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# Football Decision

## Question

With the new NFL season about to start, I thought a football logic puzzle would be timely.

You are the coach of a football team. Your team is down 14 points with a few minutes to go. You are driving and score a touchdown to go down by 8. Should you go for a 2-point conversion or kick a 1-point PAT?

For simplicity, assume that a kick is 100% and the 2-point conversion is 50%. These numbers are pretty close to reality in the NFL, though the rules have changed for this year and we have yet to see what effect they will have.

You can also assume the other team won't score again. If this were to happen, it's extremely unlikely that you could win. Also, assume that overtime is a 50-50 proposition.

Also, try to answer a second part of the question. If you think it's right to kick, please determine at what rate you'd need to covert a 2-point try before you'd consider going for 2. Likewise, if you think it's right to go for 2, how low would your 2-point conversion rate have to be, before you think it would be right to kick.

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Second part

At an approximately 38.2% success rate going for 2 has a 50% success rate. So anything lower isn't worth the risk.

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Assumptions: The other team wont score again, and we will score a second touchdown.

Go for two.

Theoretically, by kicking for the extra point I will score two points. Also, theoretically, I will succeed in one out of the two 2-point conversions. In both situations I get two more points and tie to go to overtime, but if I succeed on the first 2-point conversion, I can kick a field goal after the second touchdown and win.

So doing the numbers:

Extra point: 100% chance of a tie and 50% chance of winning or if you go for one then the second time go for two you still only have a 50% chance of winning. The only difference is what you put your hope for the win in.

Two Points: You have a 50% chance of converting the first one and when you do you have a 100% chance of winning by kicking a field goal.

If you miss the first (50%) you have a 50% chance to make the second so a 25% chance of that outcome. In this case you only tie and go to overtime with a 50% chance of winning or 12.5% overall. Putting this together with the first part gives us a total of 62.5% chance of winning.

The other part will require paper instead of just my head so I will get back to you with that.

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Second part

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Well done. The amazing thing is I've NEVER seen an NFL coach do this! These teams are worth billions and each win must be worth millions to them, but they can't make a simple decision that might get them an extra win every few years.

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i would like to teach a new method and rules of this game. Then i give continuous trying to my team members and i will win the game.

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