While I can't help much in the way of assessing the correlation (at
least in a numerical sense), I have provided some code below to
visualize the data bringing in an additional variable for the preseason
ranking of the team according to the AP poll as it appears here:
http://sports.espn.go.com/ncf/rankingsindex?seasonYear=2007weekNumber=1
seasonType=2) - Note that I did not double check my transcriptions of
the preseason rankings so I do not guarantee my accuracy.
Here's the R code to create the graphic.
load('BCS.RDA')
# Add pre-season ranking via the AP Top 25
BCS$preseason -
c(11,28,2,36,29,8,3,9,NA,35,6,1,26,46,40,29,23,13,4,5,12,18,NA,
32,7,34,16,14,24,7,44,43,41,25,NA,NA,37,NA,17)
rankp - c(BCS$UR, BCS$HR, 1:dim(BCS)[1], BCS$preseason)
comp - rep(BCS$Cavg, 4)
poll - rep(c('Harris','USA Today','BCS','Pre-Season'),
each=dim(BCS)[1])
dat - data.frame(Rank=rankp, Cavg=comp, poll=poll,
school=rep(rownames(BCS),4))
dat$schoolordered - factor(dat$school, levels=rownames(BCS),
labels=rownames(BCS), order=TRUE)
bigcavg - sort(BCS$Cavg)[29:39]
library(lattice)
new.back - trellis.par.get(background)
new.back$col - white
newcol - trellis.par.get(superpose.symbol)
newcol$col - c('red','blue','black','green4','black')
newcol$pch - c(4,1,16,6)
new.pan - trellis.par.get(strip.background)
new.pan$col - c('grey90','white')
trellis.par.set(background, new.back)
trellis.par.set(superpose.symbol, newcol)
trellis.par.set(strip.background,new.pan)
xyplot(Cavg ~ Rank|schoolordered, group=poll,
data=subset(dat, Rank = 20),
type=c('p'),
xlim=c(-1.5,21.5),
panel=function(x,y,...){
panel.abline(h=bigcavg, col='grey80')
panel.abline(v=seq(0,20,5), col='grey60')
panel.superpose(x,y,...)
},
xlab='Poll Rank',ylab='Computer Average',
key=list(
points=list(col=trellis.par.get('superpose.symbol')$col[1:4],
pch=trellis.par.get('superpose.symbol')$pch[1:4]),
text=list(lab=sort(unique(poll)),
col=trellis.par.get('superpose.symbol')$col[1:4]),
columns=4, title='Poll System', cex=1)
)
Notes on the output
1) Panels are arranged in order of BCS standing which is also
characterized by the red x.
2) The top 10 Cavg scores are provided as horizontal lines in each
panel.
3) For clarity I took a subset of the original data set only looking at
rankings = 20.
Some comments
1) Arizona State: While 1-3 are consistent, AZ St. polls differ quite a
bit w/ the BCS ranking being pulled up by the computers.
2) USC and OK St. and GA: Both have lower Cavg scores, but high human
polls (Harris and USA Today) which tend to coincide w/ the preseason
ranking.
3) As for bias, #2 seems to show some bias in the human polls, though I
would not say the computer ranking is not w/o flaw.
Basically, I can't find the magic bullet, and I imagine the debate will
continue on what is the best way to determine the two best teams to play
for the championship - a far from perfect scenario. Yet another debate
of the use of Super Crunching if I may borrow from Ian Ayres. Open to
any ideas/opinions.
Cheers,
-Mat
-Original Message-
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]
On Behalf Of Horace Tso
Sent: Thursday, October 25, 2007 3:39 PM
To: R Help; Douglas Bates
Subject: Re: [R] Appropriate measure of correlation with'zero-inflated'
data?
Doug and the football fans out there,
I'm no football expert myself. But here is what my colleague said after
reading the posting.
I can't help you with the equation, but I can say that the polls are
very poor predictors of performance. The reason they do such a bad job
is that pollsters rank the teams even before the season starts based on
perceived talent. That ranking system makes it hard for a team to move
up the polls as long as the teams in front of them keep winning. Also,
polling introduces many personal biases.
College football could easily solve the problem with a play-off system,
but the powerful football conferences wouldn't make as much money, so
they won't agree to it.
Cheers.
Horace
Douglas Bates [EMAIL PROTECTED] 10/25/2007 10:58:24 AM
I have reached the correlation section in a course that I teach and I
hit upon the idea of using data from the weekly Bowl Championship
Series (BCS) rankings to illustrate different techniques for assessing
correlation.
For those not familiar with college football in the United States
(where football refers to American football, not what is called
soccer here and football in most other countries) I should explain
that many, many universities and colleges have football teams but each
team only plays 10-15 games per season, so not every team will play
every other team. The game is so rough that it is not feasible to
play more than one match per week and a national playoff after the
regular season is impractical. It would take too
