A sending-off doesn't affect the outcome of World Cup games, at least if it happens in the second half:
We make use of a unique dataset containing all games played in a World Cup Championship between 1930 and 2002 and follow a twofold econometric strategy: We start with a conditional maximum likelihood estimator which is independent of the relative strength of the teams before we extend this estimator to take the relative strength of the teams and the minute of the expulsion into account. Our results indicate that the scoring intensities of both teams do not differ after the expulsion. Conducting scenario analysis reveals that the impact of a red card depends on the minute of the expulsion and does not have an impact at all if given at the end of the first half or later.
Here's the full paper (pdf).
It raises a deep issue in labour economics. If the marginal product of a footballer in the second half of a game is zero, what other workers have zero marginal product?