π-ratings (Pi-ratings) are nonlinear power ratings based on changes in play-by-play win probabilities throughout a game, naturally deemphasizing non-competitive game situations without applying arbitrary cutoffs. π-ratings are adjusted for strength of schedule (SOS) and represent the probability of beating an average FBS opponent (i.e., a team with a 50% π-rating) on a neutral field. π-ratings strike a natural balance between Elo-style ranking systems that only account for wins and losses, good for explaining past results, and pure points-based systems that are designed for predicting future outcomes.
λ-ratings (Lambda-ratings) are linear power ratings that reflect the expected margin of victory or defeat against an average FBS opponent on a neutral field (i.e., a team with a λ-rating = 0.0). These are classical power ratings in that they measure how many points better or worse a team is than average in a linear fashion. To obtain a predicted net score between two teams at a neutral site, simply take the difference in the two teams’ λ-ratings.
Examples
In the 2022 preseason, Alabama has an initial π-rating = 99% and a λ-rating = +28.3. The most average FBS team is Kansas, with a π-rating = 50% and a λ-rating = +0.0.
Thus, at a neutral site (no home-field advantage for either team), Alabama is estimated to have a 99-percent chance of beating Kansas, and the Crimson Tide would be predicted to beat the Jayhawks by 28.3 points, on average, if the game were replayed hundreds or thousands of times.
Quotients
The Quotient in the rightmost column is the basic, SOS-adjusted statistic that forms the basis of both π-ratings and λ-ratings. Derived from statistical predictive models covering 15 years of FBS football games, the Quotient is equal to λ / 246.4. Knowing the Quotient is useful for computing more advanced win probabilities and net score predictions between any two FBS teams at any stadium (home, away, neutral, etc.). Even partial home-field advantage can be assigned, which can be useful for “neutral” games that presumably favor one team over the other, like Georgia playing Oregon at Mercedes-Benz Stadium in Atlanta in Week 1 of the 2022 college football season. The Quotient-based formulas are given at the bottom of the page, below the power ratings lookup table below.
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Pi & Lambda Ratings Lookup Table
TeamCode Rank Team Nickname Head Coach π-Rating λ-Rating Quotient
8
1
Alabama
Crimson Tide
Nick Saban
99%
28.3
0.115
257
2
Georgia
Bulldogs
Kirby Smart
99%
27.6
0.112
518
3
Ohio State
Buckeyes
Ryan Day
98%
26.9
0.109
147
4
Clemson
Tigers
Dabo Swinney
95%
19.8
0.080
418
5
Michigan
Wolverines
Jim Harbaugh
95%
18.8
0.076
697
6
Texas A&M
Aggies
Jimbo Fisher
93%
16.9
0.069
694
7
Tennessee
Volunteers
Josh Heupel
92%
15.5
0.063
430
8
Mississippi State
Bulldogs
Mike Leach
90%
14.7
0.060
539
9
Penn State
Nittany Lions
James Franklin
90%
14.0
0.057
545
10
Pittsburgh
Panthers
Pat Narduzzi
88%
12.8
0.052
796
11
Wisconsin
Badgers
Paul Chryst
88%
12.7
0.052
367
12
Louisville
Cardinals
Scott Satterfield
87%
12.5
0.051
559
13
Purdue
Boilermakers
Jeff Brohm
87%
12.4
0.050
463
14
Nebraska
Cornhuskers
Scott Frost
87%
12.3
0.050
703
15
Texas
Longhorns
Steve Sarkisian
87%
12.3
0.050
416
16
Michigan State
Spartans
Mel Tucker
87%
12.1
0.049
513
17
Notre Dame
Fighting Irish
Marcus Freeman
86%
12.1
0.049
732
18
Utah
Utes
Kyle Whittingham
86%
12.0
0.049
365
19
LSU
Tigers
Brian Kelly
86%
11.8
0.048
235
20
Florida
Gators
Billy Napier
86%
11.8
0.048
428
21
Minnesota
Golden Gophers
P.J. Fleck
86%
11.8
0.048
31
22
Arkansas
Razorbacks
Sam Pittman
86%
11.8
0.048
522
23
Oklahoma
Sooners
Brent Venables
86%
11.7
0.047
234
24
Florida State
Seminoles
Mike Norvell
85%
11.2
0.045
415
25
Miami (FL)
Hurricanes
Mario Cristobal
84%
10.9
0.044
657
26
USC
Trojans
Lincoln Riley
84%
10.9
0.044
529
27
Oregon
Ducks
Dan Lanning
84%
10.8
0.044
37
28
Auburn
Tigers
Bryan Harsin
84%
10.7
0.043
334
29
Kentucky
Wildcats
Mark Stoops
83%
10.5
0.043
490
30
NC State
Wolfpack
Dave Doeren
83%
10.2
0.041
521
31
Oklahoma State
Cowboys
Mike Gundy
83%
10.2
0.041
698
32
TCU
Horned Frogs
Sonny Dykes
82%
10.0
0.041
433
33
Ole Miss
Rebels
Lane Kiffin
80%
9.1
0.037
648
34
South Carolina
Gamecocks
Shane Beamer
80%
9.1
0.037
140
35
Cincinnati
Bearcats
Luke Fickell
80%
9.0
0.037
749
36
Wake Forest
Demon Deacons
Dave Clawson
80%
8.9
0.036
312
37
Iowa
Hawkeyes
Kirk Ferentz
79%
8.6
0.035
51
38
Baylor
Bears
Dave Aranda
79%
8.5
0.034
77
39
BYU
Cougars
Kalani Sitake
77%
8.0
0.032
110
40
UCLA
Bruins
Chip Kelly
76%
7.4
0.030
327
41
Kansas State
Wildcats
Chris Klieman
75%
7.2
0.029
29
42
Arizona
Wildcats
Jedd Fisch
75%
7.1
0.029
392
43
Maryland
Terrapins
Mike Locksley
74%
6.8
0.028
434
44
Missouri
Tigers
Eliah Drinkwitz
73%
6.5
0.026
768
45
West Virginia
Mountaineers
Neal Brown
69%
5.3
0.022
457
46
North Carolina
Tar Heels
Mack Brown
67%
4.8
0.019
128
47
UCF
Knights
Gus Malzahn
66%
4.3
0.017
528
48
Oregon State
Beavers
Jonathan Smith
65%
4.1
0.017
754
49
Washington State
Cougars
Jake Dickert
65%
4.0
0.016
746
50
Virginia
Cavaliers
Tony Elliott
64%
3.8
0.015
721
51
Air Force
Falcons
Troy Calhoun
64%
3.8
0.015
311
52
Iowa State
Cyclones
Matt Campbell
64%
3.7
0.015
756
53
Washington
Huskies
Kalen DeBoer
63%
3.4
0.014
66
54
Boise State
Broncos
Andy Avalos
61%
3.0
0.012
28
55
Arizona State
Sun Devils
Herm Edwards
61%
2.8
0.011
663
56
SMU
Mustangs
Rhett Lashlee
60%
2.6
0.011
688
57
Syracuse
Orange
Dino Babers
56%
1.6
0.006
27
58
App State
Mountaineers
Shawn Clark
56%
1.6
0.006
96
59
Fresno State
Bulldogs
Jeff Tedford
56%
1.4
0.006
674
60
Stanford
Cardinal
David Shaw
55%
1.3
0.005
700
61
Texas Tech
Red Raiders
Joey McGuire
52%
0.5
0.002
149
62
Coastal Carolina
Chanticleers
Jamey Chadwell
51%
0.3
0.001
651
63
South Florida
Bulls
Jeff Scott
51%
0.3
0.001
328
64
Kansas
Jayhawks
Lance Leipold
50%
0.0
0.000
709
65
Toledo
Rockets
Jason Candle
49%
-0.1
0.000
706
66
UTSA
Roadrunners
Jeff Traylor
49%
-0.2
-0.001
404
67
Memphis
Tigers
Ryan Silverfield
49%
-0.3
-0.001
288
68
Houston
Cougars
Dana Holgorsen
46%
-1.1
-0.004
355
69
Liberty
Flames
Hugh Freeze
45%
-1.3
-0.005
587
70
Rutgers
Scarlet Knights
Greg Schiano
45%
-1.4
-0.006
9
71
UAB
Blazers
Bryant Vincent
43%
-1.8
-0.007
254
72
Georgia State
Panthers
Shawn Elliott
43%
-1.8
-0.007
725
73
Army
Black Knights
Jeff Monken
41%
-2.4
-0.010
67
74
Boston College
Eagles
Jeff Hafley
41%
-2.4
-0.010
255
75
Georgia Tech
Yellow Jackets
Geoff Collins
41%
-2.5
-0.010
306
76
Indiana
Hoosiers
Tom Allen
40%
-2.6
-0.011
671
77
Louisiana
Ragin' Cajuns
Michael Desormeaux
39%
-2.8
-0.011
388
78
Marshall
Thundering Herd
Charles Huff
39%
-3.0
-0.012
718
79
Tulane
Green Wave
Willie Fritz
38%
-3.1
-0.013
107
80
Cal
Golden Bears
Justin Wilcox
38%
-3.1
-0.013
626
81
San Diego State
Aztecs
Brady Hoke
37%
-3.4
-0.014
301
82
Illinois
Fighting Illini
Bret Bielema
36%
-3.8
-0.015
736
83
Vanderbilt
Commodores
Clark Lea
35%
-4.0
-0.016
317
84
James Madison
Dukes
Curt Cignetti
34%
-4.2
-0.017
129
85
Central Michigan
Chippewas
Jim McElwain
33%
-4.6
-0.019
742
86
Virginia Tech
Hokies
Brent Pry
33%
-4.7
-0.019
196
87
East Carolina
Pirates
Mike Houston
32%
-5.0
-0.020
503
88
Northern Illinois
Huskies
Thomas Hammock
31%
-5.2
-0.021
157
89
Colorado
Buffaloes
Karl Dorrell
30%
-5.4
-0.022
509
90
Northwestern
Wildcats
Pat Fitzgerald
30%
-5.6
-0.023
497
91
North Texas
Mean Green
Seth Littrell
30%
-5.6
-0.023
414
92
Miami (OH)
RedHawks
Chuck Martin
29%
-5.8
-0.024
458
93
Charlotte
49ers
Will Healy
28%
-6.1
-0.025
772
94
Western Kentucky
Hilltoppers
Tyson Helton
27%
-6.4
-0.026
664
95
Southern Miss
Golden Eagles
Will Hall
26%
-6.7
-0.027
731
96
Utah State
Aggies
Blake Anderson
26%
-6.9
-0.028
193
97
Duke
Blue Devils
Mike Elko
24%
-7.5
-0.030
726
98
Navy
Midshipmen
Ken Niumatalolo
21%
-8.6
-0.035
574
99
Rice
Owls
Mike Bloomgren
21%
-8.7
-0.035
419
100
MTSU
Blue Raiders
Rick Stockstill
20%
-9.1
-0.037
523
101
Old Dominion
Monarchs
Ricky Rahne
20%
-9.1
-0.037
253
102
Georgia Southern
Eagles
Clay Helton
19%
-9.4
-0.038
704
103
UTEP
Miners
Dana Dimel
19%
-9.6
-0.039
229
104
Florida Atlantic
Owls
Willie Taggart
19%
-9.6
-0.039
719
105
Tulsa
Golden Hurricane
Philip Montgomery
17%
-10.4
-0.042
716
106
Troy
Trojans
Jon Sumrall
16%
-10.7
-0.043
774
107
Western Michigan
Broncos
Tim Lester
16%
-11.0
-0.045
331
108
Kent State
Golden Flashes
Sean Lewis
15%
-11.1
-0.045
670
109
Texas State
Bobcats
Jake Spavital
15%
-11.5
-0.047
366
110
Louisiana Tech
Bulldogs
Sonny Cumbie
14%
-11.9
-0.048
71
111
Bowling Green
Falcons
Scot Loeffler
13%
-12.1
-0.049
811
112
Wyoming
Cowboys
Craig Bohl
13%
-12.2
-0.050
204
113
Eastern Michigan
Eagles
Chris Creighton
13%
-12.4
-0.050
86
114
Buffalo
Bulls
Maurice Linguist
13%
-12.4
-0.050
630
115
San Jose State
Spartans
Brent Brennan
12%
-12.7
-0.052
465
116
UNLV
Rebels
Marcus Arroyo
11%
-13.5
-0.055
231
117
FIU
Panthers
Mike MacIntyre
10%
-14.0
-0.057
156
118
Colorado State
Rams
Jay Norvell
10%
-14.3
-0.058
400
119
UMASS
Minutemen
Don Brown
9%
-14.9
-0.060
519
120
Ohio
Bobcats
Tim Albin
9%
-15.2
-0.062
30
121
Arkansas State
Red Wolves
Butch Jones
8%
-15.9
-0.065
498
122
ULM
Warhawks
Terry Bowden
7%
-16.5
-0.067
646
123
South Alabama
Jaguars
Kane Wommack
7%
-16.8
-0.068
473
124
New Mexico
Lobos
Danny Gonzales
6%
-17.5
-0.071
466
125
Nevada
Wolf Pack
Ken Wilson
5%
-18.6
-0.075
472
126
NM State
Aggies
Jerry Kill
5%
-19.7
-0.080
690
127
Temple
Owls
Stan Drayton
5%
-19.8
-0.080
47
128
Ball State
Cardinals
Mike Neu
4%
-20.5
-0.083
164
129
UCONN
Huskies
Jim Mora
4%
-21.1
-0.086
5
130
Akron
Zips
Joe Moorhead
3%
-22.3
-0.091
277
131
Hawai'i
Rainbow Warriors
Timmy Chang
3%
-23.0
-0.093
Rank Team Nickname Head Coach π-Rating λ-Rating
TeamCode | Rank | Team | Nickname | Head Coach | π-Rating | λ-Rating | Quotient |
---|---|---|---|---|---|---|---|
8 | 1 | Alabama | Crimson Tide | Nick Saban | 99% | 28.3 | 0.115 |
257 | 2 | Georgia | Bulldogs | Kirby Smart | 99% | 27.6 | 0.112 |
518 | 3 | Ohio State | Buckeyes | Ryan Day | 98% | 26.9 | 0.109 |
147 | 4 | Clemson | Tigers | Dabo Swinney | 95% | 19.8 | 0.080 |
418 | 5 | Michigan | Wolverines | Jim Harbaugh | 95% | 18.8 | 0.076 |
697 | 6 | Texas A&M | Aggies | Jimbo Fisher | 93% | 16.9 | 0.069 |
694 | 7 | Tennessee | Volunteers | Josh Heupel | 92% | 15.5 | 0.063 |
430 | 8 | Mississippi State | Bulldogs | Mike Leach | 90% | 14.7 | 0.060 |
539 | 9 | Penn State | Nittany Lions | James Franklin | 90% | 14.0 | 0.057 |
545 | 10 | Pittsburgh | Panthers | Pat Narduzzi | 88% | 12.8 | 0.052 |
796 | 11 | Wisconsin | Badgers | Paul Chryst | 88% | 12.7 | 0.052 |
367 | 12 | Louisville | Cardinals | Scott Satterfield | 87% | 12.5 | 0.051 |
559 | 13 | Purdue | Boilermakers | Jeff Brohm | 87% | 12.4 | 0.050 |
463 | 14 | Nebraska | Cornhuskers | Scott Frost | 87% | 12.3 | 0.050 |
703 | 15 | Texas | Longhorns | Steve Sarkisian | 87% | 12.3 | 0.050 |
416 | 16 | Michigan State | Spartans | Mel Tucker | 87% | 12.1 | 0.049 |
513 | 17 | Notre Dame | Fighting Irish | Marcus Freeman | 86% | 12.1 | 0.049 |
732 | 18 | Utah | Utes | Kyle Whittingham | 86% | 12.0 | 0.049 |
365 | 19 | LSU | Tigers | Brian Kelly | 86% | 11.8 | 0.048 |
235 | 20 | Florida | Gators | Billy Napier | 86% | 11.8 | 0.048 |
428 | 21 | Minnesota | Golden Gophers | P.J. Fleck | 86% | 11.8 | 0.048 |
31 | 22 | Arkansas | Razorbacks | Sam Pittman | 86% | 11.8 | 0.048 |
522 | 23 | Oklahoma | Sooners | Brent Venables | 86% | 11.7 | 0.047 |
234 | 24 | Florida State | Seminoles | Mike Norvell | 85% | 11.2 | 0.045 |
415 | 25 | Miami (FL) | Hurricanes | Mario Cristobal | 84% | 10.9 | 0.044 |
657 | 26 | USC | Trojans | Lincoln Riley | 84% | 10.9 | 0.044 |
529 | 27 | Oregon | Ducks | Dan Lanning | 84% | 10.8 | 0.044 |
37 | 28 | Auburn | Tigers | Bryan Harsin | 84% | 10.7 | 0.043 |
334 | 29 | Kentucky | Wildcats | Mark Stoops | 83% | 10.5 | 0.043 |
490 | 30 | NC State | Wolfpack | Dave Doeren | 83% | 10.2 | 0.041 |
521 | 31 | Oklahoma State | Cowboys | Mike Gundy | 83% | 10.2 | 0.041 |
698 | 32 | TCU | Horned Frogs | Sonny Dykes | 82% | 10.0 | 0.041 |
433 | 33 | Ole Miss | Rebels | Lane Kiffin | 80% | 9.1 | 0.037 |
648 | 34 | South Carolina | Gamecocks | Shane Beamer | 80% | 9.1 | 0.037 |
140 | 35 | Cincinnati | Bearcats | Luke Fickell | 80% | 9.0 | 0.037 |
749 | 36 | Wake Forest | Demon Deacons | Dave Clawson | 80% | 8.9 | 0.036 |
312 | 37 | Iowa | Hawkeyes | Kirk Ferentz | 79% | 8.6 | 0.035 |
51 | 38 | Baylor | Bears | Dave Aranda | 79% | 8.5 | 0.034 |
77 | 39 | BYU | Cougars | Kalani Sitake | 77% | 8.0 | 0.032 |
110 | 40 | UCLA | Bruins | Chip Kelly | 76% | 7.4 | 0.030 |
327 | 41 | Kansas State | Wildcats | Chris Klieman | 75% | 7.2 | 0.029 |
29 | 42 | Arizona | Wildcats | Jedd Fisch | 75% | 7.1 | 0.029 |
392 | 43 | Maryland | Terrapins | Mike Locksley | 74% | 6.8 | 0.028 |
434 | 44 | Missouri | Tigers | Eliah Drinkwitz | 73% | 6.5 | 0.026 |
768 | 45 | West Virginia | Mountaineers | Neal Brown | 69% | 5.3 | 0.022 |
457 | 46 | North Carolina | Tar Heels | Mack Brown | 67% | 4.8 | 0.019 |
128 | 47 | UCF | Knights | Gus Malzahn | 66% | 4.3 | 0.017 |
528 | 48 | Oregon State | Beavers | Jonathan Smith | 65% | 4.1 | 0.017 |
754 | 49 | Washington State | Cougars | Jake Dickert | 65% | 4.0 | 0.016 |
746 | 50 | Virginia | Cavaliers | Tony Elliott | 64% | 3.8 | 0.015 |
721 | 51 | Air Force | Falcons | Troy Calhoun | 64% | 3.8 | 0.015 |
311 | 52 | Iowa State | Cyclones | Matt Campbell | 64% | 3.7 | 0.015 |
756 | 53 | Washington | Huskies | Kalen DeBoer | 63% | 3.4 | 0.014 |
66 | 54 | Boise State | Broncos | Andy Avalos | 61% | 3.0 | 0.012 |
28 | 55 | Arizona State | Sun Devils | Herm Edwards | 61% | 2.8 | 0.011 |
663 | 56 | SMU | Mustangs | Rhett Lashlee | 60% | 2.6 | 0.011 |
688 | 57 | Syracuse | Orange | Dino Babers | 56% | 1.6 | 0.006 |
27 | 58 | App State | Mountaineers | Shawn Clark | 56% | 1.6 | 0.006 |
96 | 59 | Fresno State | Bulldogs | Jeff Tedford | 56% | 1.4 | 0.006 |
674 | 60 | Stanford | Cardinal | David Shaw | 55% | 1.3 | 0.005 |
700 | 61 | Texas Tech | Red Raiders | Joey McGuire | 52% | 0.5 | 0.002 |
149 | 62 | Coastal Carolina | Chanticleers | Jamey Chadwell | 51% | 0.3 | 0.001 |
651 | 63 | South Florida | Bulls | Jeff Scott | 51% | 0.3 | 0.001 |
328 | 64 | Kansas | Jayhawks | Lance Leipold | 50% | 0.0 | 0.000 |
709 | 65 | Toledo | Rockets | Jason Candle | 49% | -0.1 | 0.000 |
706 | 66 | UTSA | Roadrunners | Jeff Traylor | 49% | -0.2 | -0.001 |
404 | 67 | Memphis | Tigers | Ryan Silverfield | 49% | -0.3 | -0.001 |
288 | 68 | Houston | Cougars | Dana Holgorsen | 46% | -1.1 | -0.004 |
355 | 69 | Liberty | Flames | Hugh Freeze | 45% | -1.3 | -0.005 |
587 | 70 | Rutgers | Scarlet Knights | Greg Schiano | 45% | -1.4 | -0.006 |
9 | 71 | UAB | Blazers | Bryant Vincent | 43% | -1.8 | -0.007 |
254 | 72 | Georgia State | Panthers | Shawn Elliott | 43% | -1.8 | -0.007 |
725 | 73 | Army | Black Knights | Jeff Monken | 41% | -2.4 | -0.010 |
67 | 74 | Boston College | Eagles | Jeff Hafley | 41% | -2.4 | -0.010 |
255 | 75 | Georgia Tech | Yellow Jackets | Geoff Collins | 41% | -2.5 | -0.010 |
306 | 76 | Indiana | Hoosiers | Tom Allen | 40% | -2.6 | -0.011 |
671 | 77 | Louisiana | Ragin' Cajuns | Michael Desormeaux | 39% | -2.8 | -0.011 |
388 | 78 | Marshall | Thundering Herd | Charles Huff | 39% | -3.0 | -0.012 |
718 | 79 | Tulane | Green Wave | Willie Fritz | 38% | -3.1 | -0.013 |
107 | 80 | Cal | Golden Bears | Justin Wilcox | 38% | -3.1 | -0.013 |
626 | 81 | San Diego State | Aztecs | Brady Hoke | 37% | -3.4 | -0.014 |
301 | 82 | Illinois | Fighting Illini | Bret Bielema | 36% | -3.8 | -0.015 |
736 | 83 | Vanderbilt | Commodores | Clark Lea | 35% | -4.0 | -0.016 |
317 | 84 | James Madison | Dukes | Curt Cignetti | 34% | -4.2 | -0.017 |
129 | 85 | Central Michigan | Chippewas | Jim McElwain | 33% | -4.6 | -0.019 |
742 | 86 | Virginia Tech | Hokies | Brent Pry | 33% | -4.7 | -0.019 |
196 | 87 | East Carolina | Pirates | Mike Houston | 32% | -5.0 | -0.020 |
503 | 88 | Northern Illinois | Huskies | Thomas Hammock | 31% | -5.2 | -0.021 |
157 | 89 | Colorado | Buffaloes | Karl Dorrell | 30% | -5.4 | -0.022 |
509 | 90 | Northwestern | Wildcats | Pat Fitzgerald | 30% | -5.6 | -0.023 |
497 | 91 | North Texas | Mean Green | Seth Littrell | 30% | -5.6 | -0.023 |
414 | 92 | Miami (OH) | RedHawks | Chuck Martin | 29% | -5.8 | -0.024 |
458 | 93 | Charlotte | 49ers | Will Healy | 28% | -6.1 | -0.025 |
772 | 94 | Western Kentucky | Hilltoppers | Tyson Helton | 27% | -6.4 | -0.026 |
664 | 95 | Southern Miss | Golden Eagles | Will Hall | 26% | -6.7 | -0.027 |
731 | 96 | Utah State | Aggies | Blake Anderson | 26% | -6.9 | -0.028 |
193 | 97 | Duke | Blue Devils | Mike Elko | 24% | -7.5 | -0.030 |
726 | 98 | Navy | Midshipmen | Ken Niumatalolo | 21% | -8.6 | -0.035 |
574 | 99 | Rice | Owls | Mike Bloomgren | 21% | -8.7 | -0.035 |
419 | 100 | MTSU | Blue Raiders | Rick Stockstill | 20% | -9.1 | -0.037 |
523 | 101 | Old Dominion | Monarchs | Ricky Rahne | 20% | -9.1 | -0.037 |
253 | 102 | Georgia Southern | Eagles | Clay Helton | 19% | -9.4 | -0.038 |
704 | 103 | UTEP | Miners | Dana Dimel | 19% | -9.6 | -0.039 |
229 | 104 | Florida Atlantic | Owls | Willie Taggart | 19% | -9.6 | -0.039 |
719 | 105 | Tulsa | Golden Hurricane | Philip Montgomery | 17% | -10.4 | -0.042 |
716 | 106 | Troy | Trojans | Jon Sumrall | 16% | -10.7 | -0.043 |
774 | 107 | Western Michigan | Broncos | Tim Lester | 16% | -11.0 | -0.045 |
331 | 108 | Kent State | Golden Flashes | Sean Lewis | 15% | -11.1 | -0.045 |
670 | 109 | Texas State | Bobcats | Jake Spavital | 15% | -11.5 | -0.047 |
366 | 110 | Louisiana Tech | Bulldogs | Sonny Cumbie | 14% | -11.9 | -0.048 |
71 | 111 | Bowling Green | Falcons | Scot Loeffler | 13% | -12.1 | -0.049 |
811 | 112 | Wyoming | Cowboys | Craig Bohl | 13% | -12.2 | -0.050 |
204 | 113 | Eastern Michigan | Eagles | Chris Creighton | 13% | -12.4 | -0.050 |
86 | 114 | Buffalo | Bulls | Maurice Linguist | 13% | -12.4 | -0.050 |
630 | 115 | San Jose State | Spartans | Brent Brennan | 12% | -12.7 | -0.052 |
465 | 116 | UNLV | Rebels | Marcus Arroyo | 11% | -13.5 | -0.055 |
231 | 117 | FIU | Panthers | Mike MacIntyre | 10% | -14.0 | -0.057 |
156 | 118 | Colorado State | Rams | Jay Norvell | 10% | -14.3 | -0.058 |
400 | 119 | UMASS | Minutemen | Don Brown | 9% | -14.9 | -0.060 |
519 | 120 | Ohio | Bobcats | Tim Albin | 9% | -15.2 | -0.062 |
30 | 121 | Arkansas State | Red Wolves | Butch Jones | 8% | -15.9 | -0.065 |
498 | 122 | ULM | Warhawks | Terry Bowden | 7% | -16.5 | -0.067 |
646 | 123 | South Alabama | Jaguars | Kane Wommack | 7% | -16.8 | -0.068 |
473 | 124 | New Mexico | Lobos | Danny Gonzales | 6% | -17.5 | -0.071 |
466 | 125 | Nevada | Wolf Pack | Ken Wilson | 5% | -18.6 | -0.075 |
472 | 126 | NM State | Aggies | Jerry Kill | 5% | -19.7 | -0.080 |
690 | 127 | Temple | Owls | Stan Drayton | 5% | -19.8 | -0.080 |
47 | 128 | Ball State | Cardinals | Mike Neu | 4% | -20.5 | -0.083 |
164 | 129 | UCONN | Huskies | Jim Mora | 4% | -21.1 | -0.086 |
5 | 130 | Akron | Zips | Joe Moorhead | 3% | -22.3 | -0.091 |
277 | 131 | Hawai'i | Rainbow Warriors | Timmy Chang | 3% | -23.0 | -0.093 |
Rank | Team | Nickname | Head Coach | π-Rating | λ-Rating |
Quotient Formulas
To compute the win probability of Team A vs Team B, look up their corresponding Quotients.
We’ll label these Q(A) and Q(B). All the computations below will be relative to Team A; i.e., the win probability and net points predictions will be for Team A.
Next, determine the home-field advantage (HFA) index:
- HFA = -0.50 → Team B’s home stadium
- HFA = 0.00 → Purely neutral site
- HFA = 0.50 → Team A’s home stadium
Alternative HFA indexes can also be used, which requires some judgment on behalf of the user. For example, in the aforementioned Oregon v. Georgia game in Atlanta, the College Football Atlas prediction models would assume an HFA = -0.25 for Oregon, since they are traveling across the country to the home state of the Bulldogs and will likely play in front of a hostile crowd. However, Georgia is not ascribed a full home-field advantage since they, too, must travel at least some distance and play away from the familiar confines of Sanford Stadium in Athens.
Note that there is no perfect answer for the HFA index. Use your best judgment. Choosing something reasonable within the [-0.50,+0.50] range will yield good results.
Once you have acquired team Quotients and set the HFA index, you can calculate win probability and predicted net score using the following formulas:
- First, compute Q = Q(A) – Q(B)
Net Score Prediction
- Net Score (A) = 5.34*HFA + 246.4*Q
Estimated Win Probability
- Win Probability (A) = 100 * { 1 / [ 1 + exp(-0.764*HFA – 37.8*Q) ] }
In the Win Probability formulas, exp refers to the natural exponent function. Calculators and spreadsheets, like Excel, will make this function readily available. The factor 100 converts the initial win proportion into the more familiar win probability.