Football – substitution

A spanish banker has made some interesting observations about a football coach’s substitution choice.

The coach can make a last substitution. He can substitute an attacker for a defender or vice-versa. With more attackers the team  more likely to score but also more likely to be scored against. Substituting a defender makes the final score less uncertain. Hence there is some link with Ellsberg’s paradox. What should the coach do? How should he decide?

 

 

A classic solution would be to estimate the probability of getting through the round, depending on the choice made. But is this right?

 

Pause for thought …

 

As the above banker observes, a ‘dilemma’ arises in something like the 2012’s last round of group C matches where the probabilities depend, reflexively, on the decisions of each other. He gives the details in terms of game theory. But what is the general approach?

 

 

The  classic approach is to set up a game between the coaches. One gets a payoff matrix from which the ‘maximin’ strategy can be determined? Is this the best approach?

 

 

If you are in doubt, then that is ‘radical uncertainty’. If not, then consider the alternative in the article: perhaps you should have been in doubt. The implications, as described in the article, have a wider importance, and not just for Spanish bankers.

See Also

Other Puzzles, and my notes on uncertainty.

Dave Marsay 

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About Dave Marsay
Mathematician with an interest in 'good' reasoning.

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