Comparing the performance of USA and Brazil defense against Germany yields a couple of interesting facts:

- USA's defense is more Reliable in averting goals
- Brazil's defense is more Effective in terms of foul management

Here is the analysis

## Data: MLS Match Center

## Analysis

## Highlights:

- Brazil's Effectiveness is characteristed by the ability to win more fouls than losing. US on the other hand was not quite successful in wining more fouls than losing.
- US defense is far more Reliable than Brazil's in terms of averting goals (0.15 to Brazil's 0.03)
- Both teams' defense were close in Efficiecy and Impact (Efficiency is equal to Impact in this case as we are looking at the total team defense)

## Consipiracy Theory: Did Germany need to play as aggressive with US than with Brazil?

Let us further analyze the intent behind both the games from Germany's perspective. Using Game Theory, let's see how the outcome would have affected Germany

Had Germany lost to USA, they would have still advanced to the next round due to that awesome anhiliation of Portugal in the first game. On the other hand if Ghana beat Portugal with a really large margin) , that would have impacted Germany's postion. Using **Nash Equilibrium** and the concept of **Payoff Matrix,** here is the outcome explained mathematically

## So why was Germany still trying to win against the USA?

- Germany is winning team - there is something to be said about the versatility and pride of this team.
- Algeria is an easier opponent than Belgium in the next round. So maintaining group leadership was an imperative to get to the quarter finals
- Germany is far more experienced and a technically better team than USA. However, US defense played a far more Reliable game than Brazil.

Do team think in this way - using Nash Equilibrium (Game Theory) and Stochastic amalysis? It is catching-up...

## Revised Analysis

Here is the new outcome matrrix after we discussed why Germany wants to win and not draw

I used some arbitrary weights to arrive at the payoff matrix, below:

These weights are based on each teams incentive to Win, Lose or Draw. We assume that there is equal probability for all three outcomes. We know that US would place an equal importance to a loss or draw as it helps them just advance. Winning against Germany will be more important to them as it motivates them better to play the next round by improving their confidence level. Based on these assumptions, here is a simple payoff matrix:

All three options represent Nash Equilibria as those are the maximum (and only possible) values in the corresponding rows and column. Since the outcome of a Win, Loss or Draw would not effect the outcome of USA's next round game (playing Belgium) AND the other condition (Ghana beating Portugal by a big margin) was out of USA's control, the outcome of the match was a Germany win...