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To compare the amount of skill and luck in these games Sherman would have us
carry out an analysis of variance in the same way we did for our medical
example. Here the players are the groups and the games are the treatments.  The
group means are the averages of the players winnings and are in the last row of
the data. 
The grand mean (gm) is the sum of all the winnings divided by 35
which gives us a grand mean of -.105714. The sums of squares within  groups
is the  sum of  the squares of the differences between the winnings and the
player's mean winnings:
<center><math>(-6.75 -1.934)^2 + ... + (-1.42-2.489)^2 = 758.499,.</math></center>
The sums of squares between groups is the sum of the squares of the differences
between the winnings and the grand mean:
<math>(-6.75 - gm)^2  + ...+  (-1.42-gm)^2 = 311. 447.</math>
Thus the total sums of squares is
758.499 + 311.447 = 1069.95.


Sherman assumes that the variation  in the amount won within groups  is
Sherman assumes that the variation  in the amount won within groups  is
primarily due to luck and  calls this ``Random Variance'' and the variation
primarily due to luck and  calls this ``Random Variance'' and the variation
between groups is due primarily  to skill and calls this ``Systematic Variance".  
between groups is due primarily  to skill and calls this ``Systematic Variance".  
He then defines
He then defines:
 
<center>Game's Skill Percentage = <math>{Systematic Variance}{Systematic Variance + Random Variance}</math> </center>


$${\rm Game's\ Skill\ Percentage} = \frac{\rm Systematic\
Variance}{{\rm(Systematic\  Variance} + {\rm Random\  Variance})}\,,$$
and similarly,
and similarly,
$${\rm Game's\ Luck\ Percentage} = \frac{\rm Random\ Variance}{{\rm(Systematic\
 
Variance} + {\rm Random\  Variance})}\,.$$
<center>Games Luck Percentage =<math> {Random Variance} {Sysatematic Variance + Random Variance}</math></center>
 
So, in our poker game, the Random Variance is 758.499 and the Systematic
So, in our poker game, the Random Variance is 758.499 and the Systematic
variance is 311.477. So the Skill Percentage  is 29.1\% and  the Luck Percentage
variance is 311.477. So the Skill Percentage  is 29.1% and  the Luck Percentage
is 70.9\%.
is 70.9%.
\par
 
In his second article, Sherman reports  the Skill Percentage  he obtained using
In his second article, Sherman reports  the Skill Percentage  he obtained using
data from a number of different types of games.  For example, using data for
data from a number of different types of games.  For example, using data for
Major League Batting, the Skill Percentage for hits was 39\% and for home runs
Major League Batting, the Skill Percentage for hits was 39% and for home runs
was 68 \%. For NBA  Basketball it was 75\% for points scored. For poker stars in
was 68%. For NBA  Basketball it was 75% for points scored. For poker stars in
weekly tournaments it was 35\%.
weekly tournaments it was 35%.
\par
 
Sherman concludes his articles with the remarks:
Sherman concludes his articles with the remarks:


\begin{quotation} If two persons play the same game, why don't both achieve the
<blockquote> If two persons play the same game, why don't both achieve the
same results? The purpose of last month's article and this article was to
same results? The purpose of last month's article and this article was to
address this question.  This article suggests that there are two answers to this
address this question.  This article suggests that there are two answers to this
Line 52: Line 32:
estimates involved in playing poker  (or at least tournament poker) are not very
estimates involved in playing poker  (or at least tournament poker) are not very
different from other sport outcomes which are widely accepted as
different from other sport outcomes which are widely accepted as
skillful.\end{quotation}
skillful.{\blockquote}
\vskip .2in
 
\noindent
Discussion questions:
Discussion questions:
\vskip .1in
 
\noindent
(1) Do you think that Sherman's measure of skill and luck in a game is
(1) Do you think that Sherman's measure of skill and luck in a game is
reasonable?  If not, why not?
reasonable?  If not, why not?
\vskip .1in
 
\noindent
(2) There is a form of poker modeled after duplicate bridge.  Do you think that
(2) There is a form of poker modeled after duplicate bridge.  Do you think that
the congressional decision should apply to this form of gambling?
the congressional decision should apply to this form of gambling?

Revision as of 22:04, 17 October 2007

Sherman assumes that the variation in the amount won within groups is primarily due to luck and calls this ``Random Variance and the variation between groups is due primarily to skill and calls this ``Systematic Variance". He then defines:

Game's Skill Percentage = <math>{Systematic Variance}{Systematic Variance + Random Variance}</math>

and similarly,

Games Luck Percentage =<math> {Random Variance} {Sysatematic Variance + Random Variance}</math>

So, in our poker game, the Random Variance is 758.499 and the Systematic variance is 311.477. So the Skill Percentage is 29.1% and the Luck Percentage is 70.9%.

In his second article, Sherman reports the Skill Percentage he obtained using data from a number of different types of games. For example, using data for Major League Batting, the Skill Percentage for hits was 39% and for home runs was 68%. For NBA Basketball it was 75% for points scored. For poker stars in weekly tournaments it was 35%.

Sherman concludes his articles with the remarks:

If two persons play the same game, why don't both achieve the

same results? The purpose of last month's article and this article was to address this question. This article suggests that there are two answers to this question: Skill (or systematic variance) or Luck (or random variance). Using both the correlation approach described last month and the ANOVA approach described in this article, one can estimate the amount of skill involved in any game. Last, and maybe most importantly, Table 4 demonstrated that the skill estimates involved in playing poker (or at least tournament poker) are not very different from other sport outcomes which are widely accepted as skillful.{\blockquote}

Discussion questions:

(1) Do you think that Sherman's measure of skill and luck in a game is reasonable? If not, why not?

(2) There is a form of poker modeled after duplicate bridge. Do you think that the congressional decision should apply to this form of gambling?

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