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Since the Death Eaters seem to be the topic du jour, according to Goblet of Fire, approximately 100,000 witches and wizards attended the Quidditch World Cup (Chapter 8 - pages 88 and 98 - (UK) - The Quidditch World Cup)

Now my math skills are even worse than J.K. Rowling's, but it seems that between seven and sixteen Death Eaters were responsible for the kerfuffle. How is it that 100,000 +/- individuals, as well as the entire Ministry of Magic (GoF - page 115 - (UK) The Dark Mark), including the Department of Magical Law Enforcement, could not corral sixteen Death Eaters and keep them from rioting and engaging in the torture of Muggles?

Here's how I came up with a guesstimate of seven to sixteen Death Eaters. The Death Eaters identified in the chapter The Death Eaters in Goblet of Fire are:

  • Barty Crouch Jr. (Stayed at Hogwarts during Voldemort's return/Acted alone at the Quidditch World Cup)
  • Avery (Jr. or Sr.?)
  • Wormtail
  • Lucius Malfoy
  • Walden Macnair
  • Crabbe
  • Goyle
  • Nott
  • An unknown number of other Death Eaters

It doesn't seem the number of Death Eaters at the graveyard was very high. The remaining Death Eaters who might have been present are Alecto and Amycus Carrow, Thorfinn Rowle, Yaxley, Jugson, Selwyn, Wilkes, and Gibbons.

Igor Karkaroff defected and fled. We all know about Snape. Bellatrix Lestrange, Rodolphus Lestrange, Rabastan Lestrange, Antonin Dolohov, Augustus Rookwood, Mulciber (Jr. or Sr.?), and Travers are in Azkaban at the time of the Quidditch World Cup.

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    Well, as for the 1,00,00 individuals, in a similar situation in the Muggle-world, when a group of accomplished thugs plays havoc in public (not necessarily with advanced weapons), do we interfere in person (even if we are physically fit to tackle one or two men) or wait for the police? – N Unnikrishnan Jun 20 '14 at 22:02
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    The Death Eaters are known to be organized, and ruthless, having done abduction, torture, and murder in the past. They are present as a group, with potential supporters in the people around you, and the always-present fear of You-Know-Who in the background. Would you be willing to be "the one" stepping forward to openly oppose them? Unmasked? Potentially with your family right behind you to catch a lethal spell, by accident or intentional? Humans are quite "brave" in a group, but usually cowards when alone. That's just the way we tick. – DevSolar Oct 19 '15 at 12:54
  • I don't understand why they weren't stopped, simply by the fact that there are thousands of wizards there with immense power. Seriously, I doubt it would be hard to defeat 16 Death Eaters when there are literally wizards with the power to disarm, disable and generally defeat them. This was a major flaw in my opinion, even though I understand it's just for plot reasons. Not even some magical thing to prevent people to do such things. Maybe not everyone possesses the knowledge or even the ability, but most of them should be educated especially on how to defend against the Dark Arts. – user67574 Jun 15 '16 at 21:52
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It wasn't that they couldn't overpower them, it's that they had to do it in such a way as to protect the Roberts family (the muggle who ran the campground):

The crowd beneath the Roberts family was larger than ever; they could see the Ministry wizards trying to get through it to the hooded wizards in the center, but they were having great difficulty. It looked as though they were scared to perform any spell that might make the Roberts family fall.

Beyond that, there was more than one campground, reducing the numbers immediately there (of both spectators and the ministry). And there was the psychological fear - it seems the Death Eaters were so feared that most of the witches and wizards just ran away so as not to cross them.

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    Also, no one could have known at that moment how many Death Eaters are actually there. Darkness, confusion, maybe some magical means could have prevented the wizards and witches from accurately determining their numbers, making them more likely to flee instead of fighting, thereby reducing the number of active resistance to such levels that could be overpowered by the coordinated attackers. Seeing other wizards fall would of course cause the others to consider running. – zovits Mar 11 '14 at 9:30
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To address ALL of your points:

  1. 100,000 people:

    For those who have never been to a football match (real football, where you kick a round ball with one's feet :)

    A vast majority of those 100,000 people would have been partied out, drunk or getting drunk, and in general in no condition to participate in a Dark-Wizard Swat Response, on a spur of the moment. For a representative sample, see a scene of a bunch of them trying to impress a couple of Veela.

    Plus, I get the impression that many of them would rather join in a spot of Muggle-baiting rather than round up the perps. There was a full-blown riot with a crowd.

    And most are just random scared civilians, who're not fit to fight Death Eaters on a good day:

    There came a bang from the other side of the trees that was louder than anything they had heard. Several people nearby screamed.

    Malfoy chuckled softly. 'Scare easily, don't they?' he said lazily. 'I suppose your daddy told you all to hide? What's he up to – trying to rescue the Muggles?'

  2. the entire Ministry of Magic

    A vast majority of the MoM are paper pushers like Percy. Not everyone at MoM is a trained hit wizard or an auror. Most of them wouldn't exactly be of much use in a magical duel.

  3. Department of Magical Law Enforcement

    First, they didn't even know what was going on - yes, there was a "riot", but they didn't get alerted to something far worse till the very end when Dark Mark was sent up by Barty Crouch Jr.

    Second, they were spread all over the Cup grounds when this started. Then, they had to deal with panicked crowds (see Kevin's answer for the quote: The crowd beneath the Roberts family was larger than ever; they could see the Ministry wizards trying to get through it). Then, they had to actually get to where DEs were.

    And Kevin's answer already covered the problems faced when they did get there.

And then, Death Eaters disapparated:

'We're too late,' said the witch in the woollen dressing-gown, shaking her head. 'They'll have Disapparated.'

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