From: COWAN@ssrl01.slac.stanford.edu (Paul L. Cowan)
Subject: Re: Lies, D**n Lies, etc (Re: PSU is Overrated!)
Organization: Pacific-Plate Residents (Motto: 54-40 or Bust!)
Date: Fri, 16 Oct 1992 17:37:27 GMT
X-News-Reader: VMS NEWS 1.24

In <Bw4B2B.ICM@acsu.buffalo.edu> v262xxve@ubvmsd.cc.buffalo.edu writes:

:  In article <1992Oct13.192335.1921@morrow.stanford.edu>, 
:   COWAN@ssrl01.slac.stanford.edu (Paul L. Cowan) writes...
:  #lies, d**n lies and statistics thread: Few team are ranked in the final top 
:  #ten with as many as 3 losses. Considering the very top teams have often gone
:  #undefeated, let's say the average record of a team finishing in the top ten
:  #is roughly 10.5-1.5 (.875).
:  
:  Actually, that is pretty close to last year's .889 for an average 
:  10.672-1.328
:  record (assuming a tie is half a win and half a loss).  So, one would
:  expect the ``average'' team to have a record of .111 against the Top Ten
:  teams.  However, considering that PSU was considered better than average
:  during the past twenty years, one would expect better.
:  
:  # That means that on the average the teams that 
:  #played final-top-10 teams have a winning record of something like .125 in 
:  #games against these teams. So, Penn State's winning percentage is almost double 
:  #the average in such games, and that is a record sustained over 25 years!
:  #Looked at from the proper perspective a *statistic* of 10-41 sounds pretty
:  #impressive.
:  
------------ Mr Pitts's calculations full of *statistics* deleted ----------

:  It certainly has won more than its share and teams like Pacific and Kent
:  have won fewer than their share.  But, we aren't comparing PSU to UOP
:  or Kent, we're comparing them to the average attainment of all teams.
:  And against that measuring stick, Penn State does not fare so well.
:  
:  Timothy C. Pitts             
:  V262XXVE@ubvms.cc.buffalo.edu

Okay, time for lesson number 4 in lies, d**n lies and statistics. The
stat (attributed to the AP) that PSU is 10-41 against teams who
*finished* in the top ten has been called into questioned by another
post, but my original point was that statistics can be deceiving and
10-41 is NOT BAD! Mr. Pitts implies that this record is comparable to
Kent State's but not in the top ten.

The first thing that one must understand is that on the team that finish
in the top ten are the ones that didn't lose many games 
(pretty obvious, huh?) Since no one wins fewer than zero games against 
such teams, the proper description for the expected distribution of wins 
is given by Poisson's statistics (you could look it up).

My top-of-the-head estimate was that teams that finished in the top
ten typically lost only 1/8=.125 of their games. So in the 51 games
that PSU has (allegedly) played against teams that finished in the
top ten the average number of wins one would expect is 6.375. 

Poisson's distribution predicts the following for a random process
with an average of 6.375: 

No. of wins:             0   1   2   3   4   5   6   7   8   9   10
Percentage of teams:    0.2  1   3   7  12  15  16  15  12   8    5

Thus 94% of teams playing 51 games against teams who *finished* with a
.875 winning percentage are expected to have 10 or fewer wins in these
games, leaving one to expect only 6% of teams to do better than PSU.
Since there were roughly 100 Div I-A teams during most of Paterno's
tenure, this would place PSU firmly amoung the top ten. 

Mr. Pitts points out that last year the actuall losing percentage of 
teams that finished in the top ten was only 1/9=.111. This drops the
expected average number of wins in 51 games to 5.661. With this
average, Poisson predicts that only 3% of teams will win more than 
10 games. This makes JoePa's record appear even more impressive.

Of course the actual records of college teams may not resemble a
Poisson distribution over the last 25 (or so) years. My point is not
to convince anyone how great PSU or JoePa are based on my statistical
analysis (lies, d**n lies, etc), but simply to show the pitfall of
saying "JoePa is 10-41 blah-blah-blah and therefore PSU is overrated"
or that "against that measuring stick, Penn State does not fare so
well."  Despite one's first reaction, proper analysis shows that 10-41 
(if accurate) is in fact a darned good record.

---------------------------------------------------------------------------
P. L. Cowan     Please send replies, comments etc. (no flames thank you) to 
COWAN@ANL.GOV  (I'm posting from my own account, but not the preferred one)
        "Gentlemen, you can't fight in here! This is a War Room!"
from _Dr._Strangelove_or:_How_I_Learned_to_Stop_Worrying_and_Love_the_Bomb_
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---------------------------------------------------------------------------
P. L. Cowan     Please send replies, comments etc. (no flames thank you) to 
COWAN@ANL.GOV  (I'm posting from my own account, but not the preferred one)
        "Gentlemen, you can't fight in here! This is a War Room!"
from _Dr._Strangelove_or:_How_I_Learned_to_Stop_Worrying_and_Love_the_Bomb_
---------------------------------------------------------------------------