Thursday, October 22, 2009

Methodology

My methodology for developing these rankings is based on the following three questions:

1. Given only a game's final score: if that score were the average score of an infinite number of games played between teams A and B, what are the chances team A beats B in any given game?
2. What are A's chances against B on a neutral site?
3. What are A's chances against an average team on a neutral site?

Now to delve a little further into each one.
1. Bill James came up with a fantastic formula called Pythagorean expectation.  The numbers in this formula are squared (for baseball), but only because it's convenient, and close enough; the exponent is actually a bit different, and will vary from sport to sport.  Basketball would use a variant around 15, the NFL in the mid-2s and NCAA football around 3.  (To find that number, I would simply solve for the number that gives the lowest standard deviation among the average differences of actual vs. expected win percentages.)

This comes in handy when figuring out how two teams fared against each other.  For example: if you were to take all bowl games Penn State has played in (since 1922) and only had the total number of points to go on, you'd see that they scored 855 and allowed 671.  Using the Pythagorean formula - revised for college football - you'd come out with (855 ^ 3) / ((855 ^ 3)+(671 ^ 3)) = 0.674.  You could conclude that in those 41 games, they'd win approximately 2 out of every 3.  In fact, their record is 26-13-2, or 0.658, a mere 0.016 difference.

Likewise, given any single game, you can measure their strength of victory using the same technique, to find each team's "game score."  If you were to always shutout your opponent, you'd win 100% of the time, so a shutout yields a score of 1.0.  A tie would yield a 0.5, and a 31-10 win would give you a 0.968.  In other words, if all you knew was that a game played over and over again averaged 31-10 for team A, you'd expect that team to win almost 97% of the time.

2. To make these results more relevant, we then account for home field advantage.  Since the home team, in general, wins about 60% of the time, we can build that advantage into the formula by raising the visiting team's score and lowering the home team's.  If two teams score the same number of points, but one team has home field every time, we can assume that the visiting team is actually a bit better and would win more often if playing on a neutral site or at home.  Therefore, a different formula is used for each, such that an average 20-17 win for the home team (or a game score of about 0.6) turns into a 0.5 for both teams, as they are essentially even when accounting for home field.  Here are the formulas, where GS represents the game score reached in step 1:
Home team: (GS * (1-0.6)) / ((GS * (1-0.6) + ((1-GS) * 0.6))
Away team: (GS * 0.6) / ((GS * 0.6) + ((1-GS) * (1-0.6)))

3. At this point, we can tell how each team did against each other in a given game, and average all the games together to get a pretty accurate measure of how they've done.  But we want to compare them to the league as a whole, which is where strength of schedule comes in.  By replacing 0.6 in the latter (away team) formula above with the opponent's site-adjusted game score average, we arrive at a better measure of how good a game was played by any team on any given day.  That is, if a bad team loses a close game to the best team in football, they deserve credit for not being blown out.

The problem that comes into play here is one of circular references: you can't use each team's "final" adjusted number to adjust that of another team it's played.  To avoid this, I simply run step 3 based on the numbers returned from step 2 and then use those results, and then replace them over and over again until the results get more and more narrow and any further iterations don't affect the rankings.

Keep in mind, this doesn't take wins and losses into account.  A team that has a few very close losses to good teams (like the 2009 Sooners) will still rank highly - I don't presume it will take the place of the BCS anytime soon but it is a pretty good way to rank teams' overall performance and determine how they will do in the future.

Wednesday, October 14, 2009

Week 5 NFL Rankings

...And for part two, here are my NFL rankings after Week 5 of the 2009 season.  I'll explain the rating system in the next post.



Team

W
L
T
G
W%
PF
PA
1
New Orleans Saints
.886
4
0
0
4
1.000
144
66
2
Indianapolis Colts
.883
5
0
0
5
1.000
137
71
3
Denver Broncos
.865
5
0
0
5
1.000
99
43
4
New York Giants
.856
5
0
0
5
1.000
151
71
5
Cincinnati Bengals
.809
3
1
0
4
.750
78
70
6
Baltimore Ravens
.797
3
2
0
5
.600
138
97
7
New England Patriots
.747
3
2
0
5
.600
104
91
8
Pittsburgh Steelers
.743
3
2
0
5
.600
113
98
9
Chicago Bears
.743
3
1
0
4
.750
105
78
10
Minnesota Vikings
.721
5
0
0
5
1.000
156
90
11
Dallas Cowboys
.714
3
2
0
5
.600
122
98
12
San Diego Chargers
.712
2
2
0
4
.500
101
102
13
San Francisco 49ers
.660
3
2
0
5
.600
112
98
14
Miami Dolphins
.648
2
3
0
5
.400
112
106
15
New York Jets
.637
3
2
0
5
.600
101
88
16
Seattle Seahawks
.621
2
3
0
5
.400
115
82
17
Green Bay Packers
.589
2
2
0
4
.500
104
93
18
Atlanta Falcons
.564
3
1
0
4
.750
102
63
19
Arizona Cardinals
.538
2
2
0
4
.500
85
89
20
Philadelphia Eagles
.514
3
1
0
4
.750
127
86
21
Houston Texans
.491
2
3
0
5
.400
115
120
22
Jacksonville Jaguars
.384
2
3
0
5
.400
97
127
23
Detroit Lions
.356
1
4
0
5
.200
103
162
24
Kansas City Chiefs
.312
0
5
0
5
.000
84
138
25
Tennessee Titans
.307
0
5
0
5
.000
84
139
26
Carolina Panthers
.297
1
3
0
4
.250
57
104
27
Cleveland Browns
.261
1
3
0
4
.250
35
98
28
Washington Redskins
.205
2
3
0
5
.400
73
82
29
Oakland Raiders
.183
1
4
0
5
.200
49
130
30
Buffalo Bills
.135
1
4
0
5
.200
77
116
31
Tampa Bay Buccaneers
.110
0
5
0
5
.000
68
140
32
St. Louis Rams
.098
0
5
0
5
.000
34
146

NCAA Football Rankings

Welcome to 2nd and 2! Below are my inaugural college football rankings, as of Tuesday, 10/13/09. This is a computer ranking system that I will explain in a later post.

Keep in mind these ratings ONLY account for FBS (Div. 1A) games; that is, where both teams appear on this list. NFL rankings to come.

Team W L Pct PF PA Rate
1 Florida 4 0 1.000 133 29 .956
2 Alabama 6 0 1.000 222 75 .933
3 Boise State 4 0 1.000 167 56 .892
4 Nebraska 4 1 .800 184 40 .875
5 Texas 5 0 1.000 236 75 .858
6 TCU 4 0 1.000 103 55 .853
7 Virginia Tech 5 1 .833 205 106 .831
8 South Florida 3 0 1.000 86 40 .826
9 Cincinnati 4 0 1.000 140 66 .817
10 Iowa 5 0 1.000 137 79 .762
11 Oklahoma 2 2 .500 111 42 .762
12 USC 4 1 .800 144 43 .749
13 Kansas 4 0 1.000 154 87 .707
14 Arizona 2 2 .500 106 101 .696
15 Miami (FL) 3 1 .750 99 102 .696
16 Oregon 5 1 .833 195 98 .688
17 LSU 5 1 .833 138 87 .668
18 Virginia 2 2 .500 111 77 .666
19 Utah 4 1 .800 137 93 .662
20 Georgia Tech 4 1 .800 162 142 .662
21 Ohio State 5 1 .833 178 72 .654
22 South Carolina 4 1 .800 126 96 .651
23 Clemson 2 3 .400 120 89 .636
24 Pittsburgh 4 1 .800 171 110 .635
25 Stanford 4 2 .667 184 122 .621
26 Notre Dame 4 1 .800 163 119 .619
27 Fresno State 1 3 .250 127 130 .608
28 West Virginia 3 1 .750 134 98 .603
29 Connecticut 2 2 .500 84 74 .599
30 BYU 5 1 .833 232 131 .594
31 Oregon State 3 2 .600 139 131 .592
32 Arkansas 2 2 .500 139 129 .581
33 Washington 3 3 .500 161 171 .574
34 Kentucky 2 3 .400 126 134 .571
35 Michigan 4 2 .667 198 147 .568
36 Northern Illinois 2 2 .500 117 86 .567
37 Florida State 1 4 .200 160 160 .558
38 Wisconsin 4 1 .800 144 140 .558
39 UCLA 3 2 .600 101 86 .557
40 Tennessee 3 3 .500 192 117 .554
41 Auburn 5 1 .833 230 163 .552
42 Duke 2 2 .500 126 125 .551
43 Rutgers 2 1 .667 72 75 .542
44 Ole Miss 2 2 .500 81 59 .541
45 Cal 2 2 .500 93 106 .523
46 Arkansas State 0 3 .000 57 92 .517
47 Arizona State 2 2 .500 99 76 .510
48 Colorado State 2 3 .400 127 134 .504
49 Missouri 3 1 .750 107 77 .504
50 Houston 3 1 .750 146 145 .504
51 Penn State 4 1 .800 135 58 .504
52 Minnesota 4 2 .667 162 143 .501
53 Texas Tech 3 2 .600 221 115 .500
54 Michigan State 2 3 .400 137 134 .497
55 Iowa State 2 3 .400 127 124 .492
56 Idaho 5 1 .833 172 153 .492
57 Boston College 3 2 .600 110 125 .480
58 Troy 2 2 .500 77 128 .477
59 Oklahoma State 3 1 .750 136 110 .477
60 North Carolina 2 2 .500 53 67 .475
61 Air Force 2 3 .400 106 83 .472
62 Wake Forest 3 2 .600 141 124 .466
63 Baylor 2 2 .500 84 99 .458
64 Marshall 3 2 .600 102 109 .455
65 Ohio 3 2 .600 133 131 .450
66 Central Michigan 4 1 .800 159 88 .450
67 Southern Miss 2 3 .400 131 143 .439
68 Navy 4 2 .667 190 121 .435
69 Colorado 1 4 .200 117 150 .427
70 Georgia 3 3 .500 155 184 .422
71 Bowling Green 2 4 .333 148 186 .414
72 Mississippi State 1 4 .200 120 155 .411
73 Texas A&M 3 2 .600 185 138 .401
74 Purdue 1 5 .167 171 183 .399
75 Middle Tennessee 3 2 .600 121 134 .392
76 Louisiana-Monroe 2 2 .500 109 157 .390
77 East Carolina 2 3 .400 98 125 .388
78 Indiana 2 3 .400 115 156 .385
79 Tulsa 3 1 .750 108 78 .382
80 North Texas 1 4 .200 112 169 .377
81 Florida International 1 4 .200 132 172 .374
82 Central Florida 2 2 .500 88 76 .374
83 Western Michigan 2 3 .400 135 144 .357
84 NC State 1 3 .250 93 117 .356
85 SMU 2 2 .500 94 123 .353
86 Northwestern 3 2 .600 128 123 .349
87 Louisville 1 3 .250 76 119 .347
88 Temple 3 1 .750 91 75 .342
89 UL Lafayette 2 2 .500 58 135 .339
90 Nevada 2 3 .400 141 143 .338
91 UTEP 2 4 .333 147 209 .335
92 Toledo 3 3 .500 189 247 .323
93 Wyoming 3 2 .600 107 133 .322
94 Florida Atlantic 0 4 .000 72 144 .298
95 UAB 2 3 .400 140 159 .295
96 San Diego State 1 3 .250 82 110 .281
97 Utah State 0 4 .000 81 128 .280
98 Maryland 1 4 .200 113 181 .280
99 Kansas State 1 3 .250 62 129 .265
100 Syracuse 1 4 .200 97 153 .253
101 Army 3 3 .500 112 127 .242
102 Buffalo 1 4 .200 93 151 .241
103 Vanderbilt 1 4 .200 68 94 .233
104 UNLV 1 4 .200 131 208 .226
105 Washington State 1 5 .167 89 200 .213
106 San Jose State 0 4 .000 59 151 .207
107 Memphis 1 3 .250 79 110 .202
108 Kent State 1 4 .200 100 154 .197
109 Ball State 0 5 .000 106 159 .176
110 Miami (OH) 0 6 .000 64 220 .175
111 Hawai'i 1 2 .333 77 81 .164
112 New Mexico State 2 3 .400 75 127 .149
113 Tulane 1 3 .250 43 138 .140
114 Western Kentucky 0 4 .000 62 173 .134
115 Eastern Michigan 0 5 .000 75 179 .107
116 Louisiana Tech 0 3 .000 41 106 .067
117 New Mexico 0 6 .000 87 227 .067
118 Rice 0 6 .000 99 266 .061
119 Illinois 0 4 .000 40 126 .060
120 Akron 0 4 .000 56 136 .053