The Numbers Game

Strength of Schedule Revisited

2009-10-04T22:16:00.000-07:00

In the previous discussion of schedule strength, I posed a system better than the one I was currently using, which was simply an average of opponents' team ratings. To recap this system:

Strength of Schedule
Rank all teams according to their Team Rating score.
Each opponent ranked in the top 10 is worth 3 points.
Each opponent ranked 11-30 is worth 2 points.
Each opponent ranked 31-70 is worth 1 point.
Each opponent ranked 71-100 is worth 0.5 points.
Each opponent ranked 101-120 is worth 0 points.
Each 1-AA opponent is worth 0 points.

In addition to this, teams get a bonus for playing away games. Specifically, +0.5 for playing an away game at a team in the top 70, and +0.25 for teams 71-100. Teams in the bottom 20 are so bad that playing them at home is not really a factor.

In past years, I've noticed that sometimes schedule strength is dominated by one or two conferences. Looking over results from previous seasons, it seems clear that, on the conference level, schedule strength comes down to two factors. Average team rating of the conference, and the number of non-conference games played. The first element is blindingly obvious. The better your conference is, the tougher your schedule. The second part might not be so clear. As much as people like to look down on other conferences for their scheduling of cupcakes, when it comes down to it, there's not much variation between the level of inter-league competition (especially within the 6 BCS conferences). The key is the number of non-conference games played. Since any cupcake you schedule is unlikely to be better than the average team in your conference, playing more cupcakes can only reduce your overall schedule strength.

Let's take a look at schedule strength by conference for the 2008 season.

Strength of Schedule (Conference Averages)
	Rating	SoS (Rank)	SoS (Raw)
SEC	0.534	25.42	1.415
Big Ten	0.525	38.36	1.319
Big XII	0.519	36.17	1.329
Big East	0.499	55.13	1.215
Pac-10	0.492	15.40	1.522
ACC	0.487	59.58	1.191
Mtn West	0.485	50.89	1.236
MAC	0.445	98.08	0.941
CUSA	0.444	91.08	0.974
WAC	0.441	83.44	1.096
Sun Belt	0.410	109.75	0.823

Among the 6 BCS conferences, all except the Pac-10 and Big East play 4 non-conference games a season. So the among the ACC, Big Ten, Big XII, and SEC you'd expect that their average schedule strength would be reflected by the average team rating and that's exactly what we saw last season. Now, when the NCAA expanded the schedule to 12 games, the Pac-10 used the extra game to make a proper round-robin conference schedule. So while the other BCS schools were rushing to ink deals with the Towsons and Charleston Southerns of the world, Pac-10 teams added another Pac-10 team. Look at the table. The Pac-10 was, on average, the second worst BCS conference last season, but had the highest average SoS. Conversely, the Big East who play 5 games out of conference had an average SoS worse than the Mountain West!

Sam's Big Poll (Week 9)

2007-10-31T17:58:00.001-07:00

Don't let Craig James see but South Florida is still in the top 5! Seriously though, the Bulls have the 8th best Team Rating, two quality wins (Auburn and West Virginia), and a good Strength of Schedule so who's to say they're not a top shelf team? Well, I'll come out an say it, they're not a top shelf team. They're second shelf, but they're certainly better than the pollsters, who were just waiting for them to lose, think. On to other things: Colorado, WTF? It seems every year my system produces a Colorado. A team that gets ranked way ahead of where they ought to be. Colorado is riding a tough schedule and a quality win over Oklahoma to an unthinkable 13 ranking. We'll just hope it all sorts out over the next few weeks.

Ranking = 1.2*Team Rating + 1.2*W/L Factor + 0.9*Schedule Strength

Div 1-A 2007 Rankings (Week 9)
Rank	Team Name	Score	W	L	Team Rating	W/L Factor	Schedule Strength
1	Ohio State	2.82516	9	0	1	1	91
2	LSU	2.75557	7	1	3	8	18
3	South Florida	2.70267	6	2	8	9	9
4	Oregon	2.64914	7	1	6	7	35
5	Kansas	2.63407	8	0	2	2	107
6	Auburn	2.53472	6	3	13	24	5
7	West Virginia	2.49175	7	1	5	10	61
8	Oklahoma	2.48475	7	1	4	11	65
9	Boston College	2.43798	8	0	11	3	88
10	Arizona State	2.38452	8	0	7	4	116
11	Connecticut	2.36607	7	1	9	6	100
12	Missouri	2.33941	7	1	17	12	52
13	Colorado	2.31471	5	4	40	36	3
14	California	2.30830	5	3	31	25	10
15	Virginia	2.25424	7	2	49	14	28
16	Kentucky	2.23688	6	3	30	16	40
17	Penn State	2.23665	6	3	14	32	29
18	Florida	2.20823	5	3	19	37	17
19	Texas	2.19880	6	2	16	18	55
20	Michigan	2.15957	7	2	12	17	84
21	Boise State	2.15825	7	1	21	13	104
22	Alabama	2.15362	6	2	27	15	62
23	USC	2.14710	6	2	20	19	66
24	Georgia	2.14123	6	2	36	26	32
25	Illinois	2.12235	6	3	39	31	30
26	Rutgers	2.11486	5	3	34	35	21
27	Virginia Tech	2.11276	6	2	28	27	49
28	Clemson	2.10884	6	2	22	28	63
29	Kansas State	2.06990	5	3	18	48	33
30	Wisconsin	2.05673	7	2	23	20	92
31	Cincinnati	2.03528	6	2	10	29	109
32	Purdue	2.00366	7	2	44	21	80
33	Brigham Young	1.99511	5	2	26	33	73
34	Oklahoma State	1.98258	5	3	32	49	34
35	Troy	1.98217	6	2	33	22	95
36	Oregon State	1.97806	5	3	57	50	13
37	Hawaii	1.97293	8	0	29	5	120
38	Texas A&M	1.97254	6	3	43	38	43
39	South Carolina	1.96896	6	3	38	39	46
40	New Mexico	1.94519	6	2	45	30	81
41	Arkansas	1.94473	5	3	15	51	74
42	Georgia Tech	1.93498	5	3	25	52	56
43	Wake Forest	1.93087	6	2	46	23	96
44	Mississippi State	1.93075	5	4	71	55	11
45	Florida State	1.92275	5	3	42	40	57
46	Tennessee	1.91988	5	3	60	41	36
47	Air Force	1.88752	6	3	41	42	69
48	Michigan State	1.87198	5	4	37	57	50
49	Utah	1.86930	6	3	35	34	98
50	Texas Tech	1.86710	6	3	24	43	103
51	Louisville	1.86678	5	4	53	63	16
52	Tulsa	1.86653	5	3	65	44	44
53	UCF	1.85581	5	3	59	45	53
54	Houston	1.85251	5	3	48	46	67
55	Washington	1.82518	2	6	62	92	1
56	Wyoming	1.80258	5	3	56	47	75
57	Washington State	1.79643	3	5	72	73	6
58	Miami (FL)	1.79520	5	3	54	56	54
59	Fresno State	1.78080	5	3	58	53	58
60	East Carolina	1.76432	5	4	74	58	41
61	Maryland	1.76009	4	4	52	67	22
62	Vanderbilt	1.74537	5	3	50	54	82
63	Nebraska	1.74062	4	5	64	64	20
64	Stanford	1.72846	3	5	81	74	7
65	UCLA	1.70896	5	3	55	59	68
66	TCU	1.68803	4	4	47	60	76
67	Pittsburgh	1.62513	3	5	67	75	23
68	Indiana	1.61892	5	4	68	61	64
69	Central Michigan	1.57765	5	4	75	65	47
70	Florida Atlantic	1.50360	4	4	83	66	59
71	Northwestern	1.49981	5	4	76	70	60
72	Iowa	1.49240	4	5	63	71	70
73	Ball State	1.47532	5	4	51	62	117
74	Mississippi	1.47073	2	7	88	95	8
75	Arizona	1.44404	3	6	66	93	42
76	North Carolina State	1.39363	3	5	77	86	45
77	Middle Tennessee	1.38047	4	5	61	78	99
78	Akron	1.37979	3	5	102	85	24
79	Nevada	1.36509	4	4	70	68	110
80	UTEP	1.35824	4	4	69	79	89
81	UNLV	1.35220	2	7	84	96	31
82	Miami (OH)	1.32932	4	5	94	72	71
83	Arkansas State	1.31778	3	5	80	81	77
84	Notre Dame	1.31147	1	7	114	104	2
85	Bowling Green	1.29426	4	4	78	76	105
86	Baylor	1.27525	3	5	111	87	26
87	Southern Miss	1.27094	4	4	79	80	101
88	Navy	1.25710	4	4	73	77	112
89	North Carolina	1.24928	2	6	91	102	19
90	Louisiana Tech	1.22636	3	5	92	88	78
91	San Diego State	1.21141	2	5	112	101	14
92	Duke	1.19014	1	7	110	105	15
93	New Mexico State	1.18557	4	5	100	97	48
94	Louisiana-Monroe	1.18288	3	5	90	91	86
95	San Jose State	1.14055	3	5	117	89	37
96	Toledo	1.13543	4	5	87	83	111
97	Buffalo	1.12119	4	5	82	90	113
98	Temple	1.10701	3	5	103	82	106
99	Memphis	1.10585	4	4	99	69	119
100	Ohio	1.08326	4	5	89	84	115
101	Syracuse	1.07407	2	6	115	100	38
102	Army	1.03709	3	5	96	98	97
103	Eastern Michigan	0.99015	3	6	106	99	93
104	Colorado State	0.96719	1	7	85	109	79
105	Western Kentucky	0.96538	3	3	119	94	72
106	Western Michigan	0.94764	3	6	97	107	85
107	Iowa State	0.93818	1	8	101	114	12
108	Kent State	0.92431	3	6	98	106	94
109	Minnesota	0.89571	1	8	86	111	51
110	Southern Methodist	0.87132	1	7	95	108	90
111	Marshall	0.84769	1	7	93	116	27
112	UAB	0.82277	2	6	113	103	102
113	North Texas	0.79961	1	7	116	110	39
114	Utah State	0.79805	0	8	104	117	25
115	Florida International	0.71146	0	8	120	112	4
116	Tulane	0.56342	2	6	105	113	108
117	Louisiana-Lafayette	0.49052	1	7	107	115	114
118	Idaho	0.43436	1	8	108	119	87
119	Rice	0.39790	1	7	109	120	83
120	Northern Illinois	0.11221	1	8	118	118	118

Sam's Big Poll (Week 8)

2007-10-22T19:36:00.000-07:00

Sweet Christ It's Week 8!

Ranking = 1.2*Team Rating + 1.2*W/L Factor + 0.9*Schedule Strength

Div 1-A 2007 Rankings (Week 8)
Rank	Team Name	Score	W	L	Team Rating	W/L Factor	Schedule Strength
1	Ohio State	2.66458	8	0	1	2	108
2	South Florida	2.64658	6	1	7	9	13
3	LSU	2.63943	7	1	3	7	33
4	Oklahoma	2.60081	7	1	4	1	72
5	Kansas	2.49765	7	0	2	3	116
6	Oregon	2.48522	6	1	6	10	23
7	Auburn	2.47287	5	3	17	34	3
8	Missouri	2.38529	6	1	12	13	24
9	Florida	2.35023	5	2	11	22	9
10	Arizona State	2.34365	7	0	5	4	117
11	Kentucky	2.34115	6	2	20	17	21
12	Virginia	2.33831	7	1	37	8	34
13	West Virginia	2.33675	6	1	8	11	77
14	Boston College	2.32702	7	0	14	5	107
15	California	2.25540	5	2	27	18	25
16	Penn State	2.20367	6	2	9	20	73
17	Texas	2.17086	5	2	15	23	40
18	Rutgers	2.16265	5	2	28	19	41
19	Michigan	2.15413	6	2	16	21	53
20	Virginia Tech	2.14428	6	1	31	14	68
21	Colorado	2.13526	4	4	38	44	7
22	Kansas State	2.09874	4	3	24	45	11
23	Connecticut	2.09603	6	1	13	15	111
24	USC	2.08876	6	1	18	12	112
25	Cincinnati	2.06068	6	2	10	24	94
26	Illinois	2.04922	5	3	39	40	18
27	Boise State	2.02474	6	1	21	16	114
28	South Carolina	2.02440	6	2	35	25	54
29	Alabama	2.01677	6	2	30	26	64
30	Air Force	1.99903	6	2	33	27	65
31	Brigham Young	1.97397	5	2	25	35	78
32	Oregon State	1.96869	4	3	56	59	6
33	Wisconsin	1.96334	6	2	29	28	84
34	Tennessee	1.94860	4	3	53	46	10
35	Michigan State	1.94744	5	3	32	41	44
36	Georgia	1.93138	5	2	41	36	57
37	Oklahoma State	1.92965	5	3	34	47	28
38	Texas Tech	1.92613	6	2	22	29	109
39	Texas A&M	1.92133	6	2	42	30	80
40	Clemson	1.91870	5	2	23	37	97
41	Hawaii	1.91737	7	0	36	6	120
42	Wake Forest	1.89955	5	2	54	31	69
43	Washington	1.89515	2	5	52	82	1
44	Georgia Tech	1.89376	5	3	26	48	59
45	UCLA	1.88406	5	2	45	43	35
46	Arkansas	1.87002	4	3	19	60	48
47	Florida State	1.86484	4	3	44	49	30
48	Troy	1.86279	5	2	46	32	92
49	Purdue	1.84500	6	2	51	33	95
50	Maryland	1.83307	4	3	50	61	16
51	Miami (FL)	1.82206	5	3	57	42	55
52	New Mexico	1.81729	5	2	40	38	98
53	Stanford	1.78448	3	4	71	68	8
54	Tulsa	1.75934	4	3	63	50	42
55	Fresno State	1.75373	5	2	55	39	99
56	Wyoming	1.73247	4	3	59	51	62
57	Houston	1.73247	4	3	43	52	81
58	UCF	1.71406	4	3	67	53	58
59	Navy	1.68739	4	3	68	54	63
60	Indiana	1.67777	5	3	60	55	82
61	Florida Atlantic	1.67693	4	3	80	56	43
62	Utah	1.66874	5	3	48	57	96
63	Louisville	1.66497	4	4	58	73	19
64	Nebraska	1.65408	4	4	66	62	45
65	TCU	1.65267	4	4	47	63	79
66	Washington State	1.62372	2	5	83	83	4
67	Pittsburgh	1.61480	3	4	64	70	31
68	Vanderbilt	1.60986	4	3	61	64	70
69	Mississippi State	1.60474	4	4	82	69	14
70	Ball State	1.54292	5	3	49	58	115
71	East Carolina	1.51839	4	4	79	67	39
72	Bowling Green	1.51436	4	3	70	65	89
73	Northwestern	1.50240	5	3	73	66	83
74	Akron	1.41960	3	4	92	77	20
75	Miami (OH)	1.40852	4	4	91	71	60
76	Central Michigan	1.40542	4	4	81	75	46
77	Iowa	1.36637	3	5	72	81	47
78	Mississippi	1.36447	2	6	87	86	15
79	UTEP	1.36186	4	3	77	72	93
80	Arkansas State	1.34142	3	4	69	76	90
81	Southern Miss	1.32360	4	3	75	74	104
82	Arizona	1.32144	2	6	62	101	22
83	Notre Dame	1.30518	1	7	114	104	2
84	Middle Tennessee	1.27226	3	5	65	85	85
85	Nevada	1.26514	3	4	76	78	100
86	Baylor	1.26091	3	4	106	79	49
87	UNLV	1.20473	2	6	86	87	66
88	North Carolina	1.19365	2	5	84	96	36
89	North Carolina State	1.17596	2	5	88	97	37
90	Buffalo	1.15649	3	5	85	94	67
91	San Diego State	1.14922	2	5	113	98	12
92	Temple	1.14854	3	5	98	80	86
93	Western Michigan	1.13379	3	5	89	92	74
94	Duke	1.10477	1	6	103	102	26
95	New Mexico State	1.09185	4	4	94	90	87
96	Army	1.07874	3	5	96	93	75
97	Colorado State	1.05132	1	6	74	109	50
98	San Jose State	1.05058	3	5	117	84	56
99	Syracuse	1.04895	2	6	115	95	29
100	Louisiana-Monroe	1.03927	2	5	93	100	71
101	Louisiana Tech	1.02390	2	5	90	106	51
102	Kent State	1.01005	3	5	99	103	61
103	Western Kentucky	1.00896	3	3	118	88	52
104	Toledo	0.97866	3	5	104	91	103
105	Memphis	0.94046	3	4	107	89	113
106	UAB	0.87916	2	5	111	99	101
107	Minnesota	0.83833	1	7	78	112	76
108	Southern Methodist	0.80584	1	6	97	108	102
109	Eastern Michigan	0.77315	2	6	112	107	88
110	North Texas	0.72583	1	6	119	110	27
111	Utah State	0.68916	0	7	101	115	32
112	Ohio	0.67886	3	5	100	105	119
113	Florida International	0.65172	0	7	120	113	5
114	Tulane	0.61662	2	5	110	111	105
115	Iowa State	0.58691	1	7	109	116	38
116	Marshall	0.58190	0	7	95	120	17
117	Louisiana-Lafayette	0.49052	1	7	108	114	106
118	Rice	0.40659	1	6	105	117	91
119	Idaho	0.28545	1	7	102	118	110
120	Northern Illinois	0.09993	1	7	116	119	118

Sam's Big Poll (Week 7)

2007-10-15T20:00:00.000-07:00

So the Tigers lost to Kentucky and South Florida is #1? It just doesn't feel real. I think the most interesting thing about this week it what's shown in the BCS rankings. All of the computer systems have the Bulls as the #1 team, while Ohio State is the consensus #1 amongst the polls. Do I think South Florida is the best team in the nation? Absolutely not. But I'm just as certain that Ohio State isn't either. This is a very clear case of bias in the polls. Lou Holtz even said it on Gameday Final, people won't vote South Florida #1 because they're South Florida. USF has wins over West Virginia and Auburn, both ranked teams. Ohio State hasn't played anyone better than Washington and despite racking up over 400 yards and almost 33 points per game, they have the 70th ranked offensive modulus. And normally I'd say wait until they play some real competition, but the Big Ten is so miserable this year, it may never happen. I wouldn't be suprised to see OSU ride their defense to a 12-0 record. On a slightly different note, Why the hell is USC still in the top 10? USC scraped past [generic mediocre Pac-10 team] this weekend and have been rewarded with an average 11th place ranking in the 4 major polls. In my rankings they lost 11 spots. A bit severe perhaps, but if other teams are stepping up while you're laying eggs, don't expect to keep your position just because you manage to add one to the W column. It's clearly too much to ask pollsters to use their brains when they rank teams. I can't blame the coaches, they're busy, but this is the sportswriters's jobs. Enough ranting, here's the rankings!

Ranking = 1.2*Team Rating + 1.2*W/L Factor + 0.9*Schedule Strength

Div 1-A 2007 Rankings (Week 7)
Rank	Team Name	Score	W	L	Team Rating	W/L Factor	Schedule Strength
1	South Florida	2.78123	6	0	5	1	38
2	LSU	2.71481	6	1	3	8	19
3	Ohio State	2.63564	7	0	1	2	105
4	Kentucky	2.56752	6	1	18	7	16
5	Auburn	2.53548	5	2	19	22	5
6	California	2.52888	5	1	23	9	15
7	Oregon	2.47753	5	1	6	12	25
8	Oklahoma	2.46199	6	1	4	10	48
9	Kansas	2.43729	6	0	2	3	111
10	Florida	2.38154	4	2	9	28	9
11	West Virginia	2.33399	5	1	8	13	57
12	Arizona State	2.26753	7	0	10	4	112
13	Missouri	2.22313	5	1	21	19	45
14	Kansas State	2.20455	4	2	13	45	11
15	Tennessee	2.19605	4	2	30	29	10
16	South Carolina	2.18531	6	1	29	14	49
17	Texas	2.18383	5	2	14	24	34
18	Colorado	2.17312	4	3	38	44	8
19	Cincinnati	2.13803	6	1	11	15	99
20	Penn State	2.13315	5	2	7	25	76
21	Boston College	2.10404	7	0	16	5	119
22	Illinois	2.10001	5	2	35	23	35
23	Michigan	2.09288	5	2	20	27	39
24	Texas Tech	2.08584	6	1	12	16	106
25	Virginia	2.06154	6	1	41	11	77
26	USC	2.06111	5	1	24	17	96
27	Wisconsin	2.01926	5	2	37	30	29
28	Georgia	2.00960	5	2	42	31	30
29	Brigham Young	2.00754	4	2	22	32	58
30	Troy	2.00340	4	2	64	33	18
31	Oregon State	1.98614	4	3	50	58	7
32	Virginia Tech	1.98040	6	1	34	18	100
33	Washington	1.96053	2	4	48	77	1
34	Connecticut	1.92550	5	1	17	20	115
35	Tulsa	1.92498	4	2	49	34	46
36	Hawaii	1.92304	7	0	31	6	120
37	Maryland	1.92003	4	2	45	46	26
38	Boise State	1.90689	5	1	15	21	118
39	Nebraska	1.89467	4	3	58	51	20
40	Air Force	1.85372	5	2	47	35	71
41	Purdue	1.84995	5	2	65	36	50
42	Texas A&M	1.84897	5	2	51	37	72
43	Navy	1.84627	4	2	56	38	59
44	Alabama	1.83979	5	2	39	39	78
45	Michigan State	1.79408	5	2	27	26	110
46	Wake Forest	1.78537	4	2	60	40	73
47	Wyoming	1.77861	4	2	52	41	91
48	Florida Atlantic	1.77119	3	3	84	59	12
49	Rutgers	1.75170	4	2	26	47	97
50	Mississippi State	1.75023	4	3	78	60	17
51	Stanford	1.74878	2	4	73	78	4
52	Oklahoma State	1.74756	4	3	28	61	62
53	Indiana	1.74677	5	2	59	42	87
54	Fresno State	1.74181	4	2	68	48	54
55	Florida State	1.73986	4	2	40	43	102
56	UCLA	1.73359	4	2	44	57	65
57	New Mexico	1.72041	4	2	36	49	94
58	TCU	1.71202	4	3	43	52	79
59	East Carolina	1.70297	4	3	76	53	40
60	Georgia Tech	1.67405	4	3	32	62	80
61	Arkansas	1.63781	3	3	25	70	66
62	Miami (FL)	1.63538	4	3	66	54	81
63	Washington State	1.61989	2	5	87	81	6
64	Clemson	1.59891	4	2	33	50	113
65	Houston	1.59859	3	3	53	63	83
66	Northwestern	1.58931	4	3	69	69	31
67	Utah	1.55600	4	3	54	55	107
68	UCF	1.55186	3	3	74	64	67
69	Bowling Green	1.52401	3	3	71	68	47
70	Arkansas State	1.51676	3	3	55	67	68
71	Miami (OH)	1.47822	4	3	93	56	88
72	Central Michigan	1.47720	4	3	62	66	74
73	Ball State	1.47347	4	3	46	65	109
74	Buffalo	1.47232	3	4	70	76	36
75	Arizona	1.44926	2	5	57	97	13
76	Akron	1.44819	3	4	89	74	22
77	Notre Dame	1.44135	1	6	111	102	2
78	Iowa	1.43337	3	4	61	75	63
79	Louisville	1.36837	4	3	67	73	89
80	Mississippi	1.36129	2	5	80	82	37
81	Vanderbilt	1.31627	3	3	75	71	98
82	Baylor	1.30053	3	4	101	79	41
83	UTEP	1.29628	4	3	77	72	101
84	Pittsburgh	1.28348	2	4	63	90	55
85	North Carolina	1.28299	2	5	86	98	23
86	Southern Miss	1.27022	3	3	79	84	69
87	Western Michigan	1.26764	3	4	88	86	42
88	UNLV	1.23990	2	5	82	83	75
89	San Jose State	1.23080	3	4	113	80	43
90	Nevada	1.22335	2	4	72	91	60
91	Minnesota	1.16159	1	6	85	103	44
92	San Diego State	1.14567	2	4	115	92	21
93	Duke	1.12268	1	6	103	104	32
94	Western Kentucky	1.10699	2	3	119	85	33
95	Toledo	1.09937	2	5	95	99	51
96	Kent State	1.07873	3	4	96	101	52
97	Army	1.06925	3	4	90	87	93
98	Middle Tennessee	1.06568	2	5	81	96	90
99	Temple	1.04407	2	5	99	89	82
100	Southern Methodist	1.01163	1	5	91	100	84
101	Syracuse	1.00898	1	6	118	106	14
102	Louisiana Tech	1.00843	2	4	97	93	92
103	UAB	0.99084	2	4	109	94	85
104	New Mexico State	0.93378	3	4	104	105	64
105	Louisiana-Monroe	0.85533	1	5	92	108	86
106	Ohio	0.83942	3	4	105	88	117
107	Florida International	0.83127	0	6	120	109	3
108	North Carolina State	0.82321	1	5	102	110	70
109	Colorado State	0.81581	0	6	83	113	56
110	North Texas	0.80434	1	5	117	111	27
111	Utah State	0.79738	0	6	107	112	28
112	Memphis	0.78629	2	4	108	95	116
113	Eastern Michigan	0.69322	2	5	114	107	103
114	Rice	0.57153	1	5	106	115	61
115	Iowa State	0.55941	1	6	100	118	53
116	Marshall	0.49536	0	6	94	120	24
117	Louisiana-Lafayette	0.42350	1	6	110	114	104
118	Idaho	0.40443	1	6	98	116	108
119	Tulane	0.34168	1	5	116	117	95
120	Northern Illinois	0.18398	1	6	112	119	114

Sam's Big Poll (Week 6)

2007-10-08T13:12:00.001-07:00

Here's the rankings for week 6. LSU's back on top following their defeat of the Gators in the single most intense football game I've seen in years. The ranks of undefeated teams has fallen to 11, many of which have pretty dubious credentials and are almost certainly destined to be exposed. Of the unbeatens, only LSU, Cal, and South Florida have faced serious competition. None of the other eight have schedule strength's in the top 80. BC, Cincinnati, UConn and Hawaii have SoS rankings of 112, 114, 119, and 120.

Ranking = 1.2*Team Rating + 1.2*W/L Factor + 0.9*Schedule Strength

Div 1-A 2007 Rankings (Week 6)
Rank	Team Name	Score	W	L	Team Rating	W/L Factor	Schedule Strength
1	LSU	3.010	6	0	2	3	37
2	South Florida	2.777	5	0	13	1	44
3	Ohio State	2.764	6	0	1	4	82
4	California	2.698	5	0	24	2	35
5	Oregon	2.601	4	1	10	16	11
6	Oklahoma	2.589	5	1	4	13	38
7	Kansas	2.587	5	0	3	5	96
8	Arizona State	2.574	6	0	5	6	83
9	Missouri	2.444	5	0	15	7	80
10	Colorado	2.404	4	2	29	28	13
11	Auburn	2.401	4	2	17	29	14
12	Cincinnati	2.375	6	0	6	8	114
13	Florida	2.360	4	2	8	31	19
14	South Carolina	2.353	5	1	21	17	27
15	USC	2.340	4	1	19	18	36
16	Illinois	2.314	5	1	30	12	67
17	Boston College	2.308	6	0	14	9	112
18	Washington	2.301	2	3	28	53	2
19	Kentucky	2.262	5	1	16	19	59
20	Connecticut	2.225	5	0	9	10	119
21	West Virginia	2.224	5	1	11	14	99
22	Boise State	2.187	4	1	7	30	97
23	Tennessee	2.184	3	2	41	39	7
24	Wisconsin	2.177	5	1	31	20	68
25	Texas	2.172	4	2	25	32	28
26	Penn State	2.171	4	2	12	33	60
27	Kansas State	2.156	3	2	22	54	8
28	Wyoming	2.153	4	1	40	21	52
29	Nebraska	2.109	4	2	38	34	29
30	Florida State	2.106	4	1	34	22	81
31	Troy	2.060	4	2	57	35	20
32	Virginia Tech	2.046	5	1	48	23	77
33	Tulsa	2.035	3	2	51	40	17
34	Purdue	2.020	5	1	49	24	84
35	Brigham Young	2.005	3	2	27	41	45
36	Virginia	1.998	5	1	46	15	100
37	Indiana	1.994	5	1	43	25	93
38	Texas Tech	1.984	5	1	18	26	115
39	Stanford	1.978	2	3	70	67	1
40	Hawaii	1.970	6	0	32	11	120
41	UCLA	1.946	4	2	47	52	30
42	Michigan	1.939	4	2	23	38	78
43	Texas A&M	1.929	5	1	42	27	106
44	Oregon State	1.898	3	3	58	68	4
45	Alabama	1.892	4	2	35	42	71
46	Mississippi State	1.888	4	2	75	43	25
47	Akron	1.887	3	3	86	55	5
48	Maryland	1.882	4	2	53	44	48
49	Rutgers	1.864	3	2	26	56	53
50	Georgia	1.840	4	2	44	45	72
51	Miami (FL)	1.830	4	2	59	36	79
52	Wake Forest	1.830	3	2	66	46	46
53	TCU	1.822	3	3	33	57	61
54	Air Force	1.801	4	2	65	47	62
55	Navy	1.765	3	2	62	48	73
56	Arkansas	1.759	3	2	20	58	92
57	Bowling Green	1.717	3	2	60	49	87
58	Michigan State	1.715	4	2	36	37	116
59	UCF	1.682	3	2	50	50	104
60	East Carolina	1.677	3	3	76	59	41
61	Fresno State	1.663	3	2	68	60	54
62	Houston	1.651	2	3	54	69	47
63	Washington State	1.642	2	4	67	78	15
64	Oklahoma State	1.642	3	3	39	70	69
65	Clemson	1.630	4	2	45	51	113
66	Northwestern	1.621	3	3	77	71	31
67	Georgia Tech	1.591	3	3	37	72	85
68	Florida Atlantic	1.591	3	3	87	61	49
69	New Mexico	1.588	3	2	64	62	88
70	Miami (OH)	1.569	3	3	113	63	21
71	Utah	1.558	3	3	55	64	101
72	Mississippi	1.537	2	4	79	79	32
73	Arkansas State	1.521	2	3	74	73	55
74	UTEP	1.518	4	2	69	66	90
75	San Diego State	1.508	2	3	107	87	3
76	Arizona	1.491	2	4	61	92	22
77	Vanderbilt	1.471	3	2	78	65	98
78	Buffalo	1.463	2	4	71	80	50
79	Central Michigan	1.451	3	3	63	84	63
80	Iowa	1.420	2	4	56	81	86
81	Ball State	1.384	3	3	52	77	109
82	Duke	1.348	1	5	89	100	16
83	Western Kentucky	1.333	2	2	116	82	23
84	Baylor	1.330	3	3	90	74	91
85	Pittsburgh	1.330	2	3	80	88	56
86	New Mexico State	1.311	3	3	109	89	24
87	Notre Dame	1.303	1	5	112	101	10
88	San Jose State	1.301	3	3	119	75	33
89	Western Michigan	1.298	2	4	84	93	39
90	Army	1.259	3	3	91	76	105
91	UNLV	1.259	2	4	82	83	94
92	Minnesota	1.257	1	5	81	102	42
93	North Carolina	1.196	2	4	93	94	64
94	Toledo	1.183	2	4	100	95	51
95	Louisiana-Monroe	1.162	1	4	97	96	65
96	Temple	1.149	1	5	103	103	43
97	Southern Methodist	1.141	1	4	95	97	74
98	Louisville	1.116	3	3	73	86	110
99	Southern Miss	1.110	2	3	85	104	57
100	Colorado State	1.077	0	5	72	114	18
101	Kent State	1.046	3	3	94	85	111
102	North Texas	1.034	0	5	118	107	9
103	Nevada	1.034	2	3	96	90	108
104	Middle Tennessee	0.981	1	5	88	106	75
105	Syracuse	0.979	1	5	117	105	26
106	Ohio	0.945	2	4	102	98	107
107	Memphis	0.938	2	3	92	91	117
108	Eastern Michigan	0.906	2	4	114	99	95
109	North Carolina State	0.896	1	5	101	108	70
110	Louisiana Tech	0.868	1	4	108	109	58
111	Utah State	0.847	0	6	104	116	34
112	Iowa State	0.829	1	5	83	113	76
113	UAB	0.781	1	4	106	110	89
114	Tulane	0.777	1	4	115	111	66
115	Florida International	0.773	0	6	120	112	6
116	Rice	0.753	1	4	111	115	40
117	Marshall	0.661	0	5	105	120	12
118	Louisiana-Lafayette	0.525	1	5	99	117	102
119	Idaho	0.435	1	5	98	118	103
120	Northern Illinois	0.125	1	5	110	119	118

Sam's Big Poll (Week 5)

2007-10-01T09:03:00.000-07:00

Talk amongst yourselves. Here, I'll give you a topic: Sam's Big Poll is neither big, nor a poll. Discuss.

Sure, it's just a single set of rankings, and it doesn't qualify as a "poll", but I like the name (Thanks, Lyle!) and I'm sticking to it.

The ranking is calculated as 1.2*Team Rating + W/L Factor + Schedule Strength

Div 1-A 2007 Rankings (Week 5)
Rank	Team Name	Score	W	L	Team Rating	W/L Factor	Schedule Strength
1	South Florida	2.851	4	0	7	1	21
2	LSU	2.677	5	0	1	3	98
3	California	2.559	5	0	32	2	36
4	USC	2.535	4	0	10	4	49
5	Ohio State	2.530	5	0	3	5	105
6	Wisconsin	2.471	5	0	15	6	55
7	Kentucky	2.424	5	0	11	7	84
8	Boston College	2.412	5	0	14	8	76
9	South Carolina	2.410	4	1	16	26	11
10	Oregon	2.394	4	1	9	16	37
11	Colorado	2.376	3	2	21	39	9
12	Arizona State	2.348	5	0	5	9	115
13	Nebraska	2.314	4	1	17	17	38
14	Georgia	2.309	4	1	27	27	18
15	West Virginia	2.287	4	1	6	18	74
16	Oklahoma	2.283	4	1	4	19	104
17	Missouri	2.271	4	0	43	10	77
18	Hawaii	2.225	5	0	18	11	108
19	Florida	2.222	4	1	12	20	78
20	UCLA	2.212	4	1	39	21	43
21	Texas	2.212	4	1	26	22	60
22	Auburn	2.193	3	2	24	44	16
23	Connecticut	2.188	5	0	13	12	116
24	Florida State	2.157	3	1	45	28	35
25	Cincinnati	2.144	5	0	8	13	119
26	Tulsa	2.127	3	1	46	29	44
27	Kansas	2.125	4	0	2	14	120
28	Alabama	2.105	3	2	29	51	10
29	Illinois	2.087	4	1	36	30	67
30	Brigham Young	2.063	3	2	22	45	46
31	Rutgers	2.054	3	1	20	40	72
32	Michigan State	2.034	4	1	28	23	103
33	Boise State	2.034	3	1	30	41	65
34	Clemson	2.033	4	1	40	31	83
35	Indiana	2.017	4	1	52	32	68
36	Virginia Tech	2.009	4	1	67	33	51
37	Washington	1.998	2	3	41	67	6
38	Mississippi State	1.995	3	2	83	52	5
39	Virginia	1.980	4	1	55	24	93
40	UCF	1.963	3	1	35	34	101
41	Arkansas	1.937	2	2	25	53	53
42	Wake Forest	1.928	2	2	53	54	22
43	Wyoming	1.920	3	1	48	35	97
44	Kansas State	1.909	3	1	37	42	95
45	Oklahoma State	1.900	3	2	44	55	40
46	Troy	1.893	3	2	56	46	58
47	Texas Tech	1.892	4	1	33	36	114
48	Oregon State	1.882	2	3	54	81	3
49	Georgia Tech	1.878	3	2	31	56	63
50	Tennessee	1.870	2	2	58	57	32
51	Purdue	1.869	5	0	69	15	118
52	Texas A&M	1.866	4	1	47	37	110
53	TCU	1.854	3	2	38	47	92
54	Miami (FL)	1.833	4	1	62	25	113
55	New Mexico	1.830	3	2	50	58	52
56	Bowling Green	1.828	3	1	60	38	107
57	Vanderbilt	1.799	3	1	49	43	106
58	Navy	1.763	3	2	64	48	89
59	Air Force	1.756	3	2	85	59	31
60	Michigan	1.728	3	2	19	73	85
61	Akron	1.707	2	3	90	68	15
62	Maryland	1.705	3	2	51	60	90
63	Fresno State	1.705	2	2	68	74	20
64	Houston	1.701	2	2	57	61	87
65	Arkansas State	1.694	2	2	63	62	81
66	Penn State	1.684	3	2	23	49	117
67	UTEP	1.673	3	2	71	63	70
68	Arizona	1.642	2	3	59	82	27
69	Kent State	1.635	3	2	79	64	69
70	New Mexico State	1.628	3	2	73	75	29
71	Ball State	1.619	3	2	34	66	111
72	Florida Atlantic	1.613	3	2	92	50	91
73	Washington State	1.603	2	3	81	69	50
74	Iowa	1.583	2	3	42	70	100
75	Stanford	1.552	1	3	77	83	25
76	Pittsburgh	1.535	2	3	66	84	45
77	Western Michigan	1.533	2	3	80	85	28
78	Mississippi	1.515	1	4	82	90	19
79	Baylor	1.502	3	2	94	65	94
80	Colorado State	1.475	0	4	61	101	12
81	Utah	1.466	2	3	72	71	96
82	Buffalo	1.430	1	4	75	91	48
83	Southern Miss	1.429	2	2	98	76	61
84	Miami (OH)	1.424	2	3	116	72	41
85	UNLV	1.406	2	3	76	80	79
86	Toledo	1.402	1	4	96	92	30
87	Minnesota	1.374	1	4	74	93	66
88	Louisville	1.365	3	2	70	78	102
89	San Diego State	1.364	1	3	109	102	2
90	East Carolina	1.364	2	3	91	79	75
91	North Carolina State	1.346	1	4	86	103	13
92	Tulane	1.327	1	3	111	104	4
93	Louisiana Tech	1.324	1	3	87	105	17
94	Army	1.307	2	3	95	86	73
95	Central Michigan	1.306	2	3	78	97	57
96	Northwestern	1.290	2	3	104	98	24
97	Duke	1.283	1	4	101	94	59
98	Southern Methodist	1.224	1	4	97	95	86
99	UAB	1.222	1	3	107	106	14
100	Ohio	1.218	2	3	93	87	99
101	Louisiana-Monroe	1.171	0	4	105	107	23
102	Eastern Michigan	1.162	2	3	113	88	80
103	Notre Dame	1.146	0	5	117	108	8
104	Memphis	1.139	1	3	88	109	56
105	Nevada	1.138	2	2	99	96	88
106	North Carolina	1.105	1	4	106	110	42
107	San Jose State	1.091	2	3	119	89	47
108	Idaho	1.019	1	4	84	114	54
109	Iowa State	0.991	1	4	65	116	62
110	Middle Tennessee	0.975	1	4	89	99	112
111	Syracuse	0.971	1	4	115	100	71
112	Temple	0.960	0	5	102	112	64
113	Marshall	0.958	0	4	100	119	1
114	North Texas	0.912	0	4	118	113	26
115	Florida International	0.852	0	5	120	111	7
116	Louisiana-Lafayette	0.768	0	5	103	118	33
117	Utah State	0.716	0	5	112	115	82
118	Rice	0.543	0	4	114	120	34
119	Northern Illinois	0.492	1	4	110	117	109

On Strength of Schedule

2007-08-23T13:18:00.000-07:00

In any College Football ranking system, Strength of Schedule, is a crucial component. The BCS's method of calculating SoS relies solely on Win-Loss Records (Just like everything else in the BCS). This is a less than ideal situation because a team's record is less an indicator of their strength than their performance in those games. Consider two teams with 5-5 records, Team A won it's five games handily while the losses were close and hard fought. Team B, on the other hand was blown out in their five losses and just barely scraped through the games it won. We all know Team A is better than Team B, but to the BCS they are equally strong opponents. Because of this I use the Team Rating (performance) to determine how tough an opponent is. In my ranking system, a team's Strength of Schedule is simply the average Team Rating of their Div 1-A opponents. I don't think that this is the best system, but it's easy to balance and produces expected results. Below, I'll discuss more about SoS and why a simple average is not always reflective of a schedule's actual difficulty.

What makes a schedule hard?
Is the hardest schedule the one with the greatest average strength of opponents, or is it the one that's hardest to get through undefeated? What's the difference?

Consider two schedules, one with 5 strong teams and 5 weak teams, and a second with 10 average teams. Both have an identical average strength, despite being very different. Given a top tier team, or any above average team, the schedule with 5 strong teams would probably result in a worse record than the one with 10 average teams. As you get to the below average teams, the first schedule becomes the easier one, due to the fact that a below average team has a better chance against the 5 weak teams than against any of the average teams. What we see, is that how hard a schedule is, varies from team to team and that the average difficulty of opponents does not always reflect a true strength of schedule.

A Possible Solution
First, a true SoS solution should be based on performance as opposed to W/L records. Second it should realize that there is a very substantial difference between average teams and the top 20 or so teams. Third, it should rank a schedule with 5 strong teams and 5 weak teams as more difficult than a schedule of 10 average teams.

Strength of Schedule
Rank all teams according to their Team Rating score.
Each opponent ranked in the top 10 is worth 3 points.
Each opponent ranked 11-30 is worth 2 points.
Each opponent ranked 31-70 is worth 1 point.
Each opponent ranked 71-100 is worth 0.5 points.
Each opponent ranked 101-120 is worth 0 points.
Each 1-AA opponent is worth 0 points.

Average a team's total points against the number of games played to find SoS.

This system satisfies the three criteria listed above. We'll see how this pans out over the course of the season and see if any adjustments or revisions need to be made.

The Factor

2007-08-23T12:48:00.000-07:00

Since we've already seen the performance-based aspect of the rankings it's time to unveil the achievement-based component. I call it Win/Loss Factor.

What is Win/Loss Factor?
Win/Loss Factor is based on a team's win percentage but includes bonuses for beating strong teams (Quality Wins) and penalties assessed for losing to weak teams (Embarrassing Losses). Each win is worth 1 point and each loss is worth 0 points. Quality Win and Embarrassing Loss points are given on a sliding scale based on the opponent's Team Rating. You can earn Quality Win points by beating a team with a rating greater than 0.65, and you will be assessed an Embarrassing Loss penalty by losing to a team with a rating lower than 0.4. (A rating greater than 0.65 usually places a team in the top 15 while a rating below 0.4 corresponds to the bottom 30 teams.) Here's how the scales are calculated:

QW Bonus = 0.5 + (2.5 * ([Opponent's Team Rating] - 0.65))
EL Penalty = -0.5 + (2.5 * ([Opponent's Team Rating] - 0.40))

For those not interested in doing the math, the range of bonus values for a QW is between 0.5 and 1.375 (since Team Rating is never greater than 1). In reality, teams almost never have ratings higher than 0.85 or 0.9 so the effective maximum bonus is between 1 and 1.1. The effect of this bonus is that a win against a very good team is worth at least 1.5 (as opposed to just 1), while beating the top team in the nation counts for about two wins.

Similarly, the penalty for an EL is between -0.5 and -1.5 which has the effect of taking away wins. A loss to a 1-AA team is considered to be a loss to a team with a rating of 0 and is worth the maximum penalty of -1.5.

Team Rating = (Power + Efficiency)/2

2007-08-21T10:56:00.000-07:00

One of the most important parts of my ranking system is the Team Rating. Team Rating is a value based solely on performance and independent of achievement. What's the difference? In football achievement is measured in wins, losses, and championships. Performance is how a team played, how many yards did they gain, how many points did they score, etc. Very often a team's achievement is not reflected in their performance which is why both should be considered when ranking teams. This is in stark contrast to the pollsters who tend to focus on a team's W/L record above all else. This leads to situations where weak teams luck into high rankings. Case in point, UCLA 2005. The Bruins finished 10-2 with huge blowout losses to USC and craptacular Arizona (3-8). UCLA played four close conference games and needed serious 4th quarter rallies to win or get into overtime. Three of those games were against the worst teams in the Pac-10 (Stanford [5-6], Washington St [4-7], Washington [2-9]). Yet somehow they ended up ranked 13th in the coaches poll. If you look at their Pythagorean Win Percentage, it's 57.9%, which suggests they performed at a level consistent with a 7-5 record, hardly top 15 material. This is precisely why I include a performance based component to my rankings.

What is Team Rating?
As the title of this post suggests, it's the average of a team's Power and Efficiency, which begs the question, What is Power and Efficiency?

Power
A team's Power is an average of a team's normalized Offensive and Defensive moduluses (moduli?). What does Offensive Modulus tell us? It's based on the Yards per Game statistic so, OMod is how good a team is at moving the football, adjusted for the defensive performance of it's opponents. Similarly, Defensive Modulus is based on Yards Given Up per Game and tells us how good a team is at holding the opponent to as few yards as possible. Why use yards and not points? After all, it's points that win the game. Well, the range of possible values a team's score can take goes from about 0 to 70, while a team can gain anywhere from 0 to 600 yards. A lucky break (a fumble recovered for a touchdown) has a much more significant impact (10% of the maximum value) on a team's score than it's total yardage, so yards gained will have less error than points scored.

Efficiency
Efficiency is an average of a team's normalized Yards Per Point and Yards Per Point Given Up (or as I like to call them, Offensive and Defensive Efficiency). These values tell us how good a team is at scoring and keeping their opponent from scoring. Also, as I explained in a previous post they contain other information about a team, such as special teams play and the effect of turnovers.

So by combining, in equal parts, a team's Offensive Modulus, Defensive Modulus, Offensive Efficiency, and Defensive Efficiency we get a value that contains information on a team's ability to gain yards, score points, stop it's opponents from gaining yards and scoring points, and a little bit about special teams and turnovers. Team Rating is a good composite of performance-based metrics and is completely independent of a team's W/L record.

Addendum - Why Normalize?
In order to combine two opposing statistics (one where higher values are better and one where lower values are better) in a meaningful way you have to get them both on the same scale. This is especially true if there is no limit to the possible range of values the stats can take. To normalize the values in a set, you subtract the lowest value from each member and then divide each member by the highest value. The result is a range of values from 0 to 1 where the ordering and relative distance between values is preserved. So if you normalize the Offensive Modulus, the team with the highest score has a value of 1 and the worst team has a value of 0. For Defensive modulus the opposite is true. However, since they're now scaled the same (between 1 and 0), you can average the two by subtracting the normalized defensive modulus values from 1.

YPP, YPPGU or maybe just Efficiency

2007-08-21T06:42:00.000-07:00

This post is about a stat that is frequently overlooked but can tell us a good deal about a team. I'm talking about Yards/Point and Yards/Point Given Up. To find a team's YPP, you just divide the total number of yards they've gained on the season by the total number of points they scored. The same works with the defense, YPPGU is just the total number of yards given up divided by the number of points given up. For YPP, lower numbers are better (you're scoring lots of points) and for YPPGU you want higher numbers (you're giving up very few points).

So what can we learn from these numbers?
Yards Per Point:
A team can get a low Yards Per Point number by scoring more touchdowns as opposed to field goals and getting positive field position due to good special teams play and recovering turnovers. Any points scored off of a turnover or on a return do not add any yards to the offense's totals and boost a team's YPP that much more. Just the opposite, a team that is always playing a long field, turning over the ball, and settling for field goals is going to have a very high YPP, and they probably won't win very many games either.

Yards Per Point Give Up:
A team can end up with a high Yards Per Point Given Up number by having a "bend but not break" defense that can force punts and limit the opponent to field goals. Forcing turnovers and pinning your opponent in their own territory with strong return coverage will also drive your YPPGU up. Because of these factors, I like to think of YPP and YPPGU as Offensive and Defensive Efficiency, respectively. I think it sounds better too.

So wouldn't it be nice if I could give a real world example whereby we can pierce the veil of obfuscation created by conventional statistics? Well you're in luck! We need look no further than the 2004 NC State Wolfpack Defense.

I'm confused, is my defense good or bad?

In 2004 the Wolfpack lead the nation in total defense, allowing an incredible 226 yards per game. Somehow, they only managed to win 5 of their eleven games, including a 42-0 beat down on 1-AA patsy Richmond. What explains this? Maybe they had a crappy offense? Well their offense was below average (61st), but they still finished in the black by about 120 yds/game and were never outgained by an opponent all season. Well if we take a look at their Defensive Efficiency (YPPGU), they were the second WORST in the nation allowing opponents a point for every 10.4 yards. This means they were giving their opponents a very short field. If we dig deeper into the box scores, we'll see that NC State gave up 31 turnovers (15 fumbles, 16 INTs), a -19 margin! It also didn't help the defense that NC State was 103rd in return coverage, allowing 12.4 yards per return. So yes 2004-Chuck, your defense is very good. You just need to teach the rest of the team how to hold on to the ball!

Modulus

2007-08-16T10:21:00.000-07:00

It's a classic debate... Are Pac-10 teams' offenses strong because they play against weak defenses? Are SEC teams' defenses so strong because they play against stodgy old-school offenses? Given the enormous differences in quality between the best and worst teams in Division 1-A, there needs to be a statistic that gives more information about offensive and defensive strength than the classic Yards and Points per game metrics. There needs to be a statistic that factors in the strength of a team's opponent. Laying half-a-hundred on Temple is a lot less impressive than doing the same to a team like LSU or Ohio State.

Enter the Modulus...

Modulus - A quantity that expresses the degree to which a substance possesses a property.

Modulus Example: Offensive Scoring Modulus or OSMod
The OSMod is intended to replace the Points/Game metric and will give us an idea of how good a team is at putting points on the board.

Here's how it's done:
In three of LSU's games from 2006 the Tigers beat Miss St 48-17, lost to Florida 23-10, and smashed Kentucky 49-0. To find the Tigers' OSMod for these three games we need to divide the number of points LSU scored in each game against the average number of points given up by the opposing defense.
Game 1: Miss St gave up an average 27.8 ppg in 2006. So we divide 48 by 27.8 and get 1.73.
Game 2: Florida gave up 14.5 ppg so 10/14.5 = 0.69
Game 3: Kentucky gave up 30.2 ppg, 49/30.2 = 1.62
To get the total OSMod for these three games we just average the three scores.
(1.73 + 0.69 + 1.62)/3 = 1.35

So what does this mean? It means that LSU typically scores 1.35 times as many points as it's opponents allow on average. A much more telling number than simply 35.7 ppg.

You can, of course, do this for any basic statistic although it might not be worth the effort to compute a team's modulus of penalization (or whatever you might call it).

On a week-to-week basis I keep track of the following moduli (moduluses?):
Offensive Modulus (Yards Per Game)
Defensive Modulus (Yards Given Up Per Game)
Offensive Scoring Modulus (Points Per Game)
Defensive Scoring Modulus (Points Given Up Per Game)
Passing Modulus (Passing Yards Per Game)
Pass Defense Modulus (Pass Yards Given Up Per Game)
Rushing Modulus (Rushing Yards Per Game)
Rush Defense Modulus (Rushing Yards Given Up Per Game)

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So, How much difference does it make?
Take a look at the average points per game vs the offensive scoring modulus for each of the 11 conferences and independents:

POINTS PER GAME (Conference Averages)
Big XII	26.593
WAC	26.556
Big East	26.363
Big Ten	24.715
SEC	24.176
Conference USA	23.747
Pac-10	23.712
Mountain West	22.841
Independents	21.551
ACC	21.438
MAC	21.027
Sun Belt	16.681

OFFENSIVE SCORING MODULUS (Conference Averages)
Big East	1.18272
SEC	1.14331
Big XII	1.08517
Big Ten	1.06165
Pac-10	1.03700
ACC	1.01066
Mountain West	0.97037
WAC	0.95246
Conference USA	0.92564
Independents	0.90664
MAC	0.85022
Sun Belt	0.66869

That's a pretty significant shake-up. It also tells us that when it comes to giving up points, the Big East is significantly stingier than the Big XII. Suprised anyone?
Also, only the six BCS conferences managed to crack the 1.0 mark which is the modulus version of breaking even. Another neat thing you can do with this table is divide the Points Per Game by Offensive Scoring Modulus and find out what the average number of points each conference's opponents gave up. For the SEC, it's a mere 21 ppg, for the WAC it's almost 28!

The Numbers Game

2007-08-16T09:32:00.000-07:00

The reason I started this blog was to give myself a place to post the results of my College Football Ranking system. After the 4th or 5th week of the season I'll begin posting the results and any necessary analysis. Until then I'll post the results from last year along with some explanations about how the rankings work and the reasoning behind them. Comments and criticisms are welcome. I'm not a statistician so I'd like to know if I'm pushing bad science. And, just so everyone knows where I stand I'm a Georgia Tech alumnus who grew up in Baton Rouge so...

Go Jackets!
Geaux Tigers!