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View Diary: Morning feature: The Monty Hall problem (with poll and statistics questions answered) (310 comments)

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  •  I still say you're wrong on this (2+ / 0-)
    Recommended by:
    guyeda, NCrissieB

    but there's probably no point in our getting into it again.

    •  On the coin toss or the "hot hand?" (1+ / 0-)
      Recommended by:
      plf515

      If you toss a coin and get 20 heads in a row, the probability of that happening by random chance is 0.5^20 or about 10^-6.  It's far more likely that it's either a two-headed coin, or you're not giving it a fair toss.

      As to the "hot hand," the study you've shown was only based on the last N shots.  I agree the results of the last N shots are statistical noise and don't say anything about the next shot.  But the body cues (confidence, anxiety, good shooting form, injury, fatigue, etc.) do, and they exist independent of the results of the last N shots.  The player can have made the last N shots but just sprained an ankle, or missed the last N shots but you can see the he's confident, relaxed, and using good form.

      If he made the last N shots but just sprained an ankle, you replace him with a healthy player.  If he missed the last N shots but everything else about his body says he's fine, you leave him in because given time (though perhaps not in this game!) he'll make his percentage of shots ... unless he gets frustrated about having missed several in a row.  Then maybe you rest him to let him get out of that anxiety.

      •  On the coin toss I agree with you (1+ / 0-)
        Recommended by:
        NCrissieB

        If you  get 20 heads (or 10, or even 5) in a row, you start to get suspicious.

        On the shooting - I guess we are disagreeing as to what a streak is.  If the previous N shots tell you nothing about the next shot, to me, that proves that streaks don't happen.  

        •  Streaks are statistical noise. (1+ / 0-)
          Recommended by:
          plf515

          If a 50% field goal shooter in basketball makes four shots in a row, that tells me nothing.  That's going to about once in any 32 series of four shots ... and every shot he takes can be treated as starting a new series.  So assume he's one of his team's scorers, so he probably averages about 18 shots a game.  That's an average 15 chances per game to go on a "streak" of four made shots in a row.  (If he takes 18 shots a game, shots 16, 17, and 18 can't start a four-in-a-row "streak" as he won't have enough shots left to finish it.  Only his first 15 shots can start a "streak.")  The probability he'll have such a "streak" by random noise is:

          p = 1-((31/32)^15) = 0.379

          or about 38%.

          Explanation for non-math-geeks: the probability of his making four shots in a row, given a 1/2 chance of each, is 1/2 x 1/2 x 1/2 x 1/2 = 1/32.  If the probability that a given shot will start a four-in-a-row "streak" is 1/32, then the probability that a given shot will not begin such a "streak" is 31/32.

          The probability that none of his first 15 shots will begin such a streak is (31/32)^15 or 0.621.  Subtract from 1, and you have the probability that at least one shot will start such a "streak," or about 38%.

          Note to math-geeks: I'm pretty confident on the math here, but do let me know if I've made a mistake, please?

          That's a high enough percentage that it shouldn't be surprising if he has a four-in-a-row "streak."  You should expect it by by statistical noise - the ordinary clumping of random events - just as given 18 coin tosses you have a 38% chance of at least one streak of four "heads" outcomes.

          So yes, "streaks" are statistical noise.

          But good play isn't.  Good play is a function of training, experience, fundamentals, strategy and decision making, confidence or anxiety, fatigue, and injury.  A player's training and experience are reasonably stable for a given season, but the rest can and will vary game-to-game, and within a game, because he/she is human.

          Note: As a coach I focused on decision making and fatigue.  Decision making and confidence/anxiety are interrelated.  You can usually see confidence or anxiety in a player's face and body, but it will also be evident in his/her decisions.  Fatigue degrades decision making and fundamentals.  A player with tired legs will make mistakes because he/she can't get to the right spot in time, and his/her legs aren't supplying enough power for a proper shooting form.

          In terms of shooting, a player who's "playing well" is using good shooting form (fundamentals), working for and taking good shots (strategy and decision making), is confident rather than anxious, has fresh legs, and is healthy.  But his season-long statistics include times when one or more of those conditions is not true: he/she is using bad form, forcing bad shots, anxious rather than confident, fatigued, and/or injured.  In fact, his/her season-long statistics are skewed toward periods when he/she is not "playing well," because it's less likely that all of those conditions are true at any given moment.  So when he/she is "playing well" - when all of the positive conditions are true - you can expect him/her to "shoot better than his/his stats."

          But the key is this: you can't assess those conditions by looking at his/her last N shot attempts (results).  There will still a lot of statistical noise mixed into the results.  To assess those conditions, you have to look at how he/she is playing (process).

          That's why you can win that bar bet on whether the NBA 50% shooter who's made his last four shots will hit the next one, while a good coach knows to rest a player because his game is off.  The fan you're winning money from in the bar is looking at results.  The good coach is looking at process.

          •  I disagree (1+ / 0-)
            Recommended by:
            plf515

            I've thought about this some more and I disagree with you. Are these fair representations of your 2 claims above?

            1 - performance in the recent past does not affect current performance
            2 - fatigue, anxiety and injury affect performance

            I don't see how those can both be true unless each of the performance affecting factors is only an instantaneous condition. But I think fatigue (get enough sleep last night?) and injury (hamstring a little sore?) can certainly last all game.

            I think that good conditions (lots of sleep, confident, injury-free) could make a 50% shooter a 55% shooter for the night. Similarly, bad conditions (couldn't sleep, anxious, sprained finger) can make a 50% shooter a 45% shooter for the night. Either one could have a 4 shot streak, but the former is more likely to have it than the latter. For example, the likelihood of starting the game with a 4 basket streak is ~9% versus ~4%.

            How about an Office of Fact Based Initiatives?

            by factbased on Wed May 06, 2009 at 03:41:48 PM PDT

            [ Parent ]

            •  I don't know about Chrissie's (0+ / 0-)

              2nd point, I just don't have data.

              But there is a lot of data, at least for basketball, showing that there is no 'hot hand' - a player's chance of hitting a shot after, e.g. making 4 in a row is no different than the same player's chance of hitting after missing 4 in a row.

            •  Fatigue varies during the game. (1+ / 0-)
              Recommended by:
              plf515

              It's not about whether you got enough sleep last night.  It's about how a player's energy levels change over the course of a game.  A starting player runs about 8 miles in the course of an NBA game.  In a college game it's about 6 miles.  And unlike a long-distance runner, that running comes in sprints and stops.  It's exhausting, and that's why coaches rest players during the game.

              Fatigue levels definitely vary during the game.  It's not fixed for the duration of a given night.

              •  Yes, fatigue varies (1+ / 0-)
                Recommended by:
                plf515

                But unless you have evidence that lack of sleep does not affect performance, I'll stand by that point. And the others I made.

                I do believe that people greatly overestimate winning streaks. I also believe there are performance affecting factors at the beginning of a game that can be substantially in effect the entire game.

                How about an Office of Fact Based Initiatives?

                by factbased on Fri May 08, 2009 at 04:53:10 PM PDT

                [ Parent ]

                •  Argument by equivocation. (0+ / 0-)

                  I defined fatigue and injury in terms that vary within a game.  You changed their definitions to be constant throughout the game.  That's argument by equivocation.

                  Yes, there are performance factors that don't change much during a game.  I included two in my original response: training and experience.  There are also fatigue and injury issues that are fairly constant throughout a game (e.g.: stomach virus that kept a player from sleeping), or an entire season or career (e.g.: chronic, irreparable joint injury).

                  But there are also performance factors that change within a game.  Fatigue as I defined it (fresh vs. winded) and minor injuries (e.g.: muscle cramp) are among those.  They won't always show in the last N shot attempts, because you shouldn't expect much regression to the mean (the Strong Law of Large Numbers) in a sample of only 3 or 4.

                  A coach may recognize those factors and rest a player whose last N shot attempts are at or above a season norm, because the coach sees that the player isn't playing well and those last N shots are just noise.  Indeed that happens quite often, as most coaches have planned substitution rotations over the course of a game that take advantage of known game breaks (e.g.: end of 1st or 3rd quarter), to get an "extra" minute or two rest for a player when the action is stopped.

                  As to winning streaks, I agree with you.  There are sometimes reasons a team wins or loses several games in a row - e.g.: playing a series of weak opponents, or having key players out with injury - but in most cases it's just statistical noise.

                  •  When you started this thread (0+ / 0-)

                    you didn't define fatigue and injury in terms that vary within a game. Maybe I missed it elsewhere. But once you narrowed the definition of fatigue, I agreed and stood by my point about sleep or lack of sleep without using the word fatigue.

                    You seem to agree that there are game-length performance-affecting factors. So was it just semantics you disagreed with? Note that I find the existence of short-lived factors like being fresh or winded to be obvious and uncontroversial.

                    How about an Office of Fact Based Initiatives?

                    by factbased on Mon May 11, 2009 at 11:23:19 AM PDT

                    [ Parent ]

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