Why Weren't the Death Eaters Stopped at the Quidditch World Cup?

Question

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.

Answer 1

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.

Answer 2

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 the Death Eaters 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.'

Answer 3

Honestly? I think its a stretch to compare a muggle with a gun to a wizard with a wand. Even tho both are capable of disabling and or killing someone their commonality stops there. For starters a gun doesn't double as a means to block bullets and not every muggle owns a gun and out of those that do they dont all carry them everywhere they go. Not every muggle knows how to fire a gun unlike how the entire Wizarding world is trained in depth on how to use their wands, making them far more useful in a spontaneous "terrorist attack" than that of a muggle with no prior knowledge picking up a gun to stop a trained killer. Bringing me to my next point, in the final movie during the "2nd Wizarding war" which somehow is just a bunch of random death eaters against a the staff and students of hogwarts. If students with an unfinished magical education are capable of pushing back a countless number of full fledged wizard death eaters, than I'd have to agree with OP that 100,000 wizards should of been able to at bare minimum mitigate more of the damage 16 masked dark wizards were able to do. I also think most of you underestimate what 100,000 people in one localized location would look like compared to 16 people. I don't recall if anyone died during the attack on the world cup but if there were casualties, 100,000 turning on 16 would of amounted to alot less than just running.