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Here's an interesting paper I found by a guy comparing "optimization" in football to optimization in business.
It's written primarily about football.
The general idea is that a few of the decisions made by head coaches are not the optimal decisions for the situation.
For example, he argues that on 4th down and 1 from the opponents 1 yard line, you go for the touchdown rather than kick the field goal.
His reasoning is as follows:
1. If you make it, you get almost 7 points (in his study, he accounts for missed extra points, so a TD counts something like 6.96 points). Then, not only do you get the roughly 4 points above and beyond a field goal (which he puts at something like 2.97 points, or something like that), you kick off to your opponent, and "give up" some field position that way.
2. If you miss the touchdown, your opponent takes over deep in their own territory, thus reducing the success rate of their drive. And your team is essentially +25 yards in the field position battle.
3. If you kick the field goal, you only get the 3 points (almost 3 in the study) and then you also "give up" field position on the kickoff.
So his analysis says to go with #1, because if you score, it's better to get the full amount (TD + XPT) and give up the field position, OR to miss and have the opponent take over inside their own 5 (say, at their own 1), than it is to kick the field goal. In case #1 and #3, you end up "giving up" anywhere from 19-25 yards, the only real difference there is how many points you come away with.
Anyway, here's a link. It's a pretty lengthy PDF with some pretty heavy math, but I think it'll be enjoyed.
http://elsa.berkeley.edu/~dromer/papers/JPE_April06.pdf
Though this link might be better:
http://elsa.berkeley.edu/users/drome...s/nber9024.pdf
It's written primarily about football.
The general idea is that a few of the decisions made by head coaches are not the optimal decisions for the situation.
For example, he argues that on 4th down and 1 from the opponents 1 yard line, you go for the touchdown rather than kick the field goal.
His reasoning is as follows:
1. If you make it, you get almost 7 points (in his study, he accounts for missed extra points, so a TD counts something like 6.96 points). Then, not only do you get the roughly 4 points above and beyond a field goal (which he puts at something like 2.97 points, or something like that), you kick off to your opponent, and "give up" some field position that way.
2. If you miss the touchdown, your opponent takes over deep in their own territory, thus reducing the success rate of their drive. And your team is essentially +25 yards in the field position battle.
3. If you kick the field goal, you only get the 3 points (almost 3 in the study) and then you also "give up" field position on the kickoff.
So his analysis says to go with #1, because if you score, it's better to get the full amount (TD + XPT) and give up the field position, OR to miss and have the opponent take over inside their own 5 (say, at their own 1), than it is to kick the field goal. In case #1 and #3, you end up "giving up" anywhere from 19-25 yards, the only real difference there is how many points you come away with.
Anyway, here's a link. It's a pretty lengthy PDF with some pretty heavy math, but I think it'll be enjoyed.
http://elsa.berkeley.edu/~dromer/papers/JPE_April06.pdf
Though this link might be better:
http://elsa.berkeley.edu/users/drome...s/nber9024.pdf