Russian President Vladimir Putin reacts during the Ukraine crisis meeting in Minsk, Belarus, 11 February 2015. EPA/MYKOLA LAZARENKO

There's no world leader as over-analyzed as Vladimir Putin. Just last week, we learned of a 2008 Pentagon study that concluded the Russian president's "neurological development was significantly interrupted in infancy" and that Putin probably had Asperger's syndrome. He's also been called a narcissist, diagnosed with "pleonexia" (the insatiable desire to have what rightfully belongs to others), and simply been accused of being a "thug."

Whatever your own diagnosis of Putin is, there's little doubt he's a fascinating figure, and the events in Ukraine over the past 12 months have forced us all to think long and hard about his motivations. Now, with European leaders hoping to have found some kind of compromise in Ukraine and the United States recently warning it might arm the Ukrainians, we're left with an uncomfortable question: How do you deal with someone if you can't understand him at all?

That's a question Fiona Hill and Clifford Gaddy of the Brookings Institution have been thinking about for years. Hill and Gaddy, who have both studied Russian politics for decades, first released their book "Mr Putin: Operative in the Kremlin" in 2013. It quickly became one of the most respected portraits of the Russian leader. Now, with even more eyes on Putin, they've released a new edition of the book with five new chapters to bring it up to date.

One shocking takeaway from their book is how much things have changed in less than two years. At the finale of the first edition, Putin was facing down anti-government protesters who were calling for his ouster and, remarkably in hindsight, it looked like he might lose. Now, having convincingly crushed his domestic foes, Putin is facing down his international enemies. "[At the end of the first edition] we had a question about Putin playing chicken with the Russian public," Hill says. "Now we see him playing chicken with all of us."

The original version of "Mr. Putin" painted a remarkably complicated picture of the Russian leader. Looking over his entire  personal history, Hill and Gaddy came up with six identities that factor into his decision-making -- what they call the Statist, the History Man, the Survivalist, the Outsider, the Free Marketeer and the Case Officer -- that they now use to understand his international outlook.

These identities overlap and sometimes conflict with each other, making the Russian leader uniquely difficult to understand. His place in history is unusual: He's a product of the collapse of the Soviet Union, yet he completely missed perestroika while working as a KGB spy in Dresden, and that influences how he runs Russia. "It is a security-centric system, run by a guy who is an intelligence operative," Gaddy says. "And there’s just never been anything like that in modern history."

In many ways, the fascination with Putin's personality is a result of how hyper-personalized his government is, something that has become worse since the first edition of the book. Even in the Soviet-era there was some form of collective decision-making, yet in Russia today Putin often seems like the sole decision-maker. "In Putin’s Russia today -- and this becomes worse and worse for every day that goes by -- nobody knows what this guy is thinking," Gaddy explains. "He invites people in. He still listens to people. They're able to brief him, and he absorbs their opinions and views. And then he makes a decision."

As Gaddy points out, it's not just us who can't understand him. His isolated decision-making process means that speculation about Putin's motives grips Russians, too: When he announced in a March 2014 speech in Moscow that Crimea would join Russia, many of the audience -- who were Russia's most senior lawmakers, we should remember -- seemed visibly uncomfortable at what their leader might announce. "It could be, 'We’re going to launch World War III,'" Gaddy says. When Putin's plans for Crimea are revealed, some of the crowd suddenly relaxed: Some even chuckled.

Does spending so much time analyzing Putin's personality have its drawbacks? There's certainly a risk of oversimplification or caricature. Hill says that the two biggest mistakes they see are either under- or overestimating the Russian leader. Those who underestimate Putin think he won't "fight and fight dirty," Hill says. Unfortunately, she's sure he will, and Hill argues that Putin has taken on the tactics of insurgency such as practiced by the mujahideen against the Soviet Union in Afghanistan.

"We have people now [arguing we should] send in lethal weapons to the Ukrainians, but he’ll just escalate further," Hill says, before pointing to another reference in recent history. "It’ll be like the scenes we saw in Iraq where the Iraq army were dispossessed of their weaponry."

Perhaps even more ominously, there's the risk of overestimating Putin. He had little experience of the Western world until he became Russian president, and even now he seems to have little understanding of how the United States actually works.

"We’re in a very dangerous dynamic," Hill explains. "Putin is going to keep upping the ante, and he doesn't understand how we work. Over a period of time, we will be obliged to actually do something. Think about it, in every single conflict like this -- Yugoslavia, Iraq, Afghanistan, over and over again -- we end up where we send in troops."

Out of the many analyses of the Russian president that have gone around over the past few years, Hill and Gaddy single out one attributed to Angela Merkel as unusually perceptive. Last year, the German chancellor was reported to have told President Obama that Putin was living "in an another world." At the time, this was interpreted by some as a sign she thought Putin was crazy or ridiculous, something Hill argues is actually a "very inaccurate and dangerous reading." Instead it should be taken quite literally: Putin's frame of reference for how the world works is totally different to ours. He lives in a different world.

And perhaps the rest of Russia does, too. Domestic polls have shown Putin's popularity soar over the last year with perceptions of the United States plunging lower and lower, no matter how the West tries to counter him. "We can’t change their mind," Hill says. "They’re not reading The Washington Post. They’re listening to Russian state television." For many Russian's, Putin's world -- whatever is driving it -- is their world, too.