arrogant, when they’re trying to be diplomatic – a quality that Bolton lacks entirely. Bolton even maintains his arrogance about his biggest, most obvious disaster: his cheerleading for the invasion of Iraq. When Tucker Carlson, of Fox News fame, asked him if the war in Iraq had empowered his great enemies in Iran, Bolton said: “No, because I think your analysis is simple-minded, frankly.”

Calling the supremely cocky Tucker Carlson “simple-minded” is a power play in the league of cocky politics.

This takes us directly to his obvious lack of qualifications to manage national security for the world’s greatest military force. In addition to his colossal errors of judgment about Iraq, he is a hothead and a disastrously bad manager. He isn’t even on the same page as his boss about talking to North Korea, having spent a career trashing them as serial liars and conmen.

Which brings us to his kookiness. This is a national security adviser who recently advocated for a pre-emptive strike against North Korea. This is a former UN ambassador who believed the top 10 floors of the UN could be demolished with no impact on the organization. He only drops a point on the CUK scale because of the lack of occultist influence.

Anthony “the Mooch” Scaramucci is an epic example of the president’s favorite man. Cocky doesn’t come close to the extravagant strutting and preening of a man who claimed everyone else was obsessed with their own penis. The Mooch was so unqualified for the job of White House communications director that he lasted 10 or perhaps 11 days in office. That’s in a West Wing where the only qualification for a job is a pulse and never-ending praise for the boss.

Which brings us to his kookiness. For the Mooch, Trump is “perhaps the least racist” person on the planet, even though he sympathizes with neo-Nazis. Trump is also “neurologically sound” even though, well, everything he has tweeted in the last 16 months.

Overall on the CUK scale, the Mooch’s supreme cockiness balances out the relative lack of kookiness, making him a solid eight.

So to our latest member of the gang: Rudy Giuliani. According to the otherwise friendly New York Post, it was Rudy’s arrogance that killed his 2008 presidential campaign. For some reason, early state voters found it a turnoff. This is a man who endorsed Trump at the Republican convention by saying the next president would carry the Giuliani torch: “What I did for New York City, Donald Trump will do for America.”

If anyone had any doubts about Rudy’s qualifications to be the latest in a long line of Trump’s lawyers, this week was truly special. In a couple of Fox News interviews, Giuliani contradicted the previous official story about Trump’s lawyer paying hush money to the actress known as Stormy Daniels. Along the way, he exposed his new client to additional legal risk and managed to refocus the world’s attention on the president and a porn star on the National Day of Prayer. Pure genius.

Among the many kooky theories Rudy has peddled was his repeated stirring of the pot about Hillary Clinton’s health, his obvious superiority to Beyoncé, and his recent description of FBI agents as “stormtroopers”. For all this and so much more, Rudy scores another perfect 10 as a CUK.

Curious minds might wonder why this president chooses to surround himself with so many men who are cocky, unqualified and kooky. For someone so modest, so well-versed in world affairs, and so cogent, it seems so obviously out of character.