Particularly in England, there is the lingering and sometimes justifiable perception that he is a manager who reacts badly to intense scrutiny.
Hodgson's time at Liverpool unravelled on the pitch first and foremost but he was hardly helped by a series of misguided public pronouncements that reached a nadir when he lavishly praised his team after a 2-0 derby defeat against Everton.
There have been further glimpses of a similarly myopic and irritable reaction to criticism during his tenure with England, not least whenever his team's struggles with keeping possession are mentioned.
With Hodgson, there is the sense that he feels as if the English public, and certainly what he calls "the mass media", do not fully appreciate the depth either of his football knowledge or long track record in management. Travel across Europe, speak to his former clubs, players or other managers and there is near universal acclaim for his methods.
Per Agren is the former Malmo captain and was part of all five of Hodgson's teams that won the Swedish league in consecutive years from 1985 until 1989.
He believes that Hodgson's inclusive approach meant that he thrived when the pressure was at its greatest.
"There are many things that made him a great manager," says Agren.
"He was a very motivating person to be around. He had a very good handle on the players outside of the first team. He handled everyone with care and respect.
"I was not one of the most talented players in the team but he made me feel I was important.
"Before a big game, he didn't pay that much attention to the opponents. He would focus on our game plan. He was offensive for sure. He always saw the positive things and the challenge. He wanted us to enjoy the moment instead of being scared of the moment. That was a big message."
That was also Hodgson's pre-match theme on Thursday. He has sometimes looked tense ahead of a big England match but, clearly boosted by so many more options in attack, his body language was of a man relishing rather than dreading what is to come.
"We're not anxious but excited," said Hodgson.
Paul Ince played in the Inter Milan team that reached the 1997 Uefa Cup final under Hodgson and also paints a very different picture from the caricature of a cautious coach who is a bit, well, uninspiring.
"If you'd sat in a dressing room and seen him peeling the paint off the walls at half-time, you'd get a better picture of the man," said Ince.
"I've never seen anybody go quite as bananas as Roy and I include Fergie in that. I was fortunate to work under him at Inter Milan for three years and it was a real education and insight into a great manager."
Ince says that Hodgson's outward manner can hide what he calls "an inner strength and belief in himself".
Like everyone who has played under Hodgson, Ince also highlights his work on the training ground and describes those sessions as "a joy".
Hodgson's overriding aim this week will have been to ensure his players are drilled in the system he wants to employ.
Hodgson would appear to subscribe to the theory that pressure is best dealt with by focusing simply on the process of your next performance.
"Roy does it on the training ground and keeps repeating it until you can't help but understand what he wants," said Brede Hangeland, the Fulham defender.
"Roy has a very clear idea of how to do things. Maybe he will have to try to change it slightly with big-name players."
During another low point at Liverpool, Hodgson described himself as "one of the most respected coaches in Europe" and looked insulted by the suggestion that he was less suited to a higher-profile environment.
The next five days represent perhaps the ultimate chance to answer that criticism and demonstrate that he is indeed a manager who can deliver when football's pressure cooker is at its hottest.
He has been here before
This is not the first time Roy Hodgson has faced a nail-biting conclusion to a World Cup qualifying campaign. Twenty years ago his Switzerland team needed to beat Estonia in their final match to make the finals of USA 1994.
They won 4-0. Hodgson will be hoping it is a lucky omen for England.