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?
"what other workers have zero marginal product?"
Politicians! Bureaucrats!
No, that won’t work, they’ve got negative marginal product, don’t they?
Posted by: Tim Worstall | June 24, 2006 at 12:48 PM
Since all 10 remaining players must be working harder, this must mean that when 11 players are on the pitch players don't try as hard as they possibly could. So players are being paid £20,000 a week and still only perform to 70 or 80% of their ability.
What more incentives to footballers need? Competition, fame and fortune clearly aren't enough.
Posted by: Sam | June 24, 2006 at 11:12 PM
Offer them sherbet, Sam. They wouldn't sniff at it.
Posted by: dearieme | June 26, 2006 at 03:46 PM
A zero marginal product ? Well... think of an industry where the average activity of someone is to try to win zero sum games.
Finance comes to mind. Very useful to have a finance industry, but does an additional foreign exchange trader at the margin add any value given that trades are zero sum?
Also, any cirucumstances where the nature of competition is positional (winner takes all markets) tend to take a big toll on marginal products.
But of course, in such cases there is a difference between the marginal product to the employing firm, and the social value of the work performed. And once you open that box...
Posted by: rjw | June 28, 2006 at 11:32 AM
Sending off is compensated by the profits you can make investing in this great new product.
Posted by: Tamatha Wainwright | June 28, 2006 at 06:51 PM