Ducks, Warriors, and Rainbows

This post is a response for an interesting point
brought up by BobJoeJim and Semtex from
the twoplustwo forums.
What about Hawai'i?

They are obviously going to have an
outperformance number since they haven't
lost. Does this mean they are a better team
than Oregon? Ironically, if we are comparing
both by the top 5 standards, it appears so.
However, this points out how the
on-the-field results ranking (hereafter
OTFRR) needs to be used only for teams that qualify for it based 
on previous rankings--such as: as the #50 team, as the #25 team, 
as the #15 team, and so on. The same 
process used to determine the top team can
be used to whittle down who qualifies to be
considered. As IggyMcfly(2p2er) said, "Yeah,
really comparing the Top 5's expected wins
only works with Top 5 caliber teams."

To show this point in action, let's look at
Hawai'i and see how they compare to Oregon
as a #15 team and see if Hawai'i are warriors
or rainbows.

The initial confusion is this
as a top 5 team playing their respective
schedules, Hawai'i is outperforming verse
their schedule while Oregon is
underperforming.

Hawai'i is +0.225 wins
Oregon is -0.029 wins (notice the correction
from the previous post)

Oregon if #5
Houston 92.11%
Michigan 70.86%
Fresno St 93.81%
Stanford 85.56%
Cal 79.82%
Wazzu 99.00%
Washington 81.70%



WINS
12 0.0000
11 0.0000
10 0.0000
9 0.0000
8 0.0000
7 0.3382
6 0.4121
5 0.1964
4 0.0469
3 0.0059
2 0.0004
1 0.0000
0 0.0000

Hawai'i if #5
N Colorado 100.00%
La Tech 90.24%
UNLV 90.24%
Charleston So 100.00%
Idaho 99.00%
Utah St 99.00%
SJST 99.00%

WINS
12 0.0000
11 0.0000
10 0.0000
9 0.0000
8 0.0000
7 0.7901
6 0.1949
5 0.0147
4 0.0003
3 0.0000
2 0.0000
1 0.0000
0 0.0000

sidenote is that a #5 team should have a
0.968 win pct verse Hawai'i's schedule.
This is far easier than the top contenders
we visited in the previous post.

Now, let's look at how they are faring as a
#15 team playing their respective schedules.

Oregon 
+0.838W expected 5.162W 1.838L 0.737winp
Hawai'i
+0.288W expected 6.712W 0.288L 0.959winp

The details are as follows:

Oregon if #15
Houston 79.81%
Michigan 53.94%
Fresno St 88.13%
Stanford 70.86%
Cal 61.20%
Wazzu 96.11%
Washington 66.13%


WINS
12 0.0000
11 0.0000
10 0.0000
9 0.0000
8 0.0000
7 0.1046
6 0.2969
5 0.3355
4 0.1929
3 0.0597
2 0.0096
1 0.0007
0 0.0000

Hawai'i if #15
N Colorado 100.00%
La Tech 91.96%
UNLV 87.50%
Charleston So 100.00%
Idaho 99.00%
Utah St 99.00%
SJST 93.75%

WINS
12 0.0000
11 0.0000
10 0.0000
9 0.0000
8 0.0000
7 0.7393
6 0.2345
5 0.0251
4 0.0011
3 0.0000
2 0.0000
1 0.0000
0 0.0000

It's clear that Hawai'i's schedule isn't even
tough enough to test if they are truely a
top15 team. The #15 team would be
undefeated ~74% of the time facing that
schedule.

In essence, I think this knocks Hawai'i out
of competing for the top spot right now.
However, as the season goes on, there are
more 'losable' games that can 'test' and
'flesh out' where Hawai'i belongs in the
picture.

Kansas is #1! (post week 8 NCAAF musings)

Here's an interesting stat result about the 'top'
teams in the land:
Kansas +0.703
Ohio State +0.659
Arizona State +0.619
Boston College +0.461
LSU +0.376
Oregon -0.119

In my results oriented world, Kansas is the top
team in all the land. What are those numbers?
How did I get them? Well, I'll introduce that in
the rest of this post.

These are a pure results oriented ranking.  
They represent how many more (or less) wins
each respective team has verse the schedule
they played than a generic #5 team in the
land would have. That's the general idea and,
of course, it requires some breaking down as
there are quite a few assumptions
(reasonable I hope) and explanations.  

1) For each team, I gathered their opponents' 
sagarin predictor rating after week 8
Saturday games. Sagarin predictor is the best
known computer evaluation system and the
most reliable from everything I've seen. (In
an ideal world, I'd probably find a weighted
combination of all rankings, like on Massey
compare web page, and assign a rating
through that.)  

2) I then pull out the rating for the #5 team according to sagarin predictor

3) I construct a ex post facto 'spread' for
each game by taking the difference
between the #5 ranking and each
opponent's sagarin predictor and add or
subtract a blanket 3 point home-field
advantage.

4) From there, I convert the 'spread' into
a win pct by comparing
the 'spread' to the a database that has the 
actual win pcts for
each game played at that spread in college
football from 1993 to 2006 (ty to goldsheet
for that info).

5) After obtaining a win pct for a generic
#5 team against each team on the schedule,
I just add simple math to get the average
amount of wins the #5 team should have
against that schedule.

6) I then subtract the projected #5 team
win total from the actual win total for the
specific team to obtain a result for how
many wins a team has outperformed a
generic #5 team.

7) For giggles, I go further and work through
every possible combination to see what
would a generic #5's teams win total look
like against that schedule for all possible
outcomes.

Without further ado, here is some of the
grunt work for each team

Kansas
C Mich 99.00%
SE La 99.00%
Toledo 99.00%
FIU 99.00%
K St 57.34%
Baylor 99.00%
Colorado 77.37%

6.297W 0.703L 0.900%

WINS p
12 0.0000
11 0.0000
10 0.0000
9 0.0000
8 0.0000
7 0.4219
6 0.4586
5 0.1143
4 0.0051
3 0.0001
2 0.0000
1 0.0000
0 0.0000

Ohio State
Youngstown St 99.00%
Akron 99.00%
Washington 81.70%
N'Western 96.48%
Minnesota 92.59%
Purdue 77.37%
Kent St 99.00%
Mich St 88.92%

7.341W 0.659L 0.918%

WINS P
12 0.0000
11 0.0000
10 0.0000
9 0.0000
8 0.4872
7 0.3839
6 0.1124
5 0.0154
4 0.0011
3 0.0000
2 0.0000
1 0.0000
0 0.0000

Arizona State
SJ ST 99.00%
Colorado 88.13%
SD ST 96.48%
Org St 87.94%
Stanford 85.56%
Wazzu 90.24%
Washington 90.72%

6.381W 0.619L 0.912%

WINS P
12 0.0000
11 0.0000
10 0.0000
9 0.0000
8 0.0000
7 0.5185
6 0.3617
5 0.1031
4 0.0154
3 0.0013
2 0.0001
1 0.0000
0 0.0000

Boston College
Wake Forest 92.08%
NC St 98.18%
G Tech 76.39%
Army 99.00%
Umass 99.00%
B Green 99.00%
N Dame 90.24%

6.539W 0.461L 0.934%

WINS P
12 0.0000
11 0.0000
10 0.0000
9 0.0000
8 0.0000
7 0.6047
6 0.3338
5 0.0573
4 0.0041
3 0.0001
2 0.0000
1 0.0000
0 0.0000

LSU
Miss St 93.41%
V Tech 92.08%
MTSU 98.18%
S Car 88.10%
Tulane (N) 99.00%
Florida 62.03%
Kentucky 57.34%
Auburn 72.27%

6.624W 1.376L 0.828%

WINS P
12 0.0000
11 0.0000
10 0.0000
9 0.0000
8 0.1893
7 0.3900
6 0.2970
5 0.1043
4 0.0178
3 0.0015
2 0.0001
1 0.0000
0 0.0000

Oregon
Houston 92.11%
Michigan 70.86%
Fresno St 93.81%
Stanford 85.56%
Cal 79.82%
Wazzu 99.00%
Washington 90.72%

6.119W 0.881L 0.874%

WINS P
12 0.0000
11 0.0000
10 0.0000
9 0.0000
8 0.0000
7 0.3756
6 0.4119
5 0.1726
4 0.0357
3 0.0039
2 0.0002
1 0.0000
0 0.0000


Now, don't get me wrong LSU fans.  I do believe you might have the 'best' team. In no sport, however, is the title given to the 'best' team. It's given to the team that earns it on the field. While I don't think Kansas is as good as any of the teams I compared them against here. They've had the best results on the field. But, there are alot of games left and plenty of time for things to change.

BTW-I think LSU has had the toughest schedule and my analysis bears backs that notion. The key is the expected win pct for a #5 team playing the respective schedules.
LSU 0.828
Oregon 0.874
Kansas 0.900
Arizona State 0.912
Ohio State 0.918
Boston College 0.934


I might due some sensitivity analysis and see how the numbers come out if I go with the #1 sagarin predictor instead of #5.