Improbable Events, Statistics and World Cup 2014

Brazil will be hard-pressed to defeat Germany without Neymar, its star striker, in the World Cup semi-finals on June 8.

Improbable, however, doesn’t mean impossible. With Neymar, Brazil’s chances of winning was good. In his absence, the probability of winning has dipped significantly but it hasn’t become zero either.

Brazil will be looking for inspiration to 1962 when the World Cup was held in Chile. The team had lost its wunderkind, a brash young player named Pele, who had torn a thigh muscle midway through the first half of the Brazil's second game in Chile, a 0-0 draw with the Czechs. His replacement, a 22-year-old player named Amarildo, scored both goals in the 2-1 win over Spain in their next match and another in the final against Czechoslovakia that Brazil won 3-1.

Dribbling genius Garrincha was another who took up the slack, scoring four goals in the next three games as Brazil beat England, Chile and Czechoslovakia again to win their second World Cup in a row.

The question is: Is there anyone in the current Brazilian squad who can take up the roles of Amarildo and Garrincha?

Coach Luiz Felipe Scolari has hinted in training that midfielder Willian is his choice to replace Neymar against Germany. Other options include Ramires, Bernard and Hernanes. Brazil’s woes are compounded by the fact that captain Thiago Silva, the team’s defensive leader, collected his second yellow card against Colombia and will be forced to sit out the game against Germany.

Sentimental favorite Brazil should win against the machine-like and relentless Germans. If the claim is made that Brazil will win even in Neymar’s absence, the null hypothesis says, no, Brazil will lose. The alternative hypothesis, of course, is what the claim says: Brazil will win.

So here’s hoping that the Null will be rejected. Let’s hope p-value is less than 0.05 or even 0.01.

None of the players expected to take up the slack in Neymar’s absence – Willian, Ramires, Bernard or Hermanes – are anywhere close to the wizardry of Amarildo or Garrincha.

But Brazil is hosting the World Cup. It should come down to a question of mind over matter, or flair and finesse over physicality and stamina.

Let justice prevail: Brazil over Germany!

As for Argentina against Holland, this is a chance for Lionel to cement his legacy. If Messi can deliver and help Argentina win over Robben and company, he will be compared favorably with Maradona even in Argentina. The Dutch are relentless like the Germans but they also given to frequent dives and theatrics. Justice again please: Argentina over Holland!

Brazil against Argentina in the finals, now that's a match for the centuries!