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Selecting the FBS Playoff Teams: Stage #3 - Adjusting Earned Wins

In Stage #2, we calculated the Earned Wins for each team based completely on the raw number of rated wins and total losses. We will now take these unadjusted Earned Wins and use them to recalculate the Earned Wins of each team. This step will be repeated until for every team, the new calculation of Earned Wins does not differ from number of Earned Wins in the immediately preceding step.

While the computer program is running this iterative process, it will also enforce the following rules.

  • Each team's rated wins are prorated using the following formula: (12 x RW)/(RW + L). A team's Earned Wins are bounded above by the result of this proration.
  • A team's Earned Wins are constricted by its number of win points as follows:
55 win points = maximum of 11 earned wins
45 win points = maximum of 10 earned wins
36 win points = maximum of 9 earned wins
28 win points = maximum of 8 earned wins
21 win points = maximum of 7 earned wins
15 win points = maximum of 6 earned wins
10 win points = maximum of 5 earned wins
6 win points = maximum of 4 earned wins
3 win points = maximum of 3 earned wins
1 win point = maximum of 2 earned wins
0 win points = maximum of 1 earned win

These restrictions keep teams from earning wins by simply not losing to bad teams even though they have few, if any, impressive wins.

The relationship above is defined by the function MAX EW = 0.5(radical(8 x WP + 1)+1). This function is used for all win point values and not just those listed above.

  • If a rated team loses to an unrated team, the number of loss points earned by the rated team is calculated by treating the unrated team as a rated team with one exception - the unrated team's losses all earn 11 loss points.
  • A single win can earn at most 11 win points and a single loss can earn at most 11 loss points.
  • A team's loss points are constricted by its number of actual losses as follows:
1 loss = maximum of 11 loss points
2 losses = maximum of 21 loss points
3 losses = maximum of 30 loss points
4 losses = maximum of 38 loss points
5 losses = maximum of 45 loss points
6 losses = maximum of 51 loss points
7 losses = maximum of 56 loss points
8 losses = maximum of 60 loss points
9 losses = maximum of 63 loss points
10 losses = maximum of 65 loss points
11 losses = maximum of 66 loss points

These restrictions keep teams from accumulating an unrealistic number of loss points based on assumed losses and not actual losses. The relationship above is defined by MAX LP = 0.5 x L(23-L).

The table below shows the adjusted Earned Wins and the secondary Earned Wins for each rated team. Secondary Earned Wins are the result of removing the restriction that Earned Wins cannot exceed actual wins.

TEAM

W

L

EW

EW2

Air Force (CO)

2

10

0.120

0.120

Akron (OH)

5

7

2.667

2.712

Alabama

11

1

9.776

9.776

Arizona

7

5

6.232

6.232

Arizona St.

10

3

9.000

10.351

Arkansas

3

9

1.200

2.451

Arkansas St.

7

5

4.497

4.497

Army (NY)

3

9

0.323

0.323

Auburn (AL)

12

1

11.000

11.641

Ball St. (IN)

10

2

5.587

5.587

Baylor (TX)

11

1

9.735

9.735

Boise St. (ID)

8

4

4.962

4.962

Boston College (MA)

7

5

5.615

5.615

Bowling Green (OH)

10

3

5.843

5.843

Brigham Young (UT)

8

4

6.748

6.748

Buffalo (NY)

8

4

3.848

3.848

California

1

11

0.000

0.907

Central Florida

11

1

7.953

7.953

Central Michigan

6

6

2.545

2.545

Cincinnati (OH)

9

3

4.716

4.716

Clemson (SC)

10

2

8.859

8.859

Colorado

4

8

2.400

2.670

Colorado St.

7

6

2.230

2.230

Connecticut

3

9

0.615

0.615

Duke (NC)

10

3

8.061

8.061

East Carolina (NC)

9

3

5.755

5.755

Eastern Michigan

2

10

0.000

0.091

Florida

4

8

3.915

3.915

Florida Atlantic

6

6

3.538

3.538

Florida St.

13

0

11.138

11.138

Fresno St. (CA)

11

1

7.493

7.493

Georgia

8

4

7.636

8.263

Georgia Tech

7

5

6.000

6.312

Hawaii

1

11

0.029

0.029

Houston (TX)

8

4

5.540

5.540

Idaho

1

11

0.017

0.017

Illinois

4

8

2.400

2.763

Indiana

5

7

4.364

4.866

Iowa

8

4

7.200

7.208

Iowa St.

3

9

1.924

1.924

Kansas

3

9

1.659

1.659

Kansas St.

7

5

5.797

5.797

Kent St. (OH)

4

8

1.333

1.446

Kentucky

2

10

0.000

1.000

Louisiana St.

9

3

7.947

7.947

Louisiana Tech

4

8

0.554

0.554

Louisiana-Lafayette

8

4

4.475

4.475

Louisiana-Monroe

6

6

3.824

3.824

Louisville (KY)

11

1

6.642

6.642

Marshall (WV)

9

4

4.933

4.933

Maryland

7

5

4.905

4.905

Memphis (TN)

3

9

0.734

0.734

Miami (FL)

9

3

7.789

7.789

Michigan

7

5

6.780

6.780

Michigan St.

12

1

10.048

10.048

Middle Tennessee St.

8

4

4.556

4.556

Minnesota

8

4

7.117

7.117

Mississippi

7

5

6.545

6.908

Mississippi St.

6

6

5.455

5.961

Missouri

11

2

10.000

10.236

Navy (MD)

8

4

5.523

5.523

Nebraska

8

4

6.456

6.456

Nevada

4

8

2.153

2.153

Nevada-Las Vegas

7

5

4.068

4.068

New Mexico

3

9

0.301

0.301

New Mexico St.

2

10

0.092

0.092

North Carolina

6

6

5.273

5.273

North Carolina St.

3

9

1.700

1.700

North Dakota State

13

0

3.941

3.941

North Texas

8

4

5.033

5.033

Northern Illinois

12

1

7.476

7.476

Northwestern (IL)

5

7

3.600

4.075

Notre Dame (IN)

8

4

8.000

8.108

Ohio

7

5

3.531

3.531

Ohio St.

12

1

10.034

10.034

Oklahoma

10

2

9.142

9.142

Oklahoma St.

10

2

8.918

8.918

Old Dominion (VA)

8

4

1.033

1.033

Oregon

10

2

8.850

8.850

Oregon St.

6

6

5.250

5.250

Penn St.

7

5

5.930

5.930

Pittsburgh (PA)

6

6

5.515

5.515

Purdue (IN)

1

11

0.000

0.771

Rice (TX)

10

3

6.205

6.205

Rutgers (NJ)

6

6

2.839

2.839

San Diego St. (CA)

7

5

4.354

4.354

San Jose St. (CA)

6

6

3.901

3.901

South Alabama

6

6

3.076

3.076

South Carolina

10

2

9.370

9.370

South Florida

2

10

0.576

0.576

Southern California

9

4

7.967

7.967

Southern Methodist (TX)

5

7

1.923

1.923

Stanford (CA)

11

2

10.154

10.922

Syracuse (NY)

6

6

4.939

4.939

Temple (PA)

2

10

0.187

0.187

Tennessee

5

7

4.364

5.141

Texas

8

4

7.211

7.211

Texas A&M

8

4

7.636

7.687

Texas Christian

4

8

2.918

2.918

Texas St.

6

6

2.224

2.224

Texas Tech

7

5

5.441

5.441

Texas-El Paso

2

10

0.099

0.099

Texas-San Antonio

7

5

4.416

4.416

Toledo (OH)

7

5

4.855

4.855

Troy (AL)

6

6

3.334

3.334

Tulane (LA)

7

5

4.017

4.017

Tulsa (OK)

3

9

0.741

0.741

UCLA

9

3

8.642

8.642

Utah

5

7

4.364

5.200

Utah St.

8

5

4.498

4.498

Vanderbilt (TN)

8

4

6.411

6.411

Virginia

2

10

1.091

1.919

Virginia Tech

8

4

7.519

7.519

Wake Forest (NC)

4

8

3.051

3.051

Washington

8

4

7.395

7.395

Washington St.

6

6

5.455

5.839

West Virginia

4

8

2.400

2.513

Western Kentucky

8

4

4.513

4.513

Wisconsin

9

3

7.854

7.854

Wyoming

5

7

1.294

1.294

Stage #3 is now complete. Next up is the final stage: Stage #4 - Constructing the Playoff Bracket.

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