"This is a question that many statisticians, basketball players, and fans have debated upon."
You don't need (or want) the "upon" at the end of this sentence.  

The last two sentences of your introduction are somewhat repetitive:
"Most statisticians, however, have gathered evidence from studies of games, and based on
this data, they confidently argue against the idea of a hot hand existing.  Despite what players 
and fans of the game think is true, many statisticians argue that there is no mathematical 
evidence that the phenomenon is true."  Suggestion for a revised version:  "However, on the 
basis of evidence data gathered from studies of games, many statisticians argue that there
is no evidence that the ``hot hand'' is a true phenomenon."  (You have made the point that
fans and players think differently in the sentence(s) before yours.)

It would be good to number the items in your list of references.  Then when you want
to cite one of them include something like [1] in the text.

"The statisticians claim that fans are misinterpreting shot one, labeled as one event, 
to be dependent of a second shot, labeled as event two, and so on."  This needs some polishing.
Most importantly, say the second shot is *dependent on* the first, not the first shot is 
"dependent of" the second.

In your discussion of the GVT article, make it clear that they conducted several different
studies on their main question and reported the results in that one article.  

Make sure you can fit all of the columns in the table from GVT on your page.  If necessary, 
it would be OK to put it in "landscape format" by itself on a single page of your paper.
If you did that, you could also enlarge the table slightly to make it more readable.

It would be good to comment on the format of the table and the meanings of the numbers
in each column BEFORE getting into a discussion of the hypothesis test they performed
with the autocorrelation (r = serial correlation) value.  

I see you used some plots from the Maple worksheet on correlation I prepared for the 
class.  But those are actually not that relevant here because of they way they were
generated from given bivariate normal distributions.  I don't think you need them.  Instead, 
you should say more about the autocorrelation specifically.  This is a correlation coefficient 
computed from one time series and *a shifted version of the same time series.*  The purpose
of using this is to see whether there is a correlation between outcomes of earlier shots taken and 
later shots taken.    

"When analyzing these statistics, however, we must be careful not to be mislead by what 
they are saying"  -- "mislead" should be "misled"

"By proving that there is no correlation between shots does not necessarily prove
that there is no causation."  I don't know what you mean by this.  I don't know 
if anyone would argue that the outcome of one shot *CAUSES* the outcome of the 
next shot.  Rethink what you are trying to say here.  

"Making or missing a previous number of shots may still have an affect
on the player in a psychological sense."  Wrong word here -- "affect" should be "effect"

"hand hand effect" -- typo at top of page when you begin discussion of Csapo and Raab
and Peter and Marcus(?)  Also, in this whole section it was unclear to me at first what the
relation of those two papers was and which you were referring to at any given time.
Please try to clarify this.  

If "Study 1" of GVT dealt with Stanford players, I don't see the connection with Table 3
which you reproduce.  That shows freethrow probabilities for the members of the 1981-82
Boston Celtics.  I think that table is just out of place in your text.

I actually like your conclusion because it clearly shows that there are plausible
arguments on both sides of the question.  

A final thought:  In terms of the overall organization of the paper, I think mentioning
"Study 1" from the GVT article *first* might be an improvement because that clearly shows
the pretty overwhelming point of view among fans and players that the "hot hand" is real.
Then you can present the counter-arguments.