Ministry: Head of Department of Magical Games and Sports
Ludo Bagman was once a Beater for the Wimbourne Wasps Quidditch team. Now, he's the head of the Department of Magical Games and Sports. Because Bagman was a really great Quidditch player many years ago, he gets a lot of leeway to be a fool even now. A great piece of dialogue that really sums of Bagman's character appears in Chapter 7:
"Ahoy there! Bagman called happily. He was walking as though he had springs attached to the balls of his feet and was plainly in a state of wild excitement.
"Arthur, old man," he puffed as he reached the campfire, "what a day, eh? What a day! Could we have asked for more perfect weather? A cloudless night coming ... and hardly a hiccough in the arrangements ... Not much for me to do!"
Behind him, a group of haggard-looking Ministry wizards rushed past, pointing at the distant evidence of some sort of a magical fire that was sending violet sparks twenty feet into the air. (7.98-100)
At the Quidditch World Cup – only the most important event that his Office will probably ever oversee – Bagman wanders around "in a state of wild excitement." He assumes there's "not much for [him] to do," without even noticing the hardworking wizards immediately behind him who are trying to keep the event under control. Bagman is lazy and self-indulgent. He loves doing the parts of his jobs that are fun – announcing at the Quidditch World Cup and the Triwizard Cup – but he devotes zero attention to the serious parts of his job.
Ludo Bagman's childlike enthusiasm makes him seem harmless at the start. Yeah, he's not great at his Ministry job, but surely he doesn't mean any harm, right? Yet, even if Bagman doesn't actively mean to do evil, his carelessness and neglect end up leading to a lot of trouble. He doesn't bother to look into Bertha Jorkins' disappearance, which is linked directly to Voldemort's rise. Also, as we find out through Dumbledore's Pensieve, his stupidity seems to have gotten him involved with the Death Eaters thirteen years before. No one really seems to believe that he's malicious, but he's certainly too dumb to make good choices.
Because of Bagman's slightly shady past, we know that there must be something bad going on with him in Goblet of Fire. We can guess that it has something to do with Fred and George, who keep trying to corner Bagman to talk to him throughout the novel. After all, Fred and George did make a pretty substantial bet with Bagman about the outcome of the Quidditch World Cup, which the twins won. It's also suspicious that Bagman secretly offers Harry help with every Triwizard task, promising, "Nobody would know, Harry" (20.120).
It's not until the end of the book that we finally find out what Ludo Bagman's deep secret is: he's got a gambling problem. He lost a lot of money to the goblins at Gringotts with bets on the Quidditch World Cup. He tried to pay Fred and George in leprechaun gold, which disappears after a few hours, and then he refused to give them back the initial 37 Galleons they put down in the first place.
The reason Ludo Bagman has been trying to help Harry cheat is because he bet on Harry to win the Triwizard Tournament. He had hoped to win enough gold to pay off the goblins. But the goblins win in the end because Harry didn't win the Triwizard Tournament outright: he tied with Cedric. Ludo Bagman thus loses all of his money and flees the country, leaving all of his creditors high and dry. Ludo Bagman isn't terribly evil or anything – not like Barty Crouch, Jr., certainly – but his weakness of character gets both him and a lot of people around him into trouble.