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Wednesday, October 18, 2006

College Football Ranking Systems, Retrodictive Accuracy and Cyclic Triads

So, you know all about sports?

Then the concepts of "retrodictive accuracy" and "cyclic triads" should be familiar terrain to you.

As B. Jay Coleman informs us in his article, Minimizing Game Score Violations in College Football Rankings, Interfaces 35(6), pp. 483–496, ©2005 INFORMS:

"[R]etrodictive accuracy is equivalent to minimizing game score violations: the number of times a past game's winner is ranked behind the loser".

Unfortunately, this is not always possible, since, as Coleman informs us, we face the problem of "cyclic triads", where Team A beats Team B, Team B beats Team C, and Team C beats Team A.

Nevertheless, the amount of retrodictive inaccuracy in college football ranking systems is far greater than cyclic triads alone would engender, Coleman has found that even the current best ranking system from the standpoint of retrodictive accuracy still contains violations which are at least 38% higher than the minimum which can actually be achieved.

Coleman thus developed a minimum-violations ranking solution - MinV, which ranks football teams so that the minimum number of retrodictive violations occur. As Coleman writes:

"The minimum number of game score violations MinV identified for the NCAA Division 1-A college football seasons from 1994–2003 was far superior to the numbers that 58, 68, 75, and 93 different ranking systems (Massey 2004b, c) produced in the years 2000, 2001, 2002, and 2003, respectively. Massey did not report ranking violation statistics prior to 2000."

He then examined the college football games from 1994 to 2003 and applied his results:

"to determine whether the consensus top five teams in any of these 10 seasons would have been changed if one had enforced a minimum violations criterion."

Using his system, the national champion would not have changed, but the rankings of teams below Nr. 1 would have changed, in part, substantially:

MinV ranking (Actual Massey Consensus Ranking in Parentheses)

Year...Number 1...........Number 2............Number 3...........Number 4..........Number 5

1994...Nebraska (1)......Penn State (2)......Colorado (3).......Alabama (5).......Texas A&M (8)
1995...Nebraska (1)......Florida (2)...........Tennessee (3)......Florida St. (4)....Colorado (5)
1996...Florida (1).........Ohio St. (2)...........Florida St. (3).....Arizona St. (5)...Nebraska (4)
1997...Nebraska (1)......Michigan (3)........Florida (4)..........Florida St. (2)....Tennessee (5)
1998...Tennessee (1).....Ohio St. (2)..........Florida St. (3).....Wisconsin (4).....Florida (5)
1999...Florida St. (1).....Nebraska (2).......Va. Tech (3)´......Michigan (4)......Kansas St. (5)
2000..Oklahoma (1).....Nebraska (8)........Washington (6)...Miami (FL) (2)...Florida St. (3)
2001...Miami (FL) (1)...Tennessee (3)......Florida (2)..........Oregon (4).........LSU (9)
2002...Ohio St. (1)........Miami (FL) (3).....Georgia (4).........Oklahoma (5).....Texas (6)
2003...LSU (1)..............Southern Cal (2)..Oklahoma (3)......Georgia (4)........Miami, OH (6)

Table 3: Although the national champions would not have been affected, the remainder of the consensus top
five NCAA Division 1-A college football teams for the 1994–2003 seasons often would have been adjusted
had a minimum-violations restriction been enforced (consensus rankings are in parentheses). I used Massey’s (2004b, c) consensus rankings for 1996–2003 and the final Associated Press poll in 1994 and 1995. Massey did not report a consensus ranking for 1994or 1995.

Coleman also examined:

"whether the participants in any of the BCS national championship games from 1998 through 2003 would have been altered by a minimum-violations restriction."

The answer is yes, as this table by Coleman shows:

............number of........Actual BCS..................................Participants with
Year.....violations........participants................................MinV adjustments

1998.....41...................Tennessee, Florida St...................Tennessee (1), Florida St. (2)
1999.....58...................Florida St., Va. Tech.....................Florida St. (1), Va. Tech. (2)
2000....51...................Oklahoma, Florida St....................Oklahoma (1), Washington (4)
2001....51...................Miami (FL), Nebraska...................Miami (FL) (1), Oregon (4)
2002....50...................Ohio St., Miami (FL).....................Ohio St. (1), Miami (FL) (2)
2003....59...................Oklahoma, LSU............................Oklahoma (1), LSU (2)

Table 4: The Bowl Championship Series (BCS), begun in 1998, would have
selected different participants in its national championship games in 2000
and 2001 if it had adjusted its final ranking to adhere to the minimum
number of violations (actual BCS rankings are in parentheses).

But note that the retrodictive approach is not a cure-all for ranking systems.

As Coleman himself admits:

[T]he MinV ranking may not make the best predictions of future games; as Martinich (2002) demonstrated, retrodictive accuracy does not necessarily result in predictive accuracy. However, no prior researcher has assessed the relationship between these two perspectives, because none have developed systems that optimize the retrodictive component (as measured by violation percentage) for college football. MinV allows that as a future research objective.

The entire article is definitely worth a read here.

Monday, October 02, 2006

Better Football Coaching : Learning from the Best : More on Larry Kehres of the Purple Raiders of Mount Union College in Alliance, Ohio

When we see the many coaching lapses apparent for teams in NCAA Division IA, we look instructively to Mount Union in NCAA Division III.

We have previously touted Larry (known to most simply as "LK") Kehres of the Purple Raiders of Mount Union College in Alliance, Ohio as the best coach in college football.

We are not the only ones to point to the Purple Raiders as exemplary. Al Eisele in his blog at the Huffington Post, writes under the title Bush: Take a Lesson from the Mount Union College Purple Raiders:

"Kehres is one of the most successful football coaches in the country.

What's the secret to his success....

[Learning is the Measure of Teaching - No Excuses]

"I always try to get the assistant coaches who work with me to understand that if there's no learning by the kids, there's no teaching," said the 56-year-old Kehres, whose 29-year-old son Vince is one of the assistant coaches. "I've tried hard to get the coaches to accept that as the only measure of performance, and there are just no excuses accepted. If there's no learning, there's no teaching.....

[Give Credit Where Credit is Due]

If you've practiced well and prepared well and you still lose, then you have to give credit to your opponent. You have to respect the game of football and the other team.""

The site has an article which gives us more positive feedback in the same direction.
It's title?
Learning from the best (by Mark Simon)

Here are some of the things written and said about Kehres in that article by Simon:

[Motivation of Players]

"Players often say that they will run through brick walls for their coach. That's a respect that has to be earned. As Sirianni enters his first season with total control of a program, he knows what the key is....

[Getting Teams to Reach their Full Potential]

"He gets his teams to reach their full potential every year," said [Mike] Sirianni [now himself an extremely successful head coach at Washington & Jefferson College], who was a two-time All-OAC [Ohio Athletic Conference] wide receiver as a Purple Raider and won a national title in 1993. "That's one of the hardest things to do as a coach. Rowan had more talent than Mount Union every year we played them (in the Stagg Bowl) 1993, 1996, and 1998, but we won those games. Rowan had more talent, but Mount Union had the better plan. If we didn't reach our full potential in those games, we wouldn't have won them...."

[Staying Calm and Cool]

"Kehres isn't big on motivational speeches. A typical pregame talk may end something like this.

"Let's go out there at see what happens and we'll make adjustments at halftime."

"Coach Kehres gets better as the game gets tighter," Sirianni said. "When the game starts, he's calm. When it's 28-28 in the Stagg Bowl, he's calm."

[Being Innovative]

"Kehres isn't afraid to try things that may go against ordinary thinking."

[Right Treatment of Alumni and Players]

""Anybody who has been around Coach Kehres picks off certain things," said [Dean] Paul, who was there when Kehres took over the program in 1986 and though he didn’t win a national championship, was a two-time all OAC [Ohio Athletic Conference] running back and team captain. "Like the way he treats alumni.""

[Paul is coach at Thomas More College, where improvement is visible due to his coaching: "Week four of PAC football was highlighted by a pair of fantastic finishes. In league play, Thiel (2-2, 1-0 PAC) opened defense of its 2005 PAC title with a thrilling 17-14 overtime win at Thomas More (2-1, 0-1 PAC). "]

“I look at his stuff now and I'm not afraid to steal it,” Sirianni said with a laugh. “We stole (MU grads) Gary Smeck and Matt Laverde to be part of our coaching staff. We changed our preseason conditioning testing to what they do at Mount Union. We're going to recruit like them too. One of the big things I want to copy is how they treat their young kids. We're going to have an eight- or nine-game JV schedule. That’s a big part of their program. Coach Kehres coaches the second team harder than his first team. You never know when the second team is going to have to start. We hadn't done that in the past, but we will this year. Our second team kids will be worked hard.”

[Being Fair and Impartial]

Erik Raeburn, successful football coach at Coe College, and son of Larry Kehres' sister, is quoted as saying:

"I think (being related) gives me an even bigger advantage. I'm very close with him personally and professionally. I think he treated me just like all his other players."

Also of interest are these articles about Larry Kehres and the Mount Union Purple Raiders:

At the top of the mountain is Division III Mount Union, College Football Insider, Column from The Sporting News, January 5, 1998, by Tom Dienhart and Mike Huguenin, where we read:

[Long-Term Planning - Small can be Big]

"In the '70s or '80s, we wondered if it was really possible for a private college our size to compete nationally in a big-team sport," Mount Union coach Larry Kehres says. "Winning our first title in 1993 showed us we could do it. It also sends that message out to other small colleges, and to our town....

[Everyone has a Mentor]

Kehres ... credits former Mount Union teammate and current Carolina Panthers coach Dom Capers with helping him develop into a great coach...."

From the Portfolio at NYU:
COLLEGE FOOTBALL; The Division III Title Is Mount Union's Goal by Erik Boland, we take the following excerpts:

[Knowing the Game]

"He knows so much about the game,'' said running back Chuck Moore, who won the Gagliardi award this season, given to the top player in Division III. ''I love going to scouting reports on Mondays just to listen to him talk.''

[Practices are For Learning - That's Pressure]

"Rob Adamson, a junior quarterback, said Kehres's practices are one of the reasons his teams are so successful. The pressure of game day, even a national semifinal, pales compared with the pressure of practice...."


''I take the same approach during games he does,'' Grinch, the senior safety, said. ''I see how businesslike he is. That rubs off on the rest of the team...."

[Look Forward, Not Back]

''You can't let the past influence each day, except to learn from it,'' [Kehres] said."

We have coached and we agree. Kehres has it right.

Sky Earth Native America

Sky Earth Native America 1 :
American Indian Rock Art Petroglyphs Pictographs
Cave Paintings Earthworks & Mounds as Land Survey & Astronomy
Volume 1, Edition 2, 266 pages, by Andis Kaulins.

  • Sky Earth Native America 2 :
    American Indian Rock Art Petroglyphs Pictographs
    Cave Paintings Earthworks & Mounds as Land Survey & Astronomy
    Volume 2, Edition 2, 262 pages, by Andis Kaulins.

  • Both volumes have the same cover except for the labels "Volume 1" viz. "Volume 2".
    The image on the cover was created using public domain space photos of Earth from NASA.


    Both book volumes contain the following basic book description:
    "Alice Cunningham Fletcher observed in her 1902 publication in the American Anthropologist
    that there is ample evidence that some ancient cultures in Native America, e.g. the Pawnee in Nebraska,
    geographically located their villages according to patterns seen in stars of the heavens.
    See Alice C. Fletcher, Star Cult Among the Pawnee--A Preliminary Report,
    American Anthropologist, 4, 730-736, 1902.
    Ralph N. Buckstaff wrote:
    "These Indians recognized the constellations as we do, also the important stars,
    drawing them according to their magnitude.
    The groups were placed with a great deal of thought and care and show long study.
    ... They were keen observers....
    The Pawnee Indians must have had a knowledge of astronomy comparable to that of the early white men."
    See Ralph N. Buckstaff, Stars and Constellations of a Pawnee Sky Map,
    American Anthropologist, Vol. 29, Nr. 2, April-June 1927, pp. 279-285, 1927.
    In our book, we take these observations one level further
    and show that megalithic sites and petroglyphic rock carving and pictographic rock art in Native America,
    together with mounds and earthworks, were made to represent territorial geographic landmarks
    placed according to the stars of the sky using the ready map of the starry sky
    in the hermetic tradition, "as above, so below".
    That mirror image of the heavens on terrestrial land is the "Sky Earth" of Native America,
    whose "rock stars" are the real stars of the heavens, "immortalized" by rock art petroglyphs, pictographs,
    cave paintings, earthworks and mounds of various kinds (stone, earth, shells) on our Earth.
    These landmarks were placed systematically
    in North America, Central America (Meso-America) and South America
    and can to a large degree be reconstructed as the Sky Earth of Native America."

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