Math and Logic Errors

[freshmanjs]

To go along with the Words thread:

- During 1st game in the baseball series vs. Texas Tech (best of 3), announcers were making a big point that the winner of game 1 has a 79% chance of winning the series. As if that were remotely surprising. It would be surprising if it wasn't around 79%

- When JJ Redick played at Duke and was a 90% FT shooter, he was taking 10+ FT per game. Yet, inevitably, when he missed a FT, the comments followed like "Wow, a rare miss for JJ Redick." When, in fact, a miss at some point during the game was very likely.

[HereBeforeCoachK]

To go along with the Words thread:

- During 1st game in the baseball series vs. Texas Tech (best of 3), announcers were making a big point that the winner of game 1 has a 79% chance of winning the series. As if that were remotely surprising. It would be surprising if it wasn't around 79%

- When JJ Redick played at Duke and was a 90% FT shooter, he was taking 10+ FT per game. Yet, inevitably, when he missed a FT, the comments followed like "Wow, a rare miss for JJ Redick." When, in fact, a miss at some point during the game was very likely.

Math and logic are very weak spots in this country today - and of course, math IS logic, and vice versa.

I remember when Nate Silver's 538 was predicting an 83% chance for Hillary to win the election and a 17% for Trump. When many of Nate's friends and followers started acting like it was a done deal, Silver harshly warned them in one of his posts. As he said, 17% is about like taking a single die and rolling a 3. You wouldn't predict it necessarily, but you wouldn't be shocked either.

So to be remain bi partisan (though I'm hardly that, and very involved) - the left (who assumed 83% meant a sure win) and the right (talk radio making fun of Nate Silver after the fact) both got it wrong.

I only bring it up to buttress the point of the thread - that so many people don't really understand logic/math, or use it correctly. And sports announcers are, in general, particularly bad at this.

This is also why the media was wrong, and K was right to order Zoubek to miss the second FT versus Butler. Zoub was a 50% FT shooter...and the odds were in Duke's favor if their players knew it would be a miss, while Butler's did not. As it turned out, Heyward got a 1% perfect bounce right to him, and almost made a 1% shot. But K was right on the odds. You replay that 100 times, and Butler probably never comes as close as they did.

[jimsumner]

https://www.bing.com/videos/search?q...ACB3&FORM=VIRE

[OldPhiKap]

https://www.bing.com/videos/search?q...ACB3&FORM=VIRE

A classic. A modern classic (and yes, I’ll go post that phrase as one I hate on the Words thread):

https://youtu.be/Qhm7-LEBznk

[jimsumner]

Three statisticians go duck hunting.

They see a duck.

The first guy shoots and misses, 10 feet high.

The second guy shoots and misses, 10 feet low.

The third guy says "we can go home now, we got him."

[OldPhiKap]

Three statisticians go duck hunting.

They see a duck.

The first guy shoots and misses, 10 feet high.

The second guy shoots and misses, 10 feet low.

The third guy says "we can go home now, we got him."

https://youtu.be/IUK6zjtUj00

(Some lyrics not suitable for work)

[Jeffrey]

Three statisticians go duck hunting.

They see a duck.

The first guy shoots and misses, 10 feet high.

The second guy shoots and misses, 10 feet low.

The third guy says "we can go home now, we got him."

Was the third guy Dick Cheney?

[Nick]

Math and logic are very weak spots in this country today - and of course, math IS logic, and vice versa.

Math and logic have been weak spots in all countries in the entire history of civilization. It's just not a natural way of thinking for most people.

[Acymetric]

To go along with the Words thread:

- During 1st game in the baseball series vs. Texas Tech (best of 3), announcers were making a big point that the winner of game 1 has a 79% chance of winning the series. As if that were remotely surprising. It would be surprising if it wasn't around 79%

- When JJ Redick played at Duke and was a 90% FT shooter, he was taking 10+ FT per game. Yet, inevitably, when he missed a FT, the comments followed like "Wow, a rare miss for JJ Redick." When, in fact, a miss at some point during the game was very likely.

It was still rare for him to miss. Just because statistically you would expect him to miss a free throw over the course of the game does not mean a miss is expected on a given attempt. Thus, rare.

[freshmanjs]

It was still rare for him to miss. Just because statistically you would expect him to miss a free throw over the course of the game does not mean a miss is expected on a given attempt. Thus, rare.

No that's precisely the point. It wasn't rare for him to miss, it was common. If someone misses about 1 per game, you should expect them to miss 1 per game. Acting shocked when it happens is not intelligent. To put it another way, they were vastly overestimating how rare a 1-10 chance is (i.e., not rare at all in a case where there are routinely more than 10 trials). It's a bit like rolling 2 dice in repeated trials and then exclaiming "Wow, a rare 10" every time a 10 is rolled. That would be absurd.

[Jeffrey]

No that's precisely the point. It wasn't rare for him to miss, it was common. If someone misses about 1 per game, you should expect them to miss 1 per game. Acting shocked when it happens is not intelligent. To put it another way, they were vastly overestimating how rare a 1-10 chance is (i.e., not rare at all in a case where there are routinely more than 10 trials). It's a bit like rolling 2 dice in repeated trials and then exclaiming "Wow, a rare 10" every time a 10 is rolled. That would be absurd.

If a player is a 10% FT shooter and they take 10 FT's per game, then do you think it is common for them to make a FT?

[freshmanjs]

If a player is a 10% FT shooter and they take 10 FT's per game, then do you think it is common for them to make a FT?

It’s common for them to have a game in which they make a free throw. Announcers shouldn’t act shocked if it happens.

[jimsumner]

Flip a coin three times.

It comes up heads all three times.

The "law of averages" doesn't mean it is more likely to come up tails on the 4th flip.

It's still 50/50.

Amazing how many people do not understand this.

[BLPOG]

Flip a coin three times.

It comes up heads all three times.

The "law of averages" doesn't mean it is more likely to come up tails on the 4th flip.

It's still 50/50.

Amazing how many people do not understand this.

Oh, but it's even worse than that.

Flip a coin a thousand times.

It comes up heads 1000 times.

That's an unfair coin, right there.

Which means that as the number of trials increases, people that appeal to a "law of averages" are actually increasingly wrong.

[freshmanjs]

Oh, but it's even worse than that.

Flip a coin a thousand times.

It comes up heads 1000 times.

That's an unfair coin, right there.

Which means that as the number of trials increases, people that appeal to a "law of averages" are actually increasingly wrong.

I learned of a great example of this type of thing (at Fuqua actually). One of the professor's children had been diagnosed at birth with a very, very rare birth defect. I think it was like 1 in 50 million or something. The thing is, the error rate in the test was something like 1 in 25 million. The test is extraordinarily accurate, they told him. It's one of the most accurate tests that exists (all true). But still, given she had a positive test, it actually was 2/3 likely that she didn't have the defect (she didn't). Anyway, the lesson is that in the case of an observed extremely rare event, it is necessary to evaluate the likelihood that the observation is wrong. It may be more likely than the observed rare event. Similarly, in case of 1000 heads in a row, it's more likely the coin is bad (per above).

[Wander]

Saying that the Earth is flat? Or would I get a pass from DBR because I went to Duke?

[swood1000]

Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person?

A: Yes
B: No
C: Cannot be determined

[Acymetric]

Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person?

A: Yes
B: No
C: Cannot be determined

That one got me...I like it though!

[swood1000]

Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person?

A: Yes
B: No
C: Cannot be determined

A. If Anne is married, she’s looking at George, who is unmarried. If Anne is unmarried, Jack is looking at her.

[Rich]

Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person?

A: Yes
B: No
C: Cannot be determined

The obvious answer is (C) because we don't know whether Anne is married or not. She's both the "looker" and the "lookee" in this scenario so we don't know if a married person is looking at an unmarried person in either case. We know that in the case of Jack, the "looker" is married, but we don't know about Anne, the "lookee". In the case of George, we know the "lookee" is not married, but we don't know about Anne, the "looker."

But I'm probably wrong.

Edited: Of course I'm wrong.