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  1. #1
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    Math and Logic Errors

    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.

  2. #2
    Quote Originally Posted by freshmanjs View Post
    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.
    Race Bannon can drive ANYTHING!
    --and did you know Tim Matheson broke into show biz as voice of young Johnny Quest?

  3. #3
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  4. #4
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    Quote Originally Posted by freshmanjs View Post
    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.

  5. #5
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    Quote Originally Posted by Acymetric View Post
    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.

  6. #6
    Quote Originally Posted by freshmanjs View Post
    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?

  7. #7
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    Quote Originally Posted by freshmanjs View Post
    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.
    It was not rare for him to miss over the course of a game (actually, although I'm having trouble finding game logs from that far back, I suspect it was somewhat rare, I would imagine there were quite a few games where he was perfect, and several games where he missed two or maybe even 3, given that he had several fairly extended streaks), but that wasn't even the context of the quote. I suppose this probably hinges more on your threshold for "rare" events. I would qualify an event that happens 1/10 times as rare (or at least I would accept it if other folks did, it is kind of right around the threshold). It is possible for a result to be expected in a set of data, and still be a rare event given it's frequency compared to other possible outcomes.
    Last edited by Acymetric; 06-12-2018 at 02:47 PM.

  8. #8
    Quote Originally Posted by freshmanjs View Post
    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.
    In JJ's last season he didn't miss a FT in 17 games, which leaves 19 in which he missed at least one FT. There were 9 games in which he missed two or more FT's...and even one games in which he missed 5 vs George Washington shooting 2-7.

    His Junior season was much different. There were 21 games he didn't miss a single FT leaving only 12 in which he did. Of those 12, he only missed more than one FT once, going 7-10 against VT.

    When a player hits 25+ FT's without a miss, even if the odds say he'll eventually miss...it's still a surprise.

  9. #9
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    Quote Originally Posted by Jeffrey View Post
    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.

  10. #10
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    Quote Originally Posted by Acymetric View Post
    It was not rare for him to miss over the course of a game (actually, although I'm having trouble finding game logs from that far back, I suspect it was somewhat rare, I would imagine there were quite a few games where he was perfect, and several games where he missed two or maybe even 3, given that he had several fairly extended streaks), but that wasn't even the context of the quote. I suppose this probably hinges more on your threshold for "rare" events. I would qualify an event that happens 1/10 times as rare (or at least I would accept it if other folks did, it is kind of right around the threshold). It is possible for a result to be expected in a set of data, and still be a rare event given it's frequency compared to other possible outcomes.
    My view is that you need to account for both the % chance in a single trial AND the frequency of trials to evaluate whether an event is rare. I may take thousands of breaths between sneezes, but it’s not rare that I sneeze.

  11. #11
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    Quote Originally Posted by PackMan97 View Post
    In JJ's last season he didn't miss a FT in 17 games, which leaves 19 in which he missed at least one FT. There were 9 games in which he missed two or more FT's...and even one games in which he missed 5 vs George Washington shooting 2-7.

    His Junior season was much different. There were 21 games he didn't miss a single FT leaving only 12 in which he did. Of those 12, he only missed more than one FT once, going 7-10 against VT.

    When a player hits 25+ FT's without a miss, even if the odds say he'll eventually miss...it's still a surprise.
    Exactly. Some numbers by year, the only year where it might have been fair to quibble with the use of the phrase "rare" was his senior year, but by that time everyone was pre-conditioned.

    Freshman (2002-2003): 33 games played, 9 with misses - probably more uncommon than rare on a per game basis but only a slight exaggeration, not wildly inaccurate though
    Sophomore (2003-2004): 37 games played, 7 games with misses - fair to say it was rare for him to miss a FT in a game that year on a per game basis
    Junior (2004-2005): 33 games played, 11 games with misses - again, probably more uncommon than rare on a per game basis, not wildly inaccurate though
    Senior (2005-2006): 36 games played, 19 games with misses - better than even odds he would miss, his FT shooting dipped this season and misses were not rare, although still somewhat uncommon.

    I still think freshmanjs needs to consider each attempt in a vacuum, instead considering likelihood of an event occurring in a given data set(in this case, a game). At the very least, I would need a concrete, numeric threshold for what you would allow to be considered "rare".

    Edit to explain the difference between my numbers and PackMan's numbers: I counted the number of games with a miss compared to total games. PackMan's method ends up counting games where he went 0-0 as games with a miss, somewhat incorrectly.

  12. #12
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    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.

  13. #13
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    Quote Originally Posted by Acymetric View Post
    Exactly. Some numbers by year, the only year where it might have been fair to quibble with the use of the phrase "rare" was his senior year, but by that time everyone was pre-conditioned.

    Freshman (2002-2003): 33 games played, 9 with misses - probably more uncommon than rare on a per game basis but only a slight exaggeration, not wildly inaccurate though
    Sophomore (2003-2004): 37 games played, 7 games with misses - fair to say it was rare for him to miss a FT in a game that year on a per game basis
    Junior (2004-2005): 33 games played, 11 games with misses - again, probably more uncommon than rare on a per game basis, not wildly inaccurate though
    Senior (2005-2006): 36 games played, 19 games with misses - better than even odds he would miss, his FT shooting dipped this season and misses were not rare, although still somewhat uncommon.

    I still think freshmanjs needs to consider each attempt in a vacuum, instead considering likelihood of an event occurring in a given data set(in this case, a game). At the very least, I would need a concrete, numeric threshold for what you would allow to be considered "rare".
    Is it rare for a baby to be conceived?

  14. #14
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    Quote Originally Posted by freshmanjs View Post
    Is it rare for a baby to be conceived?
    No, it has happened many times since the creation of this thread, presumably. Why would someone consider it rare?

    Can you give an example of something that you could consider rare, but on the fringe (so we can get an idea of where you draw the line)?

  15. #15
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    Quote Originally Posted by Acymetric View Post
    At the very least, I would need a concrete, numeric threshold for what you would allow to be considered "rare".
    I doubt it's possible to reach an agreed numerical definition for rare. Everyone will have their own view on what that threshold is. It also probably changes depending on the thing being evaluated.

    I still submit that acting shocked about something that happens a lot (in the case of JJ, every game or 2) is silly. Now, if he were such a good FT shooter that he missed only 1-2 times in a season, then it would make more sense to me.

    I obviously agree that if there were only to be one trial and he missed, it would be mildly surprising (not sure I'd say rare).

  16. #16
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    Don’t know if this is the right thread for this but I heard an amusing puzzle recently. Apparently, the only people who can get it right are psychopaths. Give it a try, then scroll down for the answer.

    While at her own mother's funeral, a woman meets a guy she doesn't know. She thinks this guy is amazing — her dream man — and is pretty sure he could be the love of her life. However, she never asked for his name or number and afterwards could not find anyone who knows who he was. A few days later the girl kills her own sister – but why?

  17. #17
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    Quote Originally Posted by Acymetric View Post
    No, it has happened many times since the creation of this thread, presumably. Why would someone consider it rare?

    Can you give an example of something that you could consider rare, but on the fringe (so we can get an idea of where you draw the line)?
    But, that's a perfect example (as I see it). It's extraordinarily unlikely that any particular sperm will fertilize an egg. Almost impossible. However, there are so many trials, that the event isn't rare. That's why I disagree that you have to consider ONLY a single trial. I can't answer your question without knowing the frequency of trials for the thing being evaluated.

  18. #18
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    Quote Originally Posted by swood1000 View Post
    Don’t know if this is the right thread for this but I heard an amusing puzzle recently. Apparently, the only people who can get it right are psychopaths. Give it a try, then scroll down for the answer.

    While at her own mother's funeral, a woman meets a guy she doesn't know. She thinks this guy is amazing — her dream man — and is pretty sure he could be the love of her life. However, she never asked for his name or number and afterwards could not find anyone who knows who he was. A few days later the girl kills her own sister – but why?
    She wanted to meet the guy again.

  19. #19
    Quote Originally Posted by jimsumner View Post
    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.

  20. #20
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    Quote Originally Posted by swood1000 View Post
    She wanted to meet the guy again.
    How many on the board thought it was an easy question?

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