Don't worry, it's not necessary to choose one, or even all of the above. As the man himself once said, he doesn't "give a rat's ass" what others in the game might be doing or thinking. He is, as he has also said, "an island" unto himself. Some might say he's so much more than a mere island that, in many ways, he's become Leafs Nation itself.
The general manager of the Toronto Maple Leafs turned 55 early this summer. His once red hair - bulrushes for follicles - has turned the colour of spring ice. His big, glowing Irish face remains set in what appears to be constant fury, belying both the wit that lies not far beneath the surface and the sentimental sob that hides somewhat deeper. He is almost as complicated as his job description.
In a team that polarizes fans - lionized and loved by half the country, resented and ridiculed by the other half - Burke, far more than any individual player, has become the face of hockey's most powerful franchise.
And given that the Leafs began the season as the NHL's hottest club - currently sitting 4-0-0 - that polarization has risen to levels not even imagined by the Ignatieffs and Harpers of the country.
Burke is, for hockey circles, a bit of an enigma: an American who prefers Canadians; a journeyman player who chose school over dreaming; a man who is both gruff and articulate in a culture known for politeness and clichés.
It is, however, all explainable. Born in Rhode Island, Burke and his family bounced about the United States until, at 13, he found hockey in Minnesota, that most Canadian of states. His greatest skill was work ethic, and though it took him to a college education and the minor leagues, his greatest attribute, a brain, sent him to Harvard where he ended up with a law degree, an early dance with being a player's agent and a full career in hockey management. He has worked in Vancouver, Hartford, NHL headquarters, Vancouver again, Anaheim, where his team won a Stanley Cup in 2007, and Toronto, where most hockey fans living beyond the Centre of the Universe enjoy ticking off the years since the last Stanley Cup like a schoolyard taunt.
Burke's task, obviously, is to put an end to the taunts. He brings credentials from the schoolyard and street brawls - Irish against Italian - and relishes nothing more than answering a challenge, more likely today in word than deed.
He grew up, one of 10 children, in a family where the kids took turns bringing new words to the dinner table, defining them and using them properly in a sentence, which explains how Burke could announce, without using index cards, that he was looking for "pugnacity, testosterone, truculence and belligerence" in the team he was taking over.
Burke became general manager of the Leafs in the fall of 2008. The team missed the playoffs in his first season, missed them again in his second. The team, coached by Ron Wilson, a close friend of Burke's since their Providence College days but not hired by Burke, actually got worse in that short span of time, slipping from 12th place to a dreadful 15th last season.
Under normal circumstances, that might have led to calls this summer to send the bum packing, but there were none. And at the moment, it must be said, if he wished to run for mayor, it would be a one-horse, albeit Clydesdale, race.
While the differences may lie in the small matters - who the hell is Clarke MacArthur? - Burke's short time as GM has been marked by two dramatic moves. First was to trade for Boston Bruins Phil Kessel, a player seen as gifted in talent and short-changed in personality. Burke gave up what some call "the store" - a first- and second-round draft pick this year, a first round pick next year - for a player he then signed to a five-year $27-million (U.S.) contract. Only 22, Kessel hit the 30-goal mark last season, playing only 70 games, and theoretically his best years should be ahead of him. Certainly, he is off to a fine start for this season.
However, as Boston collapsed following the trade and was able to use that first first-round pick to snare Tyler Seguin, the No. 2 overall selection in 2010 and a player projected to be a superstar, the deal is destined to remain moot for years to come.
The second significant move was to trade for new captain Dion Phaneuf, a deal with the Calgary Flames that involved seven players but has a result that will settle on one, the 25-year-old defenceman who began his NHL career brilliantly but stumbled curiously. Phaneuf symbolizes "truculence and belligerence" and may well return to the career arc once projected for him.
Burke understands only too well that the proper evaluation of trades often eludes a GM's stay. It was Burke who dramatically engineered the convoluted trading day deal in 1999 that saw the Vancouver Canucks pick up the Sedin twins second and third, while the Atlanta Thrashers squandered their first pick overall to take Patrick Stefan. Stefan went nowhere, and though the twins were slow to rise and Burke's own contract not renewed, today Henrik Sedin is the league's defending scoring champion and MVP - with brother Daniel not far behind.
Burke is beyond argument an iconoclast in the game. While others were keen to have shootouts put an end to tie games, Burke was comparing the notion to having the NFL decide games "by having guys throw footballs through a tire." Though he oversees hockey's richest market, he spoke out this summer in defence of small-market teams unable to employ long-term, book-fiddling contracts. He may have himself shifted hockey's hidebound thinking when he offered immediate support for his son Brendan's public declaration that he was gay - an embrace that proved all the more significant only months later when 21-year-old Brendan Burke was killed in a car accident. The gruff man many have long thought of as a bully now speaks out often against bullying. He has been willing to change his thinking on head shots. On the other hand, he would, it often seems, defend fighting with his own fists.
This is a bright, complicated man. "The private side of Brian Burke is private," he once told reporters. "My family sees that, my friends see that. But I'm not interested in you guys understanding me."
Whether he is interested or not is not the point: reporters are vitally interested in understanding Brian Burke because he looms so large in the game, not only in the Leafs but in the league itself.
He gets results. Sometimes it comes late - the Sedins. Sometimes it comes on time - the 2007 Stanley Cup. Sometimes it catches everyone by surprise - as in the Leafs' spectacular start to this season.
When Sporting News takes a 15th-place team and projects it to finish fourth this year, it is but one small example of the enormous expectations that have come to follow Brian Burke.
This is a ship that leaves a large wake, and it is only this 2010-11 season that it can fairly be said that Burke's hands are the only ones on the wheel - and this season when the changes instituted by him will begin to form what will be his ultimate measure.