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.

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