A little probability puzzle

by rrusczyk, Jun 17, 2006, 3:21 PM

In watching the NCAA basketball tournament, I've noticed that when a team is down by 2 with time running out, the team almost always goes for a three pointer. So, here's the puzzle: Are these glory-seeking players making a mistake? Should they be going for an easier 2-point shot to send it in to overtime?

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Huh? Well I think it depends on the probabilities of making 2 and 3 point shots. But it seems like most of the time the 3 point shot makes more sense, since their expected value is like P(3pt) instead of rouoghly 0.5*P(2pt), and it doesn't seem like 2 pointers are that much easier than 3 pointers.

by probability1.01, Jun 17, 2006, 3:22 PM

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Yeah, you have to be twice as likely to make the 2-pointer to justify taking it. Also, if time is really short (like tenths of seconds) the 3-point shot maybe much more feasible than a 2-pointer.

by themonster, Jun 17, 2006, 3:22 PM

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Conventional wisdom says play for the tie at home and go for the win on the road, at least in the NBA. With the college three point line, I'd play for the win every time; nearly every college team has a 40% three point shooter. Plus missed three point shots lead to long rebounds which increases your chance of getting an offensive rebound.

by blahblahblah, Jun 17, 2006, 3:22 PM

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I usually go for the 3 pointer in games where that happens :)

I guess everyone is thinking about winning and given the lack of time the 3 pointer is usually simpler to take (and you're easier to be left unmarked there - to take a 2 pointer you'ld probably have to force it, given that the defending team will not let you inside the 6'25'' line easily).

by Valentin Vornicu, Jun 17, 2006, 3:22 PM

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Valentin Vornicu wrote:
I usually go for the 3 pointer in games where that happens :)

What a shock :)

by rrusczyk, Jun 17, 2006, 3:22 PM

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Belated USAMO blogging
Tilings: Mixing Number Theory and Geometry
How do the 'smart' students do it?
Interesting picture
What Calculators Hath Wrought
At the NCTM Convention
Looking Forward to Nationals
AoPS may be growing!
Computer Problems and an Interesting Dinner
The Price of Mathematical Ignorance
CA State MATHCOUNTS
San Diego Math Circle Parents
Prepping for Northern CA State MATHCOUNTS
Our Book Project
Recursive Thinking
Differences in course types
Play
Burnout
MATHCOUNTS Chapter Update
MATHCOUNTS Chapter
Using symmetry
Using Expected Value to Solve Problems
Counting the Same Thing Two Different Ways
Another test
Testing
Evolution in the classroom
Women in Math & Science
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About Owner
  • Posts: 16194
  • Joined: Mar 28, 2003
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  • Blog created: Jan 28, 2005
  • Total entries: 940
  • Total visits: 3312778
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