In one of the great sports books. David Remnick's 'King of the World,' Dundee recalled his involvement in the first fight with Sonny Liston, when Cassius Clay (as Ali was still called at the time) had been blinded by a substance allegedly put on Liston's gloves. He was threatening to abandon the fight, but Dundee managed to calm him down.
"Isn't experience wonderful?" reflected Dundee.
"I've only been doing this for 48 years. You can't get to where you're hysterical and lose your cool. Then you're no good to the fighter."
The pressure of the World Cup quarter-finals exposed the inexperience - and the lack of emotional control - of Maradona and Brazil coach Dunga.
In Maradona's case, he allowed himself to get carried away by euphoria. As he will surely be reflecting on the plane home, back in March his side won away to Germany with a cautious 4-4-2 formation. In South Africa he went with something more expansive and refused to change back, even when the warning lights were flashing.
After 20 minutes of the second round match against Mexico it was obvious the team was not right. The Mexicans could have been two goals up and Maradona was in earnest conversation with his assistants. There was, as German coach Joachim Loew said after the quarter-final, no balance between attack and defence.
Against Mexico two mistakes got Argentina out of jail - one by the linesman, allowing Carlos Tevez's offside goal to stand, the other from Mexico's Ricardo Osorio, who gifted Gonzalo Higuain the second - but they were not going to get away with it twice.
This is not hindsight - it was clear as day before the game against Geramny began. With the same starting line-up that played against Mexico, they were inviting a rout.
The big change that Maradona had made since March was to include Tevez in place of Juan Sebastian Veron, a switch made largely on emotional grounds.
Tevez is key to the soul of Argentine football, even more so than Lionel Messi. His upbringing in the poor outskirts of Buenos Aires, his time with Boca Juniors, his never say die spirit - it is reminiscent of Maradona himself. The two of them have a bond.
But despite the glorious finish Tevez came up with for his second goal against Mexico, his inclusion in the team was a huge mistake.
Messi's best football in the tournament came while Veron was on the pitch. They formed a partnership which looked like being the central axis of the team. No Veron meant that Messi had to drop deeper in search of the ball, but Messi setting up play for Tevez made little sense, especially in the light of the latter's poor international scoring record.
No Veron also meant no raking diagonal passes to bring Angel Di Maria into the game and left Javier Mascherano desperately overworked with the defensive midfield duties.
All this was apparent before the Germany game. But to act on it, Maradona had to first recognise it - and with Argentina's campaign riding on a wave of optimism, there was no place for a dose of realism.
If Maradona was undone by euphoria, it was anger that did for Dunga, who has always been a man on a mission to shove it down the throats of his critics. As a player, this can be useful. As a coach in charge of 23 players, it can be dangerous.
Being in charge of Brazil is not a job for the faint-hearted. There will be lots of criticism, some of it fair and thoughtful but much of it irritatingly stupid. Dealing with it may have sent Dunga over the edge.
There were signs in the tournament that he was out of his depth, that anger was controlling him instead of him channelling the anger. In the press conference after the Ivory Coast game he looked like a man in need of therapy, muttering and swearing under his breath at one of the least offensive members of the Brazilian press corps.
Whatever controversies may exist about his philosophy of play and his selection policy, there was much to admire in the work he carried out in his first coaching job - as his players showed in a magisterial first half performance against the Dutch.
But as well as picking the players and determining the tactics, one of the key functions of the coach is to set the emotional tone of the team - and here the occasion proved too big for Dunga.
On the touchline he was a nervous wreck, wailing his disapproval of every decision that went against his side, pummelling the dug out and looking a picture of despair. An uptight coach inevitably produces an uptight team.
After the Dutch equalised, Brazil suffered a collective emotional collapse, and when this happens there is no one to blame but the coach. An obsession with arguing with refereeing decisions can spread from the touchline to the pitch.
Robinho spent much of the second half protesting and with two minutes to go Gilberto Silva was pleading with the referee to give a Dutch player a yellow card - a total irrelevance at that stage in the game.
Brazil were praised as a team of '11 Dungas,' all with the warrior spirit of the man who selected the side, but that backfired badly in the quarter-final - under pressure they became 11 nervous wrecks, a reflection of their inexperienced coach.
Dealing with the rollercoaster of emotions is one of the hardest things about a World Cup. It proved too much for Dunga and Diego Maradona.
The four coaches who are left in the competition may not have quite the experience of Angelo Dundee. But they have been around the block, taken the blows, and can now have their sights set on becoming champions of the world.
Longer than usual this week, so no space for questions. Normal service resumes next week - questions on South American football to email@example.com and I'll pick out a couple for the next column.