Sometime around the fourth goal, I descended into hysterics. No exaggeration - as Toni Kroos nicked the ball from Paulinho on the 25th minute and slotted the ball into the back of the net, almost from kickoff, moving and passing around Brazil's backline like cones laid out on a training pitch, I convulsed with hysterical laughter. When the rational disappears, we must confront the irrational and unexpected, and there was little as unexpected as Brazil capitulating as they did last night. When the fifth went in I had to leave the room.

My Twitter timeline was a series of exclamations, as close to an immediate, unmediated stream-of-consciousness as it ever has been, in fact. WOAH. WHAT. NO WAY. WHAT. WHAT. WOW. WHAT. FUCK. HAHAHA. MY GOD. For the first time in years it felt like Twitter wasn't immediate enough for us - not even during the 2012 Olympics, not even during that one hour period where Mo Farah, Jessica Ennis-Hill and Greg Rutherford all won gold and the UK went delirious, had Twitter struggled to convey exactly how poorly we were understanding what we were seeing.

People calmed down and started making jokes again, though, of course, and my favourite was this:

Nate Silver stands on a bluff above Belo Horizonte, shaking his fist: "I'll get you, black swan!" "No you won't" "Yes I will." "Won't" — John Gallagher (@earlymodernjohn) July 8, 2014

Silver, of course, is the editor-in-chief of FiveThirtyEight, an ESPN-owned site with around a dozen full-time staff members who specialise in data journalism and "crunching numbers". They've been following the World Cup, generating probabilities of success for each match; before yesterday's, they had Brazil with a 65 per cent chance of beating Germany (and if Neymar and Thiago Silva had been available, that would have been scaled up to a 73 per cent chance).

Today, with hindsight, Silver has written a sort of mea culpa: "Time to eat some crow. That prediction stunk." He calls it a "black swan", a term coined by Nassim Taleb in his bestselling book of the same name. Silver writes: "Statistical models can fail at the extreme tails of a probability distribution. There often isn’t enough historical data to distinguish a 1-in-400 from a 1-in-4,000 from a 1-in-40,000 probability." Predicting the future based on past results and rankings is all well and good, but when things go wrong, they can go very, very wrong.

His discussion of why that prediction was wrong, and what it missed, is interesting for what it shows about how suited data journalism is to a sport like football. That is, when you can't quantify every factor relevant to a prediction, you're not only limited in the accuracy of your prediction - you're limited in your ability to understand how you are limited. Silver points out that the betting markets were better than the official stats in predicting what would happen; he also ponders whether the loss of Neymar and Silva had more of an impact, and whether certain players (like goalkeeper Julio Cesar) underperformed to an unusual degree. What he doesn't appear to consider, though, is what almost every single pundit was talking about before, during and after the game: the pressure of the occasion getting to the Brazilian players, haunted by the significance of the national team's defeat in the 1950 World Cup, the infamous Maracanazo.

Silver's reputation comes from outstanding work in analysing baseball and politics. He was a prominent advocate of "sabermetrics" (as popularised by the book Moneyball), breaking the individual actions of players into statistical data that could be used to scout, coach and play more effectively than was ever previously possible. His political work was incredibly fun, too - fully aware that pundits might as well be have been picking through chicken guts when analysing the 2008 US presidential election, his blog (the original 538, not the current one) calmly, coolly, without partisan preference, did the maths and predicted the winner. By 2012, not only were many pundits angered by his repeated assertion that the race was anything other than "too close to call", there had emerged an entire counter-Silver part of the blogosphere - mostly Republican - which openly freaked out about his (correct) prediction of an Obama win. Silver's work was refreshing for its honesty - no more blowhards with agendas picking over the ramifications of this gaffe or that policy announcement, instead simple, clear polling data.

Baseball and politics, of course, are not immune from black swan events - but they're also mostly very predictable, at least at the highest level. Baseball players can only perform actions that have a limited range of outcomes, making it not too dissimilar to games like chess; sampling and polling techniques are now so sophisticated that a statistician can remove almost all doubt from an electoral race. This is not a piece that argues that football is "better" than baseball or politics as a sport because it wriggles out from under any microscope that is applied to it - but instead, this is about how loving football requires an acceptance of devastation or ecstasy, without warning, with regularity.

To illustrate this, we can turn to physicist Stephen Hawking. In May, before the World Cup began, the betting firm Paddy Power invited journalists to the Savoy hotel in London to see him deliver "an exclusive research presentation of HOW ENGLAND CAN WIN THE WORLD CUP (sic)". Hawking may well be a hack - and as much as, eg, his Specsavers ad is ridiculous, turning a career in physics into lucrative endorsement opportunities and pop culture notoriety is no easy feat - but he actually produced a report, with facts, and numbers.

You can download it here. It's very clear why Hawking didn't submit it for peer review - his data sets are small and unlikely to produce results which are statistically significant, for a start - but I still like to bring it up because it's not that much more silly than FiveThirtyEight's football coverage. The factors Hawking considers in his analysis - distance from home nation to host stadium, temperature on game day, stadium altitude, kick-off time, colour of shirt (seriously, it's a factor in many competitive sports), player ages, age of captain, referee nationality, continent of origin for opposition team, team formation - are all things that do play a part in influencing the likelihood of a football match.

It's in the generalisations, though, that we can see just how hard it is to quantify this sport. Players having to travel long distances to a game obviously changes how physically prepared they are - but how much, exactly? Does it matter if they're travelling across time zones (England to Brazil in 2014) or not (England to South Africa in 2010)? What if some players are travelling further than others because they play club football in a different country? Players in their mid-20s are going to be more dynamic, faster, quicker to accelerate than players in their 30s - but has the "prime" of a professional player changed over the decades as sports scientists have improved their understanding of how to train the human body? A referee from a certain country might be biased against or towards a team in 2014 - but what if changing geopolitical circumstances change that bias over time?

It's like trying to draw an outline around your own shadow - every move of the arm changes its shape, reveals that the shadow is an ever-changing thing. There was no way to quantify the emotional state of the Brazilian team in Belo Horizonte last night before the game, nor the atmosphere created by the crowd, nor the significance of the occasion, nor the pressure David Luiz must have felt as he led his team out for the first time as captain in a World Cup semi-final and the no-doubt nagging worry in his head that something might go wrong.

This World Cup is already being spoken about as one of the greatest, if not the greatest of all, because of its shocks. It's a competition of contradiction, in this regard. Every day brought matches which ignored predetermined narratives of who "should" win and who "should" score, and yet the sum total of our surprise has been four semi-finalists who are possibly the most predictable imaginable - Brazil, Germany, the Netherlands, Argentina. In turn, we got to see Brazil taken apart by Germany more readily than any match between a giant and a minnow in the knockout rounds; it was the kind of result that should befall Costa Rica facing Italy, or Iran facing Argentina. It has been both shocking and predictable simultaneously.

I was amazed recently to discover that there isn't even an agreed-upon best way to measure possession. Football - like basketball, or hockey, and any other sport with a similar kind of freedom of expression - demands an acceptance of uncertainty in exchange for its love. The shock is the joy.