Simple 4 question quiz

[DCWildcat]

Please hand in at the end of class. No cheating.

Just take a guess. I don't want you to do all the math involved, I'm just interested in where your guesses lie (I did awful when I tried this). There is a purpose to this, I promise.

Question 1: Suppose you're flipping a coin that will land heads 50% of the time and tails the other 50%. You do an infinite series of 10 flips, where you flip it ten times, record how many times it was heads, then repeat. How often will you flip exactly 5 heads out of 10 flips?
1b: How often will you flip exactly 7 heads out of 10?
1c: How often will you flip 6 or more heads out of 10?

Question 2: Suppose that instead of flipping a coin, you're a shooter who shoots exactly 50% from the field (ignore 3s), and instead of occurences of heads vs. tails, you're counting made baskets vs. missed ones. Do the same questions as above. Are your answers for this question different from your answers to Question 1?

[Terry L. Wildcat]

DCWildcat wrote: Please hand in at the end of class. No cheating.

Just take a guess. I don't want you to do all the math involved, I'm just interested in where your guesses lie (I did awful when I tried this). There is a purpose to this, I promise.

Question 1: Suppose you're flipping a coin that will land heads 50% of the time and tails the other 50%. You do an infinite series of 10 flips, where you flip it ten times, record how many times it was heads, then repeat. How often will you flip exactly 5 heads out of 10 flips?
1b: How often will you flip exactly 7 heads out of 10?
1c: How often will you flip 6 or more heads out of 10?

Question 2: Suppose that instead of flipping a coin, you're a shooter who shoots exactly 50% from the field (ignore 3s), and instead of occurences of heads vs. tails, you're counting made baskets vs. missed ones. Do the same questions as above. Are your answers for this question different from your answers to Question 1?

1. Every time

1b/1c. Never

[kevinlw1974]

DCWildcat wrote: Please hand in at the end of class. No cheating.

Just take a guess. I don't want you to do all the math involved, I'm just interested in where your guesses lie (I did awful when I tried this). There is a purpose to this, I promise.

Question 1: Suppose you're flipping a coin that will land heads 50% of the time and tails the other 50%. You do an infinite series of 10 flips, where you flip it ten times, record how many times it was heads, then repeat. How often will you flip exactly 5 heads out of 10 flips?
1b: How often will you flip exactly 7 heads out of 10?
1c: How often will you flip 6 or more heads out of 10?

Question 2: Suppose that instead of flipping a coin, you're a shooter who shoots exactly 50% from the field (ignore 3s), and instead of occurences of heads vs. tails, you're counting made baskets vs. missed ones. Do the same questions as above. Are your answers for this question different from your answers to Question 1?
If it is an infinite number of 10 flips then the answer is infinite. The key word being infinite. I think for all the questions. Because there is not defined number you can give an answer. Of course I would be wrong.

[tauzreborn]

DCWildcat wrote: Please hand in at the end of class. No cheating.

Just take a guess. I don't want you to do all the math involved, I'm just interested in where your guesses lie (I did awful when I tried this). There is a purpose to this, I promise.

Question 1: Suppose you're flipping a coin that will land heads 50% of the time and tails the other 50%. You do an infinite series of 10 flips, where you flip it ten times, record how many times it was heads, then repeat. How often will you flip exactly 5 heads out of 10 flips?
1b: How often will you flip exactly 7 heads out of 10?
1c: How often will you flip 6 or more heads out of 10?

Question 2: Suppose that instead of flipping a coin, you're a shooter who shoots exactly 50% from the field (ignore 3s), and instead of occurences of heads vs. tails, you're counting made baskets vs. missed ones. Do the same questions as above. Are your answers for this question different from your answers to Question 1?

By "infinite," I believe he means that it was done enough times that standard deviation and probablity maybe considered valid assumptions.

If this isn't intended to be a trick question then the stats can be run, but I also do not feel like looking up the equation.

My answers:

1. ~15%

1b. ~9%

1c. ~50%

2. Not enough information.

[m0fats]

10% for every one..

since the odds of head/tails is 50/50, and there are only 10 possible ratios, then you have a 10% chance of flipping 1head/9tails, as well as 5head/5tails, and any other combination.

methink that sounds right.

[UKfaninCO]

m0fats wrote: 10% for every one..

since the odds of head/tails is 50/50, and there are only 10 possible ratios, then you have a 10% chance of flipping 1head/9tails, as well as 5head/5tails, and any other combination.

methink that sounds right.


While each series isindependant from the last, there are still only 10 possible outcomes. Having written software to simulate flipping a coin for a statistics class once, I know that, while you may get really long strings of one side or the other, the ratio of heads to tails, as you approach infinity, is close to 50/50. Very close. 10% sounds right to me but I'm not sure that answers the question.

So the answer to 1a: is 10% of the time. 1b: is also 10% of the time. 1c: is 50%.

I wouldn't answer question 2 differently. The question is about statistical probability and they are one and the same. Interestingly, while there are only 2 possible outcomes when a shooter shoots the ball, either they make it or they miss it, the probability that they will do one or the other is based on the individual and his past history. So not every shooter will be 50/50. Every coin flip is 50/50.

[audacious1]

DCWildcat wrote: Please hand in at the end of class. No cheating.

Just take a guess. I don't want you to do all the math involved, I'm just interested in where your guesses lie (I did awful when I tried this). There is a purpose to this, I promise.

Question 1: Suppose you're flipping a coin that will land heads 50% of the time and tails the other 50%. You do an infinite series of 10 flips, where you flip it ten times, record how many times it was heads, then repeat. How often will you flip exactly 5 heads out of 10 flips?
1b: How often will you flip exactly 7 heads out of 10?
1c: How often will you flip 6 or more heads out of 10?

Question 2: Suppose that instead of flipping a coin, you're a shooter who shoots exactly 50% from the field (ignore 3s), and instead of occurences of heads vs. tails, you're counting made baskets vs. missed ones. Do the same questions as above. Are your answers for this question different from your answers to Question 1?

Here are my guesses. (I haven't read past this post.)

1a:How about 28%

1b: Something like 12%?

1c: Shouldn't that be 50%?

2: Well, they should be the same, but I've got a feeling you're going to tell me I'm wrong. hehe :D

[DCWildcat]

Some really good stuff in there and thank you guys a TON for participating/playing along with my sick game (muhuhahaha). Don't worry if you got them horribly wrong; I sure as hell did, and this isn't exactly high school math. Here are the results from binomial probability:

You'll flip heads exactly 5 out of 10 times ~24.6% of the time
You'll flip heads exactly 7 out of 10 times ~11.7% of the time
You'll flip heads 6, 7, 8, 9, or 10 times out of 10 ~37.7% of the time (it's less than 50% because there are really 11 outcomes, of which I specified 5: he can make 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10 out of 10 shots, and 0-10 inclusive = 11. It's not simply 5/11 either, because, as I say below, he'll hit 5/10 more likely than 10/10, etc.).

You can calculate these at http://faculty.vassar.edu/lowry/binomialX.html if you don't believe me. The reason 1a and 1b are different is because coin flips are normally distributed; if you're flipping heads 50% of the time, it's much more likely you'll get 5 heads than 4, 4 than 3, etc.

If graphed, this will make a normal (bell) curve. For an illustration, look here: http://www.ms.uky.edu/~mai/java/stat/GaltonMachine.html
Basically, as the ball hits each peg, it has a 50% chance of going left and a 50% chance of going right. There are 8 pegs, so it'll reach this decision 8 times.
You can see the results right before your eyes.

[DCWildcat]

The second question is the important one. It’s opinion, so I can’t give an answer (I could still give overwhelming evidence for one side though…). The important part is to think of what the implications are of each answer, namely:

Answer 1: A player’s shooting will not[/i] closely match the coin flipping. Due to other variables that will not even out in the long run, a shooter’s distribution will not match the flip of the coin. This means that there must be something else at work—perhaps he’s a streaky shooter, sometimes he’s “on fire” and sometimes he’s “ice cold.”

Answer 2: A player’s shooting will[/i] closely match the coin flipping. This suggests that other variables have an insignificant effect in the long run, as his shooting won’t be any different from the flip of a coin. It suggests that the variables like streakiness that I mentioned above are nothing more than the result of normal, random statistical fluctuations and that there is no effect from being “hot” or “cold.” So if he’s a 50% shooter and he hits 7 out of 10 shots, it doesn’t mean he’s hot—just that he’s experiencing normal variance.

I’ll explain in a later post why I think:
1) Answer 2 is mostly correct, and that for the overwhelming majority of players, there is no (little at best) effect of being “hot.” In other words, most players never get hot/cold, they simply get lucky/unlucky
2) Teams exhibit the same pattern as players
3) The very real, very[/i] significant, and completely overlooked (outside of a few sports economists) effects of this. Ultimately, this has a lot to do with my belief that Tubby is a good coach for Kentucky, but I’m not sure if I want to pull that string again.

[SunBaller]

I shouldn't even respond or comment on this ludicrous waste of off-season time, but I just might as well since most other posts are just as asinine. Shooting percentages have nothing to do with "flipping a coin". There are a multitude of variables. Anyone who thinks differently has never played basketball except on their backyard un-level, un-regulation court.

Shooting percentages are based solelyon height of shooters, style of defense, style of offense, height of defenders, speed of defenders, speed of shooters, leaping ability of shooters, "hang time", leaping ability of defenders, distance from the rim, etc., etc.

Rondo couldn't hit the ocean past 15 feet, but he had an excellent shooting percentage because of "distance from the rim" shots. Lay-ups in other words. I'll take Rondo's shooting percentages over most any point guard we've had.

You will not find a mathematical probability with shooting percentages. The better athletes with closer shots will always have higher percentages.

Some folks post exactly the way Tubby Smith coaches. Don't ever forget that we're talking about the University of Kentucky Basketball.

[DCWildcat]

SunBaller wrote: I shouldn't even respond or comment on this ludicrous waste of off-season time, but I just might as well since most other posts are just as asinine. Shooting percentages have nothing to do with "flipping a coin". There are a multitude of variables. Anyone who thinks differently has never played basketball except on their backyard un-level, un-regulation court.

Shooting percentages are based solelyon height of shooters, style of defense, style of offense, height of defenders, speed of defenders, speed of shooters, leaping ability of shooters, "hang time", leaping ability of defenders, distance from the rim, etc., etc.

Rondo couldn't hit the ocean past 15 feet, but he had an excellent shooting percentage because of "distance from the rim" shots. Lay-ups in other words. I'll take Rondo's shooting percentages over most any point guard we've had.

You will not find a mathematical probability with shooting percentages. The better athletes with closer shots will always have higher percentages.

Some folks post exactly the way Tubby Smith coaches. Don't ever forget that we're talking about the University of Kentucky Basketball.

You might want to edit out some of the attacks you have in there, Sunballer.

When you're right, they're just unnecessary.
When they're wrong, they make you look like an jerk.

You may also want to open your mind a lot.

I am glad you made a post with this kind of content though, because it's exactly what I want to debate. On this opposite end of, though :D. Statisticians have uniformally rejected this kind of thinking, and I'm going to try to do the same thing, too.

[DCWildcat]

SunBaller wrote:

Shooting percentages are based solelyon height of shooters, style of defense, style of offense, height of defenders, speed of defenders, speed of shooters, leaping ability of shooters, "hang time", leaping ability of defenders, distance from the rim, etc., etc.

Think of the implications of this.

Suppose I take a shooter. He shoots 1 shot with no defense, and makes it. Then he shoots 999 more: same spot, none of the variables you mentioend (or other "big ones" like physical fatigue, effort, etc) change.

I can tell you right now he will not make 1000 consecutive shots from there. Unless you can convince me that he will, your point is incorrect.

[audacious1]

Hey, I was pretty much right, except for that 11 options part. Doh!

I thought I had it right until I read some posts that followed which made me doubt. hehe

[DCWildcat]

There's something very important to realize: probability isn't a "magic hand." There's no divine intervention from some math deity that makes a coin flip 50% heads and 50% tails. It just does flip that way.

Whether a coin will land heads or tails is dependent on a lot of things. The force of the flick. Wind. Air drag. The surface it hits. etc......

But even though it's entirely on those things, it's still going to be 50/50. Out of 100 flips repeated infinitely, roughly 68% of those will have heads appearing between 55 and 65 times. 95% of the time it will be within 50 and 70 heads. And ~99.7% of the time, it'll be within 45 and 75 heads.

Why is shooting any different? Sure, there's a lot more variables, as Sunballer pointed out. But in a very real sense, there really isn't anything different between them. I urge you not to offhandedly dismiss this and to really think about it.

If you still disagree, so be it. But realize what that commits you to:
-You cannot believe in any research from any social science field. Psychology, economics, anthropology, sociology, political science...by denying binomial probability, which is the foundation for the statistical significance measures that these fields are based around, you cannot accept any of their findings.
-Any more statistics. Never again should you talk about someone's field goal percentage, a batting average, or anything else of the sort. You don't believe in them, remember?

Shooting a basketball is flipping a coin, with more complex and more total variables.