Hot-Hand Missing From 3 Point Shootout
igor eduardo kupfer
study. The players have 25 shots from the same distance to get into rhythm,
unlike actual game situations when shot attempts are less frequent and from
varying distances. Alan Reifman has looked at a couple of these contests on
his hot-hand page (http://www.hs.ttu.edu/hdfs3390/hothand.htm) and found
precious little evidence in favour of the hypothesis that a player's
probability of making a shot can change based on the results of the previous
shot. He also describes a few of the statistical tests you can use to look for
a streaky shooter. I'll use the Runs' Test, because it comes built in with
Minitab. An online runs test calculator can be found here:
http://www.ubmail.ubalt.edu/~harsham/Business-stat/otherapplets/Randomness.htm
The runs test looks at a sequence of shots, and from the shooting percentage,
calculates how many runs of hits and misses can be expected by chance alone.
To show that it doesn't depend on how good the shooter is, I went into my
backyard and simulated the 3-point contest twice -- once, going out and
shooting cold [*], without any practice shots, and once after having shot the
ball for about half an hour.
[* Shooting cold is right -- it was -8 degrees in the outskirts of Toronto
today, with a light wind and steady snow. I froze my butt off performing this
experiment. The things I do for science... my Nobel should make up for
everything, though.]
Here are the results:
ShotNumber 5 10 15 20 25 hits misses
cold M M M M M M M M M H M M M M M M M M M M M M H M M 2 23
warm M H M H H H M H H H M H M M M H H M M H M M M M M 11 14
And here's the Minitab analysis. The "K" is the mean, ie my shooting average
for that sequence. The number beside the "p = " is the probability of shooting
the observed number of runs by chance alone, ie anti-hot-hand. Usually, if the
probability that chance caused the result is more than 5% ("alpha"), we say
that the results are not statistically significant.
Cold
K = 0.0800
The observed number of runs = 5
The expected number of runs = 4.6800
2 Observations above K 23 below
p = 0.6176
Cannot reject at alpha = 0.05
Warm
K = 0.4400
The observed number of runs = 13
The expected number of runs = 13.3200
11 Observations above K 14 below
p = 0.8944
Cannot reject at alpha = 0.05
As you can see, neither of these results were significant, even the first
sequence where I missed 9 and 12 shots in a row. What the test is saying is
that with someone shooting as badly as I did, we can expect there to be long
series of misses by chance alone.
Now, on to the 3-Point Shootout.
For anyone who has read my posts on this topic before, you won't be surprised
to find out that none of the shooters displayed any streaky behaviour. The
closest was Wesley Person's second round, which had a couple of longish
streaks. But the entire sequence did not display any more runs than could be
predicted by chance. (All results and Minitab outputs below.) None of the
other players' results had any unusual streakiness.
Well, there was one sequence which contained fewer runs than expected,
suggesting streakiness. It went like this:
ShotNumber 5 10 15 20 25 hits misses
M M M M H H H M H H H H M H M M M M M M M M M H H 10 15
K = 0.4000
The observed number of runs = 8
The expected number of runs = 13.0000
10 Observations above K 15 below
p = 0.0330
A p = .03 means that there is only a 3% chance of this result (ie the sequence
above) being generated by chance alone. So this is evidence of the hot-hand,
right? Actually, this is the exception that proves the rule. The above series
was shot by Peja Stojakovic at the beginning of Round 3. During his attempt
for shot #12, the time buzzer was inadvertently set off. Peja was visibly
disturbed -- he broke rhythm and paused for a second -- obviously wondering
why the buzzer had gone off halfway through his sequence --before resuming. He
then proceeded to miss 10 of the next 11. It took an outside disturbance to
create a series of shots that display a fewer number of runs than be expected
by chance. None of the other series of shots, performed under normal
circumstances, show any such streakiness.
3 Point Shootout Results
Round 1
ShotNumber 5 10 15 20 25 hits misses
Garrity H M M H M M H M M M M H H M M M M H M H M H H H H 11 14
Wesley M H H H H M M H M M M H H H H M M M M M M H M M M 10 15
Stojakovic H H H M M H H H H M H H H H M H M H H M H H H M H 18 7
Barry H H H M H M H M H H H H H M M M M M M H H H M H H 15 10
Person M M H M H M M H H M H M M H M H H M M H M M M H H 11 14
Walker M M M M M M H M M M H M M M M H M H H H M M M M M 6 19
Round 2
ShotNumber 5 10 15 20 25 hits misses
Person M H H M M H H H H H H H M M M M H H H H H M H H H 17 8
Stojakovic H H H H M H H H M H H H M H H H M H M H M H H M M 17 8
Barry M M H H H M H H M M M M H H M H H H H M M H H H H 15 10
Round 3
ShotNumber 5 10 15 20 25 hits misses
Person H H H H M M H H H M H H H M M H H M H M M H M M H 15 10
Stojakovic H H M H H H M H H H H H M H H M H H H H M M H H M 18 7
Runs Test Results
PatGarrity
K = 0.4400
The observed number of runs = 13
The expected number of runs = 13.3200
11 Observations above K 14 below
p = 0.8944
Cannot reject at alpha = 0.05
DavidWesley
K = 0.4000
The observed number of runs = 9
The expected number of runs = 13.0000
10 Observations above K 15 below
p = 0.0881
Cannot reject at alpha = 0.05
PejaStojakovic1
K = 0.7200
The observed number of runs = 13
The expected number of runs = 11.0800
18 Observations above K 7 below
p = 0.3255
Cannot reject at alpha = 0.05
BrentBarry1
K = 0.6000
The observed number of runs = 11
The expected number of runs = 13.0000
15 Observations above K 10 below
p = 0.3938
Cannot reject at alpha = 0.05
WesleyPerson1
K = 0.4400
The observed number of runs = 16
The expected number of runs = 13.3200
11 Observations above K 14 below
p = 0.2662
Cannot reject at alpha = 0.05
AntoineWalker
K = 0.2400
The observed number of runs = 9
The expected number of runs = 10.1200
6 Observations above K 19 below
p = 0.5237
Cannot reject at alpha = 0.05
WesleyPerson2
K = 0.6800
The observed number of runs = 8
The expected number of runs = 11.8800
17 Observations above K 8 below
p = 0.0668
Cannot reject at alpha = 0.05
PejaStojakovic2
K = 0.6800
The observed number of runs = 14
The expected number of runs = 11.8800
17 Observations above K 8 below
p = 0.3165
Cannot reject at alpha = 0.05
BrentBarry2
K = 0.6000
The observed number of runs = 10
The expected number of runs = 13.0000
15 Observations above K 10 below
p = 0.2008
Cannot reject at alpha = 0.05
WesleyPerson3
K = 0.6000
The observed number of runs = 13
The expected number of runs = 13.0000
15 Observations above K 10 below
p = 1.0000
Cannot reject at alpha = 0.05
PejaStojakovic3
K = 0.7200
The observed number of runs = 12
The expected number of runs = 11.0800
18 Observations above K 7 below
p = 0.6376
Cannot reject at alpha = 0.05
best,
ed
[watch the spam trap -- the domain is rogers com]
Neil Cerutti
eduardo kupfer wrote:
> The All-Star three point shootout provides a unique opportunity
> for a hot-hand study.
Thanks for the article.
> Well, there was one sequence which contained fewer runs than
> expected, suggesting streakiness. It went like this:
>
> ShotNumber 5 10 15 20 25 hits misses
>
> M M M M H H H M H H H H M H M M M M M M M M M H H 10 15
>
> K = 0.4000
> The observed number of runs = 8
> The expected number of runs = 13.0000
> 10 Observations above K 15 below
> p = 0.0330
>
> A p = .03 means that there is only a 3% chance of this result
> (ie the sequence above) being generated by chance alone. So
> this is evidence of the hot-hand, right?
>
> Actually, this is the exception that proves the rule.
I submit that it just shows the questionable scientific
foundations of probability. It can show the chance of something
happening, but in reality that thing is *not* determined by
chance, as you have shown below. The factors that go into
determining if a shot is a hit or a miss are just too complicated
for us, so probability is the resort.
When I flip a coin, the exact trajectory and spin I apply, plus
outside forces like wind and magnetic fields determine whether it
comes up heads or tails, not the laws of probability.
> The above series was shot by Peja Stojakovic at the beginning
> of Round 3. During his attempt for shot #12, the time buzzer
> was inadvertently set off. Peja was visibly disturbed -- he
> broke rhythm and paused for a second -- obviously wondering why
> the buzzer had gone off halfway through his sequence --before
> resuming. He then proceeded to miss 10 of the next 11. It took
> an outside disturbance to create a series of shots that display
> a fewer number of runs than be expected by chance. None of the
> other series of shots, performed under normal circumstances,
> show any such streakiness.
What about this one?
> Barry M M H H H M H H M M M M H H M H H H H M M H H H H 15 10
>
> BrentBarry1
> K = 0.6000
> The observed number of runs = 11
> The expected number of runs = 13.0000
> 15 Observations above K 10 below
> p = 0.3938
> Cannot reject at alpha = 0.05
The proportion of hits/misses after a hit: 10/4
The proportion of hits/misses after a miss: 5/5
So, after a made shot he hit 70%, and after a miss he hit 50%.
That seems quite extraordinary to me.
--
Neil Cerutti
igor eduardo kupfer
>In article <7re35v834uujq942t...@4ax.com>, igor
>eduardo kupfer wrote:
>> The All-Star three point shootout provides a unique opportunity
>> for a hot-hand study.
>
>Thanks for the article.
>
Hey Neil. No prob. I remember your previous objections to the evidence showing
an absence of hot-handish streaks, and I think I sense a theme there> I'll try
to address it.
>> Well, there was one sequence which contained fewer runs than
>> expected, suggesting streakiness. It went like this:
>>
>> ShotNumber 5 10 15 20 25 hits misses
>>
>> M M M M H H H M H H H H M H M M M M M M M M M H H 10 15
>>
>> K = 0.4000
>> The observed number of runs = 8
>> The expected number of runs = 13.0000
>> 10 Observations above K 15 below
>> p = 0.0330
>>
>> A p = .03 means that there is only a 3% chance of this result
>> (ie the sequence above) being generated by chance alone. So
>> this is evidence of the hot-hand, right?
>>
>> Actually, this is the exception that proves the rule.
>
>I submit that it just shows the questionable scientific
>foundations of probability. It can show the chance of something
>happening, but in reality that thing is *not* determined by
>chance, as you have shown below. The factors that go into
>determining if a shot is a hit or a miss are just too complicated
>for us, so probability is the resort.
>
I think you are slightly misunderstanding the thrust of scientific inquiry.
The primary goal is never to prove the existence of something -- like the
influence of hot-hands on streaks -- but rather to disprove its opposite.
Wow. That was an incredibly opaque explanation! Maybe a courtroom analogy
would be better:
Something terrible has happened -- an illegal streak has been observed! On
trial is the suspected culprit, Mr. Hot-Hand, who is thought by the
prosecutors to have caused this criminal streak. The prosecution brings many
witnesses, all testifying that they have felt the influence of Mr Hot-Hand,
who has caused them to engage in streaky behaviour in the past. Witness after
witness say the same thing.
The defense lawyer gets up to cross examine the witness. She questions whether
the witness is a capable observer of streaky behaviour, and proposes a test:
Look at these shooting results. Can the witness tell the court which results
were the work of Mr Hot-Hand's influence, and which were not? The witness
fails in this test, showing that in general, people are very good at seeing
streaky patterns where in fact none exist.
The defense presents its case: streaks happen, sometimes by chance alone. To
show this, Mr. Hot-Hand's lawyer flips a coin 100 times, gets a streak of 7
heads. Does it again and gets 6 tails in a row.
Since we know that streaks can be generated by chance, and we know that people
in general cannot tell whether a pattern exhibits streaks that are out of the
ordinary, how can the blame for the illegal streak be blamed on Mr. Hot-Hand?
The witnesses who say he is to blame are unreliable, and we already have
another cause that has been shown to be a sufficient explanations of the
streak: chance.
Verdict: there is simply not enough evidence to convict Hot-Hand. This isn't
to say he didn't do it -- it just means that he can't be held responsible when
there's a more plausible explanation.
<snip>
>
>What about this one?
>
>> Barry M M H H H M H H M M M M H H M H H H H M M H H H H 15 10
>>
>> BrentBarry1
>> K = 0.6000
>> The observed number of runs = 11
>> The expected number of runs = 13.0000
>> 15 Observations above K 10 below
>> p = 0.3938
>> Cannot reject at alpha = 0.05
>
>The proportion of hits/misses after a hit: 10/4
>The proportion of hits/misses after a miss: 5/5
>
>So, after a made shot he hit 70%, and after a miss he hit 50%.
>
>That seems quite extraordinary to me.
And now we reach the realm of the 2x2 contingency table. Usually, we might use
Chi-Squared for this test (no, not an ancient Oriental fighting art -- a
statistical test), but for smaller values of n, we can use the more precise
Fisher's Exact Probabilities test. I used an online versions from
http://faculty.vassar.edu/lowry/tab2x2.html.
Under the section marked "Data Entry" is the 2x2 table. The X values can stand
for miss and hit ("0" and "1" on table), and the Y values can be "after a hit"
and "after a miss" ("1" and "0" on table). The table will look like this:
X
Miss Hit
------------
After A Hit | | |
Y |------------|
After A Miss | | |
------------
And the table data like this:
X
0 1
-------
1| 4 | 10|
Y |-------|
0| 5 | 5 |
-------
The answer, ie the probability of those results occurring by chance, in this
context, is the one-tailed value for p, which is 0.260. This means that
there's a one in four probability of getting these results by chance alone.
This doesn't mean that the hot-hand didn't cause the results, it just means
that the results aren't unlikely enough to rule chance out -- which is all we
can ever do: rule chance out as an explanation. We can never prove the
existence of the hot-hand (unless we find some as yet unknown physical causes
that would allow people to raise their percentages _through will alone_), we
can only eliminate alternate explanations.
Larry Coon
I swore to myself I wasn't going to get involved in this
conversation again, and cursed Ed for bringing it up one
more time, excellent as his post was. But I just have to
comment on this, which entirely misses the point.
> I submit that it just shows the questionable scientific
> foundations of probability.
Probability isn't scientifically founded. It's mathematically
founded. That's even better.
> It can show the chance of something
> happening, but in reality that thing is *not* determined by
> chance, as you have shown below. The factors that go into
> determining if a shot is a hit or a miss are just too complicated
> for us, so probability is the resort.
>
> When I flip a coin, the exact trajectory and spin I apply, plus
> outside forces like wind and magnetic fields determine whether it
> comes up heads or tails, not the laws of probability.
Same fallacious argument as last year. Statistics are used
to model the behavior of non-random events ALL THE TIME. Whether
an individual event is:
1. Completely random;
2. Non-random, but too complicated to predict a priori; or
3. Non-random and easy to predict a priori,
Statistics can still be used to model the behavior of a series
of trials as long as a p value can be ascertained.
And you make the common mistake of confusing what it is that
the statistics are modeling in the first place. It's not what
happens in one trial. It's the behavior of a large set of
trials.
(Rest snipped, as Ed's follow-up already addressed it.)
Last note: Why is it that those who dismiss statistics fail to
provide a cogent argument for why the world behaves exactly as
this supposedly invalid branch of mathematics says it should?
Larry Coon
University of California
la...@assist.org
and lmc...@home.com
The NBA Salary Cap FAQ:
http://members.cox.net/lmcoon/salarycap.htm
Florent Pessaud
illuminé :
>> A p = .03 means that there is only a 3% chance of this result
>> (ie the sequence above) being generated by chance alone. So
>> this is evidence of the hot-hand, right?
>>
>> Actually, this is the exception that proves the rule.
>
>I submit that it just shows the questionable scientific
>foundations of probability
You miss the logic behind maths there...
>When I flip a coin, the exact trajectory and spin I apply, plus
>outside forces like wind and magnetic fields determine whether it
>comes up heads or tails, not the laws of probability.
Both are true. The physical forces that you describe DO apply, and the
consequences of these variations are that flipping a coin do result in
an equal chance of getting either head or tails, with a 50/50
probability.
Probability doesn"t help you predict the next coin flip. In fact, it
does the opposite, since it *proves* that you cannot predict the next
coin flip.
Or, to get back to the basketball matter, the next shoot.
--
http://www.tunabox.net
Neil Cerutti
> Neil Cerutti wrote:
>
> I swore to myself I wasn't going to get involved in this
> conversation again, and cursed Ed for bringing it up one more
> time, excellent as his post was. But I just have to comment on
> this, which entirely misses the point.
>
>> I submit that it just shows the questionable scientific
>> foundations of probability.
>
> Probability isn't scientifically founded. It's mathematically
> founded. That's even better.
How is p ascertained mathematically in this case?
>> It can show the chance of something happening, but in reality
>> that thing is *not* determined by chance, as you have shown
>> below. The factors that go into determining if a shot is a hit
>> or a miss are just too complicated for us, so probability is
>> the resort.
>>
>> When I flip a coin, the exact trajectory and spin I apply, plus
>> outside forces like wind and magnetic fields determine whether it
>> comes up heads or tails, not the laws of probability.
>
> Same fallacious argument as last year.
Maybe my argument is wrong, weak, or ill-founded, but I hope it's
not fallacious.
> Statistics are used to model the behavior of non-random events
> ALL THE TIME. Whether an individual event is:
> 1. Completely random;
> 2. Non-random, but too complicated to predict a priori; or
> 3. Non-random and easy to predict a priori,
>
> Statistics can still be used to model the behavior of a series
> of trials as long as a p value can be ascertained.
>
> Last note: Why is it that those who dismiss statistics
I don't mean to dismiss them, certainly not in general. I just
don't believe the following claim has been demonstrated: If there
is a hot-hands effect, it will be detectable using probability
and statistics. Ed seems to understand where I'm coming from.
> fail to provide a cogent argument for why the world behaves
> exactly as this supposedly invalid branch of mathematics says
> it should?
Because it was designed to model those groups of actual events.
Nobody should be amazed, after following a recipe to bake
cookies, when cookies come out of the oven.
--
Neil Cerutti
Neil Cerutti
Here's an example: Computer scientists are experienced at
inventing forumulas that create a series of numbers that look
completely random from the perspective of probability, but in
reality are completely predictable. Shall probabilty be useful
for detecting whether an XOR function has been applied as part of
such a formula?
--
Neil Cerutti
Neil Cerutti
> Since we know that streaks can be generated by chance, and we
> know that people in general cannot tell whether a pattern
> exhibits streaks that are out of the ordinary, how can the
> blame for the illegal streak be blamed on Mr. Hot-Hand? The
> witnesses who say he is to blame are unreliable, and we already
> have another cause that has been shown to be a sufficient
> explanations of the streak: chance.
>
> Verdict: there is simply not enough evidence to convict
> Hot-Hand. This isn't to say he didn't do it -- it just means
> that he can't be held responsible when there's a more plausible
> explanation.
Thanks for the vignette. I agree completely, I've just been
emphasizing the "doesn't prove he didn't do it" part.
><snip>
>>
>>What about this one?
>>
>>>Barry M M H H H M H H M M M M H H M H H H H M M H H H H 15/10
I'm not sure "chance" as you define it, is at all eliminatable.
Personally, I would start by ruling out chance. There is no way
to detect hot-hand except by a painstaking and probably
impossible forumula which would involve all the factors that
truly contribute to a shot's chance to go in.
--
Neil Cerutti
Larry Coon
> How is p ascertained mathematically in this case?
Why should p be ascertained mathematically?
> I don't mean to dismiss them, certainly not in general. I just
> don't believe the following claim has been demonstrated: If there
> is a hot-hands effect, it will be detectable using probability
> and statistics. Ed seems to understand where I'm coming from.
I understand where you're coming from, too. That's why
I said your argument is fallacious.
> Because it was designed to model those groups of actual events.
> Nobody should be amazed, after following a recipe to bake
> cookies, when cookies come out of the oven.
Bingo, thanks for making my point for me.
We have a system that when given certain input (cookie
dough ingredients, a recipe for cookies and an oven) there
is a certain result we expect (cookies). You are absolutely
correct that we are NOT amazed when the result is cookies.
But when we give the same input (cookie dough ingredients,
a recipe for cookies and an oven) and beef wellington comes
out, we take notice.
This is the same thing we're talking about with shooting.
The stats are like the recipe -- with cookies, the recipe
says, "do this, and cookies will be the result." The stats
for shooting say, "with this shooting, 'this' should be the
result." The 'this' is the expected numbers of hits and
misses over a series of trials, and even the expected streaks
that will naturally occur. When the hits/misses and the
streaks are in accordance with what the stats would predict,
it's akin to getting cookies out of the oven.
We have very precise standards for what constitutes cookies
and what constitutes beef wellington in the shooting results.
And all we've ever gotten out of this oven is cookies.
I'm certainly not amazed by this fact -- reality is behaving
exactly like it should. But some people see the expected
result and think something else must be at play. As you say,
people aren't amazed when cookies come out of the oven. But
then why aren't they equally unimpressed when an equally
predictable result occurs from shooting?
Neil Cerutti
> Neil Cerutti wrote:
>
>> How is p ascertained mathematically in this case?
>
> Why should p be ascertained mathematically?
You said the basis of this inquiry was mathematical, not
scientific. I'm attempting to show that it is in this case based
on emprical observations, i.e., science, and not mathematics, as
you claim.
>> I don't mean to dismiss them, certainly not in general. I just
>> don't believe the following claim has been demonstrated: If
>> there is a hot-hands effect, it will be detectable using
>> probability and statistics. Ed seems to understand where I'm
>> coming from.
>
> I understand where you're coming from, too. That's why I said
> your argument is fallacious.
What's the fallacy in my argument?
>> Because it was designed to model those groups of actual
>> events. Nobody should be amazed, after following a recipe to
>> bake cookies, when cookies come out of the oven.
>
> Bingo, thanks for making my point for me.
>
> We have a system that when given certain input (cookie
> dough ingredients, a recipe for cookies and an oven) there
> is a certain result we expect (cookies). You are absolutely
> correct that we are NOT amazed when the result is cookies.
I *would* be amazed if you could deduce the amount of baking
powder in the cookie recipe from observing a cookie, though.
--
Neil Cerutti
igor eduardo kupfer
>In article <3E53BA...@assist.org>, Larry Coon wrote:
>> Neil Cerutti wrote:
>>
>>> How is p ascertained mathematically in this case?
>>
>> Why should p be ascertained mathematically?
>
>You said the basis of this inquiry was mathematical, not
>scientific. I'm attempting to show that it is in this case based
>on emprical observations, i.e., science, and not mathematics, as
>you claim.
>
I am not sure about the foundations of these statistical tests. It seems to me
that they would originally have been empirically based (ie founded upon a
large number of observations), and the theoretical mathematical justifications
came after. I don't think this is any different from any statistical test.
<snip>
>>
>> We have a system that when given certain input (cookie
>> dough ingredients, a recipe for cookies and an oven) there
>> is a certain result we expect (cookies). You are absolutely
>> correct that we are NOT amazed when the result is cookies.
>
>I *would* be amazed if you could deduce the amount of baking
>powder in the cookie recipe from observing a cookie, though.
I think Larry's point is that, given a cookie, you can probably deduce that it
came from a cookie recipe, and not a beef wellington recipe. I think.
Let's back up a little. We have a result: a cookie (ie a streak). We now try
to find out what caused this result. Mathematicians have developed a recipe
that generates cookie-like results, in exactly the same manner and with the
same frequency and properties as we observe see in reality. But others
postulate another cause: they say that some people can just generate cookies,
by just willing them to exist.
Now, both causes are consistent with the known observations of cookies. But
isn't the first cause, the recipe, more plausible?
Neil Cerutti
eduardo kupfer wrote:
> On 19 Feb 2003 18:06:17 GMT, Neil Cerutti <cer...@norwich.edu>
> wrote:
>
>>In article <3E53BA...@assist.org>, Larry Coon wrote:
>>> We have a system that when given certain input (cookie dough
>>> ingredients, a recipe for cookies and an oven) there is a
>>> certain result we expect (cookies). You are absolutely
>>> correct that we are NOT amazed when the result is cookies.
>>
>>I *would* be amazed if you could deduce the amount of baking
>>powder in the cookie recipe from observing a cookie, though.
>
>
> I think Larry's point is that, given a cookie, you can probably
> deduce that it came from a cookie recipe, and not a beef
> wellington recipe. I think.
It's a slightly different metaphor than I had in mind, but I
tried to run with it. ;-)
This is the metaphor, as I see it: You ate your first chocolate
chip cookie, and you thought it was delicious. So, through years
of research, trial and error, and mathematical calculations, you
have created a recipe that makes a cookie that is "exactly" like
the one you tasted earlier. You have created a virtually
identical cookie, though you still don't know the original
recipe.
> Let's back up a little. We have a result: a cookie (ie a
> streak). We now try to find out what caused this result.
> Mathematicians have developed a recipe that generates
> cookie-like results, in exactly the same manner and with the
> same frequency and properties as we observe see in reality. But
> others postulate another cause: they say that some people can
> just generate cookies, by just willing them to exist.
>
> Now, both causes are consistent with the known observations of
> cookies. But isn't the first cause, the recipe, more plausible?
When you put it like that, yes, but I'm just supposing there is a
different recipe, not spontaneous cookie generation. For example,
it could still be true that the earth is stationary and the rest
of the universe revolves around it. The reason we think otherwise
is due to the consequences of that theory, i.e.--most of the
stars would have to be moving faster than light--not because it
would contradict our observations.
What's so absurd about supposing there is a hot-hands effect?
What is the bad consequence?
This effect contributes to the chance of an individual shot going
in the basket. Moreover, this effect has been shown to be small
enough that, in N number of trials, hit and miss distrubutions
are close enough to a theoritically random distribution as to be
indistinguishable from it, especially as you increase N.
How great would the effect have to be to be "revealed" in a
statistical test? I think perhaps too great.
Here's a small simulation to test my theory:
The computer simulates 25 shots for two players. One player is
experiencing a hot-hands effect that gives him twice the chance
to make the basket after a made shot. The other player is a
strictly random distrubtion, arrived at by random shuffling the
previous player's results.
I'm using a P of 0.30 for the hot-hands player at the beginning
or after a miss, and a P of 0.60 after a hit. (I'm using H for
hit and - for miss since I think it's easier to read.)
Can you tell which is which using statistical analysis?
P = 45
- H - H H H - - - - - H - - - - H - H - H H - - - H H H H H - H - - H
- - - - - - - - - H H H H H - - - - - - - H - - - H H H H H H H H H H
P = 65
H H - H H - - - H H - H H - H H H H - H H - H H H H - H H - H - H H -
H - H - H H H H H H H H H - - H H H - H H - - - H H H H H H H - - - -
P = 60
- H - H H H - - H - H - H H H - H H - H - H H H H - H H H H - - - - H
- H H H H - - - - H H H H H H H H H H H - - - - - - - H - H H - H H H
P = 40
H - H H - - - H - - - H H - H H H - - - H - - - H - H - - H - - - H -
- - - - - H H H - - - - H H H - - - - - - - - - - H H - H H H H H H -
P = 65
- H H - - H H H H H H - - - H H - H H H H - H H H - - H H - H H H H -
- H H H H H - - H H H H - H - - - H H H H H H H - - H H H - H H H - -
P = 57
H - H H - - - H H - - H H H H H - - - H H H H - H H H - H H H - - - -
H - H - - - - H H H H - - H H - - H H - - - - H H H H H H H H H - H -
--
Neil Cerutti
igor eduardo kupfer
>>
<snip>
>What's so absurd about supposing there is a hot-hands effect?
>What is the bad consequence?
>
Well, nothing. The original concept wasn't really about basketball and streaks
-- it was three psychologists examining the question of why people perceive
streaks when none in fact exist.
That people can see patterns that aren't really there can hardly be debated.
This can have profound consequences in the course of our daily lives -- many
religious beliefs find justification in these types of false-patterns, for
example (most amusingly, the believer who finds Jesus's face in his breakfast
pastry).
Hot-hands, should they be a perceptual illusion, is merely a benign and
colourful illustration.
>This effect contributes to the chance of an individual shot going
>in the basket. Moreover, this effect has been shown to be small
>enough that, in N number of trials, hit and miss distrubutions
>are close enough to a theoritically random distribution as to be
>indistinguishable from it, especially as you increase N.
>
>How great would the effect have to be to be "revealed" in a
>statistical test? I think perhaps too great.
>
>Here's a small simulation to test my theory:
>
>The computer simulates 25 shots for two players. One player is
>experiencing a hot-hands effect that gives him twice the chance
>to make the basket after a made shot. The other player is a
>strictly random distrubtion, arrived at by random shuffling the
>previous player's results.
>
>I'm using a P of 0.30 for the hot-hands player at the beginning
>or after a miss, and a P of 0.60 after a hit. (I'm using H for
>hit and - for miss since I think it's easier to read.)
>
Shouldn't the players p decrease after a miss? I thought the hot-hand effect
was supposed to by symmetrical.
No matter. Let's give it a shot.
>Can you tell which is which using statistical analysis?
>
>P = 45
>- H - H H H - - - - - H - - - - H - H - H H - - - H H H H H - H - - H
>- - - - - - - - - H H H H H - - - - - - - H - - - H H H H H H H H H H
>
K = 0.5429
The observed number of runs = 24
The expected number of runs = 35.7429
38 Observations above K 32 below
The test is significant at 0.0044
Ding ding ding
>P = 65
>H H - H H - - - H H - H H - H H H H - H H - H H H H - H H - H - H H -
>H - H - H H H H H H H H H - - H H H - H H - - - H H H H H H H - - - -
>
K = 0.6571
The observed number of runs = 32
The expected number of runs = 32.5429
46 Observations above K 24 below
The test is significant at 0.8845
Cannot reject at alpha = 0.05
Nope.
>P = 60
>- H - H H H - - H - H - H H H - H H - H - H H H H - H H H H - - - - H
>- H H H H - - - - H H H H H H H H H H H - - - - - - - H - H H - H H H
K = 0.4000
The observed number of runs = 30
The expected number of runs = 34.6000
28 Observations above K 42 below
The test is significant at 0.2483
Cannot reject at alpha = 0.05
Nope.
>
>P = 40
>H - H H - - - H - - - H H - H H H - - - H - - - H - H - - H - - - H -
>- - - - - H H H - - - - H H H - - - - - - - - - - H H - H H H H H H -
>
K = 0.4000
The observed number of runs = 28
The expected number of runs = 34.6000
28 Observations above K 42 below
The test is significant at 0.0976
Cannot reject at alpha = 0.05
Hmmm. Suggestive...
>P = 65
>- H H - - H H H H H H - - - H H - H H H H - H H H - - H H - H H H H -
>- H H H H H - - H H H H - H - - - H H H H H H H - - H H H - H H H - -
>
K = 0.3429
The observed number of runs = 27
The expected number of runs = 32.5429
24 Observations above K 46 below
The test is significant at 0.1380
Cannot reject at alpha = 0.05
Nope.
>P = 57
>H - H H - - - H H - - H H H H H - - - H H H H - H H H - H H H - - - -
>H - H - - - - H H H H - - H H - - H H - - - - H H H H H H H H H - H -
K = 0.5714
The observed number of runs = 28
The expected number of runs = 35.2857
40 Observations above K 30 below
The test is significant at 0.0732
Cannot reject at alpha = 0.05
Another one suggestive of streakiness. Let's try the Fisher Exact test on the
two close ones:
TABLE = [ 14 , 14 , 13 , 28 ]
Left : p-value = 0.9623373177668904
Right : p-value = 0.10085814739854194 <====not really close
2-Tail : p-value = 0.1409798995027334
------------------------------------------
TABLE = [ 26 , 14 , 13 , 16 ]
Left : p-value = 0.9723699581374565
Right : p-value = 0.07742607593244435 <=====still close
2-Tail : p-value = 0.13987724719812228
------------------------------------------
So my conclusion would be, the first sequence is definitely streaky, the last
one is worthy of a deeper analysis, maybe some autocorrelation would pick up a
subtler pattern. The others are not streaky.
95% of the above paragraph will be true.
Larry Coon
I think your article two back in this thread hasn't shown
up on my server yet, so I'm replying out of order.
> > I think Larry's point is that, given a cookie, you can probably
> > deduce that it came from a cookie recipe, and not a beef
> > wellington recipe. I think.
>
> It's a slightly different metaphor than I had in mind, but I
> tried to run with it. ;-)
My point actually was that when you get exactly what you
expect to get, there's no need to go looking for alternative
causes. If you get what you DON'T expect to get, then there's
some evidence that something's going on which might indicate
another cause.
> This is the metaphor, as I see it: You ate your first chocolate
> chip cookie, and you thought it was delicious. So, through years
> of research, trial and error, and mathematical calculations, you
> have created a recipe that makes a cookie that is "exactly" like
> the one you tasted earlier. You have created a virtually
> identical cookie, though you still don't know the original
> recipe.
Yeah, the "as I see it" is why we're having this converstation.
That's NOT an appropriate metaphor.
> > Let's back up a little. We have a result: a cookie (ie a
> > streak). We now try to find out what caused this result.
> > Mathematicians have developed a recipe that generates
> > cookie-like results, in exactly the same manner and with the
> > same frequency and properties as we observe see in reality. But
> > others postulate another cause: they say that some people can
> > just generate cookies, by just willing them to exist.
> >
> > Now, both causes are consistent with the known observations of
> > cookies. But isn't the first cause, the recipe, more plausible?
>
> When you put it like that, yes, but I'm just supposing there is a
> different recipe, not spontaneous cookie generation. For example,
> it could still be true that the earth is stationary and the rest
> of the universe revolves around it. The reason we think otherwise
> is due to the consequences of that theory, i.e.--most of the
> stars would have to be moving faster than light--not because it
> would contradict our observations.
Given the laws of the universe as we know them, if some
phenomenon is behaving exactly as our understanding of the
universe would suggesst, then there's no reason to believe
that the universe is not behaving as we understand it. This
is true whether we are referring to physics or mathematics.
> What's so absurd about supposing there is a hot-hands effect?
> What is the bad consequence?
In the hot hand itself? Nothing really, unless you really want
to understand what's going on. Of course, the same could be said
of the Easter Bunny theory, the Santa Claus theory and the Tooth
Fairy theory. I suppose there's no real harm in believing any of
them.
But extending the same general principles to things like medicine,
the same attitude can lead to the gullible acceptance of quack
medicine with real damage caused in the loss of money and health.
> This effect contributes to the chance of an individual shot going
> in the basket. Moreover, this effect has been shown to be small
> enough that, in N number of trials, hit and miss distrubutions
> are close enough to a theoritically random distribution as to be
> indistinguishable from it, especially as you increase N.
So you're saying that there's an effect which is indistinguishable
from no effect at all. I see. It's less pronounced with more
trials, which I suppose means it's more pronounced with fewer
trials. But statistics itself shows that results are more valid
with greater numbers of trials, so again, it's still
indistinguishable from no effect at all. Again, I see.
This is an inalid test -- it demonstrates nothing which is asserted.
Let me take another crack at this....I'll use your definitions, where
p=.3 always (base case), or p=.3 after a miss and p=.6 after a make (hot
hand case), with 25-trial runs. Here are a few runs for the base case:
-----H--HHH----H---H--H-H (8 hits, 2 hit-hit)
HH----HH----H----H--H---H (8 hits, 2 hit-hit)
-----H----H--H--H-H-H-H-- (7 hits, 0 hit-hit)
------H------H------HH-HH (6 hits, 2 hit-hit)
---H-H--H----H--HHH---H-- (8 hits, 2 hit-hit)
-H----H---H----H---HHHHHH (10 hits, 5 hit-hit)
-H-H-H------H------HH-H-H (8 hits, 1 hit-hit)
----H-H---H----H--H-HH--- (7 hits, 1 hit-hit)
-H-HH-HH----HH----H--H--- (9 hits, 3 hit-hit)
--H----H----HHH------HH-H (8 hits, 3 hit-hit)
And here are a few runs for the hot-hand case:
---H-HHHHH-HH----------HH (10 hits, 6 hit-hit)
---HH--HH--HHHHHHH---HH-H (14 hits, 9 hit-hit)
H-HH--H-H----H--H-H--HH-H (11 hits, 2 hit-hit)
--HHH---HHHHHH--H---HH--- (12 hits, 8 hit-hit)
-H-----H-------H--------- (3 hits, 0 hit-hit)
----HH--HHHH-H----HH--H-- (10 hits, 5 hit-hit)
--HHH-H---------------HHH (7 hits, 4 hit-hit)
-H-----H-----HH-H---HH--H (8 hits, 2 hit-hit)
---HHH-H-H---HHHH-------- (9 hits, 5 hit-hit)
-HH----HHH-----H--HHHH--- (10 hits, 6 hit-hit)
Okay, now -- statistics can tell us all of the following for a
regular binomial test (where the results do not affect each other):
-- How many hits to expect, on average.
-- How many runs of N hits to expect, given a number of runs,
where N = [0..number of trials].
-- How many hit-hit combinations to expect per run (or hit-hit-
hit, or whatever).
-- How the hit-hit combinations distrubute over a given number of
runs.
-- The size of the expected streaks.
-- The distribution of the largest steaks over a given number of
runs.
-- etc.
The first set of runs is entirely due to chance (or as close to
chance as it gets with Java's random() function) because I programmed
it that way. The second set of runs is chance + hot-hand, again,
because I programmed it that way.
So we look at actual results, and we find that they look a lot more
like the first case than the second case. In fact, that laundry
list of things stats could tell us? Reality behaves exactly like
the stats say they should. It's not that there are no streaks, it's
that reality behaves exactly as we predict it should in the absence
of any additional effect.
If, on the other hand, reality consistently looked like the second
set of trials above, then it's the equivalent of getting beef
wellington from a cookie recipe -- we'd better double-check that
recipe, because it may not be the one we were actually working with.
(source code for the above sets of trials below, in case you
really want to follow along)
// NoHotHand.java
// Program to simulate a binomial result, no hot hand assumed.
public class NoHotHand {
public static void main(String args[]) {
final int numberOfRuns = 10;
final int numberOfTrials = 25;
final double p = 0.3;
for (int i = 0; i < numberOfRuns; i++) {
int hits = 0;
int hitHit = 0;
boolean justHadAHit = false;
for (int j = 0; j < numberOfTrials; j++)
if (Math.random() < p) {
System.out.print("H");
hits++;
if (justHadAHit == true) hitHit++;
justHadAHit = true;
}
else {
System.out.print("-");
justHadAHit = false;
}
System.out.print(" (" + hits + " hits,");
System.out.println(" " + hitHit + " hit-hit)");
}
System.exit(0);
}
}
------------------------------------------------------
// HotHand.java
// Program to simulate a binomial result, with hot hand effect.
public class NoHotHand {
public static void main(String args[]) {
final int numberOfRuns = 10;
final int numberOfTrials = 25;
final double p = 0.3;
final double pHotHand = 0.6;
for (int i = 0; i < numberOfRuns; i++) {
int hits = 0;
int hitHit = 0;
boolean justHadAHit = false;
for (int j = 0; j < numberOfTrials; j++)
if (Math.random() < (justHadAHit == true ? pHotHand : p)) {
System.out.print("H");
hits++;
if (justHadAHit == true) hitHit++;
justHadAHit = true;
}
else {
System.out.print("-");
justHadAHit = false;
}
System.out.print(" (" + hits + " hits,");
System.out.println(" " + hitHit + " hit-hit)");
}
System.exit(0);
Neil Cerutti
> phenomenon is behaving exactly as our understanding of the
> universe would suggesst, then there's no reason to believe that
> the universe is not behaving as we understand it. This is true
> whether we are referring to physics or mathematics.
So random number generators in a computer... these things create
real randomness, and that is "proved" by not being able to
distinguish it from an actual random event?
>> What's so absurd about supposing there is a hot-hands effect?
>> What is the bad consequence?
>
> In the hot hand itself? Nothing really, unless you really want
> to understand what's going on. Of course, the same could be
> said of the Easter Bunny theory, the Santa Claus theory and the
> Tooth Fairy theory. I suppose there's no real harm in
> believing any of them.
No, in the Santa Claus theory, there would have to be flying
reindeer, and he would have to die when he travelled that fast
(I'm sure you've heard the joke). As for the Easter Bunny, well,
that theory has never really been fleshed out.
> But extending the same general principles to things like
> medicine, the same attitude can lead to the gullible acceptance
> of quack medicine with real damage caused in the loss of money
> and health.
So I could do studies of death rates, and if they resemble a
random distribution, then there's nothing more to worry about?
Well, people just die randomly. There must be no disease!
>> This effect contributes to the chance of an individual shot
>> going in the basket. Moreover, this effect has been shown to
>> be small enough that, in N number of trials, hit and miss
>> distrubutions are close enough to a theoritically random
>> distribution as to be indistinguishable from it, especially as
>> you increase N.
>
> So you're saying that there's an effect which is
> indistinguishable from no effect at all. I see.
Well, stuff some clothes with straw and smack it 'round, why
don't you? I'm saying there is an affect which can't be detected
using the methods we're discussing. Your assertion merely begs
the question.
> It's less pronounced with more trials, which I suppose means
> it's more pronounced with fewer trials. But statistics itself
> shows that results are more valid with greater numbers of
> trials, so again, it's still indistinguishable from no effect
> at all. Again, I see.
>
>> How great would the effect have to be to be "revealed" in a
>> statistical test? I think perhaps too great.
>>
>> Here's a small simulation to test my theory:
>>
>> The computer simulates 25 shots for two players. One player is
>> experiencing a hot-hands effect that gives him twice the chance
>> to make the basket after a made shot. The other player is a
>> strictly random distrubtion, arrived at by random shuffling the
>> previous player's results.
>>
>> I'm using a P of 0.30 for the hot-hands player at the beginning
>> or after a miss, and a P of 0.60 after a hit. (I'm using H for
>> hit and - for miss since I think it's easier to read.)
>>
>> Can you tell which is which using statistical analysis?
>>
>> P = 45
>> - H - H H H - - - - - H - - - - H - H - H H - - - H H H H H - H - - H
>> - - - - - - - - - H H H H H - - - - - - - H - - - H H H H H H H H H H
>
> This is an inalid test -- it demonstrates nothing which is
> asserted.
I'm asserting that you cannot show that the hot-hand may exist in
one trial, but probably doesn't exist with much certainty. I've
also posited a ridiculously strong hot-hands effect which
*should* be very easy to spot, in order to have a control. The
idea would be to keep lowering the effect until it becomes
"impossible" to detect.
> Let me take another crack at this....I'll use your definitions,
> where p=.3 always (base case),
That is not right way to do it. Any test should use trials with
an equal p, since the analysis starts from there.
--
Neil Cerutti
Neil Cerutti
eduardo kupfer wrote:
> On 19 Feb 2003 21:22:57 GMT, Neil Cerutti <cer...@norwich.edu>
> wrote:
> Hot-hands, should they be a perceptual illusion, is merely a
> benign and colourful illustration.
>
>>This effect contributes to the chance of an individual shot
>>going in the basket. Moreover, this effect has been shown to be
>>small enough that, in N number of trials, hit and miss
>>distrubutions are close enough to a theoritically random
>>distribution as to be indistinguishable from it, especially as
>>you increase N.
>>
>>How great would the effect have to be to be "revealed" in a
>>statistical test? I think perhaps too great.
>>
>>Here's a small simulation to test my theory:
>>
>>The computer simulates 25 shots for two players. One player is
>>experiencing a hot-hands effect that gives him twice the chance
>>to make the basket after a made shot. The other player is a
>>strictly random distrubtion, arrived at by random shuffling the
>>previous player's results.
>>
>>I'm using a P of 0.30 for the hot-hands player at the beginning
>>or after a miss, and a P of 0.60 after a hit. (I'm using H for
>>hit and - for miss since I think it's easier to read.)
>>
>
> Shouldn't the players p decrease after a miss? I thought the
> hot-hand effect was supposed to by symmetrical.
Well, you can look at it that way if you want, but this was
simpler to code, and has the same effect as a .45 first shot, .30
after and miss and .60 after a hit--only the first shot's p would
be affected by the more complicated model.
> No matter. Let's give it a shot.
>
>>Can you tell which is which using statistical analysis?
>>
>>P = 45
>>- H - H H H - - - - - H - - - - H - H - H H - - - H H H H H - H - - H
>>- - - - - - - - - H H H H H - - - - - - - H - - - H H H H H H H H H H
>>
>
> K = 0.5429
> The observed number of runs = 24
> The expected number of runs = 35.7429
> 38 Observations above K 32 below
> The test is significant at 0.0044
>
>
> Ding ding ding
I didn't explain well enough. The above is two different trials,
one hot-hand and the other that same trial randomly scrambled.
--
Neil Cerutti
timmy boumtje
>> No matter. Let's give it a shot.
>>
>>>Can you tell which is which using statistical analysis?
>>>
>>>P = 45
>>>- H - H H H - - - - - H - - - - H - H - H H - - - H H H H H - H - - H
>>>- - - - - - - - - H H H H H - - - - - - - H - - - H H H H H H H H H H
>>>
>>
>> K = 0.5429
>> The observed number of runs = 24
>> The expected number of runs = 35.7429
>> 38 Observations above K 32 below
>> The test is significant at 0.0044
>>
>>
>> Ding ding ding
>
>I didn't explain well enough. The above is two different trials,
>one hot-hand and the other that same trial randomly scrambled.
by making the non-hot hand simulation dependent on the hot-hand sim,
aren't you making it meaningless...or did i misunderstand?
if i got it right, you figured the non-hot hand's chance of making a
shot based on the hot-hand's results
is that realistic?
and anyway...can a computer sim recreate a real hot-hand situation?
do you play basketball? haven't you ever got in the zone? there are
times when the ball just feels right coming out of your hand on every
shot....and other times when it doesn't
to me..if a guy is hitting almost every shot he puts up, he's got a
hot-hand....there's no need to analyse it
mr.tim
----------------------------
rmhiphop.tripod.com
the rec.music.hiphop website
----------------------------
now ask yourself who's the one with the most to gain (BUSH!)
'fore 9-11 motherfuckers couldn't stand his name (BUSH!)
-paris
Neil Cerutti
boumtje wrote:
> On 20 Feb 2003 13:36:12 GMT, Neil Cerutti <cer...@norwich.edu>
> wrote:
>>> No matter. Let's give it a shot.
>>>
>>>>Can you tell which is which using statistical analysis?
>>>>
>>>>P = 45
>>>>- H - H H H - - - - - H - - - - H - H - H H - - - H H H H H - H - - H
>>>>- - - - - - - - - H H H H H - - - - - - - H - - - H H H H H H H H H H
>>>>
>>>
>>> K = 0.5429
>>> The observed number of runs = 24
>>> The expected number of runs = 35.7429
>>> 38 Observations above K 32 below
>>> The test is significant at 0.0044
>>>
>>>
>>> Ding ding ding
>>
>>I didn't explain well enough. The above is two different
>>trials, one hot-hand and the other that same trial randomly
>>scrambled.
>
> by making the non-hot hand simulation dependent on the hot-hand
> sim, aren't you making it meaningless...or did i misunderstand?
>
> if i got it right, you figured the non-hot hand's chance of
> making a shot based on the hot-hand's results
>
> is that realistic?
For my purposes, it is. I'm asking: What is the detectable
difference between a hot-hands shooter and a more random shooter
when they have an equal P?
> and anyway...can a computer sim recreate a real hot-hand
> situation?
>
> do you play basketball? haven't you ever got in the zone? there
> are times when the ball just feels right coming out of your
> hand on every shot....and other times when it doesn't
>
> to me..if a guy is hitting almost every shot he puts up, he's
> got a hot-hand....there's no need to analyse it
Yes, but he still doesn't normally hit more shots in a row than
you can expect. That's what's under discussion.
--
Neil Cerutti
timmy boumtje
>> if i got it right, you figured the non-hot hand's chance of
>> making a shot based on the hot-hand's results
>>
>> is that realistic?
>
>For my purposes, it is. I'm asking: What is the detectable
>difference between a hot-hands shooter and a more random shooter
>when they have an equal P?
have you thought about streak shooters and how they fit in?
2 guys can have similar % but not have the same shooting
patterns...doesn't that prove the existence of the "hot hand" (a guy
going 8 for 9 one night and 0 for 7 the next as opposed to a player
who shoots about 5 for 10 every night)?
sorry, i haven't read the whole thread so i shouldn't be jumping in
now but i'm bored and lazy
>> to me..if a guy is hitting almost every shot he puts up, he's
>> got a hot-hand....there's no need to analyse it
>
>Yes, but he still doesn't normally hit more shots in a row than
>you can expect. That's what's under discussion.
but what do you 'expect'? if someone hits 4 three pointers in a row, i
don't think that's expected of anyone....i just don't get how the
existence of the hot hand can even be in question....
maybe it isn't and i've totally missed the point
Isaac
> have you thought about streak shooters and how they fit in?
>
> 2 guys can have similar % but not have the same shooting
> patterns...doesn't that prove the existence of the "hot hand" (a guy
> going 8 for 9 one night and 0 for 7 the next as opposed to a player
> who shoots about 5 for 10 every night)?
This is exactly the phenomenon being debated. It turns out that
there neither such player (the streaky one nor the consistent
5 for 10 one) exists. All 50 per cent shooters seem to have the
mix of 8 for 9s and 0 for 7s that are predicted by chance.
Isaac
timmy boumtje
oh...i hereby promise not to post in threads that i haven't followed
all the way through..especially when drinking
but doesn't that still mean that the hot hand most likely exists?
sometimes a guy is on and sometimes he's off...oh no, right...i'm
being quiet..sorry....but, no....isn't this more easily answered
through experience than statistics?...sometimes you can't miss...you
can just feel that hot hand...i mean, i love analysing stats but...
Neil Cerutti
boumtje wrote:
> but doesn't that still mean that the hot hand most likely
> exists? sometimes a guy is on and sometimes he's off...oh no,
> right...i'm being quiet..sorry....but, no....isn't this more
> easily answered through experience than statistics?...sometimes
> you can't miss...you can just feel that hot hand...i mean, i
> love analysing stats but...
The analysis says nothing about what causes the streaks, it
merely shows that their properties are consistent with those
generated by a series of random events. So a model of shooting
that views it is "as if" it were totally random, will be quite
realistic (notwithstanding EA Sports': "He's on Fire!").
There used to be totally accurate models of the solar system that
were based on circular orbits, too. ;-)
--
Neil Cerutti
timmy boumtje
>In article <jqr95vk5a4mdkm1k2...@4ax.com>, timmy
>boumtje wrote:
>> but doesn't that still mean that the hot hand most likely
>> exists? sometimes a guy is on and sometimes he's off...oh no,
>> right...i'm being quiet..sorry....but, no....isn't this more
>> easily answered through experience than statistics?...sometimes
>> you can't miss...you can just feel that hot hand...i mean, i
>> love analysing stats but...
>
>The analysis says nothing about what causes the streaks, it
>merely shows that their properties are consistent with those
>generated by a series of random events. So a model of shooting
>that views it is "as if" it were totally random, will be quite
>realistic (notwithstanding EA Sports': "He's on Fire!").
alright...i think i get it....but if i get it, i don't actually get
why you're even bothering to talk about it.... :(
>There used to be totally accurate models of the solar system that
>were based on circular orbits, too. ;-)
how about someone create an accurate model to predict how many beers i
will drink next week....i can provide past stats if you give me enough
time to count the bottles outside
Neil Cerutti
boumtje wrote:
> On 20 Feb 2003 15:19:00 GMT, Neil Cerutti <cer...@norwich.edu>
> wrote:
>>In article <jqr95vk5a4mdkm1k2...@4ax.com>, timmy
>>boumtje wrote:
>>> but doesn't that still mean that the hot hand most likely
>>> exists? sometimes a guy is on and sometimes he's off...oh no,
>>> right...i'm being quiet..sorry....but, no....isn't this more
>>> easily answered through experience than
>>> statistics?...sometimes you can't miss...you can just feel
>>> that hot hand...i mean, i love analysing stats but...
>>
>>The analysis says nothing about what causes the streaks, it
>>merely shows that their properties are consistent with those
>>generated by a series of random events. So a model of shooting
>>that views it is "as if" it were totally random, will be quite
>>realistic (notwithstanding EA Sports': "He's on Fire!").
>
> alright...i think i get it....but if i get it, i don't actually
> get why you're even bothering to talk about it.... :(
In my case, it's because I've got a head filled with twaddle and
nonsense. I don't know about the rest of the participants.
>>There used to be totally accurate models of the solar system
>>that were based on circular orbits, too. ;-)
>
> how about someone create an accurate model to predict how many
> beers i will drink next week....i can provide past stats if you
> give me enough time to count the bottles outside
That would be off-topic. But if it's really cold outside, it
might be funny to make you count up the bottles. ;-)
--
Neil Cerutti
timmy boumtje
>> alright...i think i get it....but if i get it, i don't actually
>> get why you're even bothering to talk about it.... :(
>
>In my case, it's because I've got a head filled with twaddle and
>nonsense. I don't know about the rest of the participants.
ah..good a reason as any...i just wish there was a newsgroup called
rec.students.percentagechancethey'regonnafail.....i'd dominate that
>>>There used to be totally accurate models of the solar system
>>>that were based on circular orbits, too. ;-)
>>
>> how about someone create an accurate model to predict how many
>> beers i will drink next week....i can provide past stats if you
>> give me enough time to count the bottles outside
>
>That would be off-topic. But if it's really cold outside, it
>might be funny to make you count up the bottles. ;-)
i'm in thailand...not too cold...counting the bottles is funny, but
not haha funny
igor eduardo kupfer
wrote:
>On Thu, 20 Feb 2003 14:51:43 GMT, Isaac
><is...@latveria.castledoom.org> wrote:
>
>>On Thu, 20 Feb 2003 21:31:16 +0700, timmy boumtje <timo...@hotmail.com> wrote:
>>> have you thought about streak shooters and how they fit in?
>>>
>>> 2 guys can have similar % but not have the same shooting
>>> patterns...doesn't that prove the existence of the "hot hand" (a guy
>>> going 8 for 9 one night and 0 for 7 the next as opposed to a player
>>> who shoots about 5 for 10 every night)?
>>
>>This is exactly the phenomenon being debated. It turns out that
>>there neither such player (the streaky one nor the consistent
>>5 for 10 one) exists. All 50 per cent shooters seem to have the
>>mix of 8 for 9s and 0 for 7s that are predicted by chance.
>
>oh...i hereby promise not to post in threads that i haven't followed
>all the way through..especially when drinking
>
At 10am?
>but doesn't that still mean that the hot hand most likely exists?
>sometimes a guy is on and sometimes he's off...oh no, right...i'm
>being quiet..sorry....but, no....isn't this more easily answered
>through experience than statistics?...sometimes you can't miss...you
>can just feel that hot hand...i mean, i love analysing stats but...
>
There are mathematical procedures for detecting streaks of excessive length,
and procedures for detecting an excessive number of runs within a sequence.
Neil is questioning the ability of these procedures to detect the runs.
timmy boumtje
<igork...@example.com> wrote:
>>oh...i hereby promise not to post in threads that i haven't followed
>>all the way through..especially when drinking
>>
>
>At 10am?
i'm in a different timezone...it's now 11.27pm
>>but doesn't that still mean that the hot hand most likely exists?
>>sometimes a guy is on and sometimes he's off...oh no, right...i'm
>>being quiet..sorry....but, no....isn't this more easily answered
>>through experience than statistics?...sometimes you can't miss...you
>>can just feel that hot hand...i mean, i love analysing stats but...
>>
>
>
>There are mathematical procedures for detecting streaks of excessive length,
>and procedures for detecting an excessive number of runs within a sequence.
>Neil is questioning the ability of these procedures to detect the runs.
alright....but i think mathematical procedures can't explain the
feeling of being in the zone....maybe he can prove me wrong but i'm
not sure he's even trying to do that...my effective IQ is now 93...if
you'd like an intelligent comment please wait until about 3:00 pm my
time tomorrow, which is about 3:00am on the east coast of the US...but
until then i'd like to demonstrate how we do things here in southern
thailand...
jaaah, ja jing ja, ja jing ja, ja jing ja
jaaah, ja jing ja, ja jing ja, ja jing ja
peace
igor eduardo kupfer
>>>Can you tell which is which using statistical analysis?
>>>
>>>P = 45
>>>- H - H H H - - - - - H - - - - H - H - H H - - - H H H H H - H - - H
>>>- - - - - - - - - H H H H H - - - - - - - H - - - H H H H H H H H H H
>>>
>>
>> K = 0.5429
>> The observed number of runs = 24
>> The expected number of runs = 35.7429
>> 38 Observations above K 32 below
>> The test is significant at 0.0044
>>
>>
>> Ding ding ding
>
>I didn't explain well enough. The above is two different trials,
>one hot-hand and the other that same trial randomly scrambled.
Those are two trials? I thought it was one, wrapped. I get it now. Here we go:
P = 45
1A - H - H H H - - - - - H - - - - H - H - H H - - - H H H H H - H - - H
1B - - - - - - - - - H H H H H - - - - - - - H - - - H H H H H H H H H H <---
1A
K = 0.4571
The observed number of runs = 18
The expected number of runs = 18.3714
16 Observations above K 19 below
The test is significant at 0.8978
Cannot reject at alpha = 0.05
1B
K = 0.4571
The observed number of runs = 6
The expected number of runs = 18.3714
16 Observations above K 19 below
The test is significant at 0.0000
P = 65
2A H H - H H - - - H H - H H - H H H H - H H - H H H H - H H - H - H H -
2B H - H - H H H H H H H H H - - H H H - H H - - - H H H H H H H - - - - <---
2A
K = 0.6571
The observed number of runs = 20
The expected number of runs = 16.7714
23 Observations above K 12 below
The test is significant at 0.2174
Cannot reject at alpha = 0.05
2B
K = 0.6571
The observed number of runs = 12
The expected number of runs = 16.7714
23 Observations above K 12 below
The test is significant at 0.0683 <---pretty close, eh?
Cannot reject at alpha = 0.05
P = 60
3A - H - H H H - - H - H - H H H - H H - H - H H H H - H H H H - - - - H
3B - H H H H - - - - H H H H H H H H H H H - - - - - - - H - H H - H H H <---
3A
K = 0.6000
The observed number of runs = 20
The expected number of runs = 17.8000
21 Observations above K 14 below
The test is significant at 0.4311
Cannot reject at alpha = 0.05
3B
K = 0.6000
The observed number of runs = 10
The expected number of runs = 17.8000
21 Observations above K 14 below
The test is significant at 0.0052
P = 40
4A H - H H - - - H - - - H H - H H H - - - H - - - H - H - - H - - - H -
4B - - - - - H H H - - - - H H H - - - - - - - - - - H H - H H H H H H - <---
4A
K = 0.4000
The observed number of runs = 20
The expected number of runs = 17.8000
14 Observations above K 21 below
The test is significant at 0.4311
Cannot reject at alpha = 0.05
4B
K = 0.4000
The observed number of runs = 9
The expected number of runs = 17.8000
14 Observations above K 21 below
The test is significant at 0.0016
P = 65
5A - H H - - H H H H H H - - - H H - H H H H - H H H - - H H - H H H H -
5B - H H H H H - - H H H H - H - - - H H H H H H H - - H H H - H H H - - <---
5A
K = 0.6571
The observed number of runs = 15
The expected number of runs = 16.7714
23 Observations above K 12 below
The test is significant at 0.4986
Cannot reject at alpha = 0.05
5B
K = 0.6571
The observed number of runs = 13
The expected number of runs = 16.7714
23 Observations above K 12 below
The test is significant at 0.1496 <---
Cannot reject at alpha = 0.05
Nothing significant. But since I know, a priori, that one streak _must_ be
caused by a hot hand, I'll choose the one with the lowest p value. This is why
this test doesn't mimic reality very well -- the existence of the hot-hand is
the very thing that's being debated.
P = 57
6A H - H H - - - H H - - H H H H H - - - H H H H - H H H - H H H - - - -
6B H - H - - - - H H H H - - H H - - H H - - - - H H H H H H H H H - H
6A
K = 0.5714
The observed number of runs = 14
The expected number of runs = 18.1429
20 Observations above K 15 below
The test is significant at 0.1465
Cannot reject at alpha = 0.05
6B
K = 0.5714
The observed number of runs = 14
The expected number of runs = 18.1429
20 Observations above K 15 below
The test is significant at 0.1465
Cannot reject at alpha = 0.05
Other tests also gave similar p values for both. As far as I can tell, both of
these runs are equally likely.
igor eduardo kupfer
wrote:
>On Thu, 20 Feb 2003 11:23:16 -0500, igor eduardo kupfer
><igork...@example.com> wrote:
>
>
>>>oh...i hereby promise not to post in threads that i haven't followed
>>>all the way through..especially when drinking
>>>
<snip>
>>There are mathematical procedures for detecting streaks of excessive length,
>>and procedures for detecting an excessive number of runs within a sequence.
>>Neil is questioning the ability of these procedures to detect the runs.
>
>alright....but i think mathematical procedures can't explain the
>feeling of being in the zone....maybe he can prove me wrong but i'm
>not sure he's even trying to do that...
Nobody doubts the _feeling_ of the hot-hand, what I doubt is that this feeling
affects your shooting in any way. In fact, I think the feeling comes *after*
the shooting: first you shoot five in a row, then you think, "Hey, I got the
hot hand." Not: "Hey, I think I have a hot-hand," and then you go out and hit
five in a row.
my effective IQ is now 93...if
>you'd like an intelligent comment please wait until about 3:00 pm my
>time tomorrow, which is about 3:00am on the east coast of the US...but
>until then i'd like to demonstrate how we do things here in southern
>thailand...
>
>jaaah, ja jing ja, ja jing ja, ja jing ja
>jaaah, ja jing ja, ja jing ja, ja jing ja
>
We do things a little different in Toronto. Allow me to demonstrate:
duh da da da duh DA duh, da da dadada da da duh duh da duh DA duuuuuhhhhh
Hey, hey, mama, said the way you move gonna make you sweat, gonna make you
groove
duh da da da duh DA duh, duh da da da duh DA duh, duh da da da duh DA duh, duh
da da da duh DA duh
duh da da da duh DA duh, da da dadada da da duh duh da duh DA duuuuuhhhhh
Larry Coon
> have you thought about streak shooters and how they fit in?
>
> 2 guys can have similar % but not have the same shooting
> patterns...doesn't that prove the existence of the "hot hand" (a guy
> going 8 for 9 one night and 0 for 7 the next as opposed to a player
> who shoots about 5 for 10 every night)?
>
> sorry, i haven't read the whole thread so i shouldn't be jumping in
> now but i'm bored and lazy
Also, it's tough to follow the thread because it's been
going on, off-and-on, for a year. After it dies out,
someone either brings up an asinine argument a few months
later, or someone like Ed brings up some cogent additional
information, as happened here.
You brought up a couple of points that have been discussed
to death, however:
-- About the shooter "feeling it." Hard to differentiate
cause & effect, is one discussion point.
-- About steak shooters.
-- About what you'd "expect," as you say below.
If you really want to read more about it, here is some of
the previous discussion. Sorry about the long links. To
quote Blaise Pascal, I lack the time to make them short.
> but what do you 'expect'? if someone hits 4 three pointers in a row, i
> don't think that's expected of anyone....i just don't get how the
> existence of the hot hand can even be in question....
This is fully discussed in the above threads as well, but here's a
quickie:
-- The three point FG% league-wide is 34.87% right now, if the
"average player" takes a three-point shot, he'll have a 34.87%
chance of making it.
-- Two shots made in a row is 0.3487^2, or about 12.16%. In about
12.16% of the two-shot sequences league-wide, you'd expect
make-make.
-- Likewise, three shots made in a row is 0.3487^3, or about 4.24%.
-- And four in a row is 0.3487^4, or about 1.48%.
So just by chance alone, you'd expect about 1.48% of the four-shot
sequences (or about one out of every 68) to be make-make-make-make.
This is without any hot hand. This is without any intra-shot
influence. This is just pure, random chance. How many four-shot
sequences have occurred in the league so far this season?
If we look at the actual four-shot sequences in the league so far,
and we find that about one out of every 68 indeed is four makes in
a row, do we need to invent any additional phenomenon that's
already explained entirely by probability?
Think about human nature:
1. The human brain is naturally pattern-finding. All sorts of
studies show that people will find patterns in things where
none exist.
2. People tend to remember the hits and quickly forget about
the misses.
3. It's easy to confuse correlation with causation.
Is it any wonder then, that people have invented the hot hand to
explain something which naturally occurs anyway?
Neil Cerutti
eduardo kupfer wrote:
> On 20 Feb 2003 13:36:12 GMT, Neil Cerutti <cer...@norwich.edu>
> wrote:
>
>>>>Can you tell which is which using statistical analysis?
> now. Here we go:
Cool.
> 1A 0.8978
> 1B 0.0000
>
> 2A 0.2174
> 2B 0.0683 <---pretty close, eh?
>
> 3A 0.4311
> 3B 0.0052
>
> 4A 0.4311
> 4B 0.0016
>
> 5A 0.4986
> 5B 0.1496 <---
>
> Nothing significant. But since I know, a priori, that one
> streak _must_ be caused by a hot hand, I'll choose the one with
> the lowest p value. This is why this test doesn't mimic reality
> very well -- the existence of the hot-hand is the very thing
> that's being debated.
I wanted to see how accurate it was at recognizing a powerful
hot-hands effect. It turns out it was extremely good, with only
one case that was too close to call, and in that case, the random
distribution was an unlikely one.
In further trials, lowering the effect to +0.10 could generate
quite likely results, but not at huge trial sizes calculated with
Chi-squared. I had to lower it all the way to +0.05 to get
distributions whose likelyhood was on the map.
--
Neil Cerutti
igor eduardo kupfer
<snip>
>I wanted to see how accurate it was at recognizing a powerful
>hot-hands effect. It turns out it was extremely good, with only
>one case that was too close to call, and in that case, the random
>distribution was an unlikely one.
>
>In further trials, lowering the effect to +0.10 could generate
>quite likely results, but not at huge trial sizes calculated with
>Chi-squared. I had to lower it all the way to +0.05 to get
>distributions whose likelyhood was on the map.
I wonder which is easier: detecting streaks within a long series of trials, or
within many series of shorter trials. I guess it depends on the definition of
"easy."
I just ran a bunch of sims and the runs test, using a weaker hot-hand effect
of +/- 0.1 with the first p = .3 [so that p(hit | hit) = .4, and
p(hit | miss) = .2]. The Runs test detected hot-hands in 2504 of the 10000
simulations, roughly 1/4. With the hot-hand effect removed, hot-hands were
detected in 571 of 10000 simulations, about 5% -- my alpha level.
I'm pretty confident that should someone display a hot-hand consistently, the
Runs Test should be able to find it. It will have to take a good number of
trials, though.
(I wish I knew some programming, though. I had to do these sims
semi-manually.)
BTW good luck with Blount -- I always liked the guy. But I hope that doesn't
mean Battie's seriously hurt.