Case 3, Sub-analysis 1: 2006 - 2009 Rivals 250 Lists as Population Source, Scaling Competition by Winning Percentage (1999-2008)

Continuing from the Case 3 analysis, in this study I look scale the competitive effect of other schools by how much recent success they've had, which is obviously helpful in attracting recruits.

It's amazing how fast momentum can swing in programs (on even less than a ten year scale), partivularly nearby neighbors, as seen in the change of fortunes at Auburn and Alabama in the past three years or with Miami dropping off just before Florida arose from a few mediocre seasons to start the decade.

The scaling factor I use for this study is really more of a "dilution factor" (in contrast to the scale factor when considering AQ/non-AQ teams). It serves to reduce how much weight is given to the winning percentage as described by the formula:

To provide an example, compare School A with a winning percentage of 0.750 versus School B with a winning percentage of 0.250. So a scale factor of zero means the competitive effect of School A is multiplied by (0 + 0.75)/(1 + 0) = 0.75 and similarly School B's effect is multiplied by 0.25. When the scale factor is increased to say, 1, then the competitive effect of School A is multiplied by (1 + 0.75)/(1 + 1) = 0.875 and for school B the multiplication factor is 0.625. In other words, the gap between their recruiting influence is diminished as the scale factor serves to wash out the winning percentage scaling.

Unfortunately I don't have too much commentary to offer on this sub-analysis, I believe this scaling factor will be much more interesting for the normalized probability analysis. there are notable changes though vicible in the various maps. Proceeding from Figure 2 - 7, the scaling by win percentage is increased with Figure 8 showing the map before any subtraction occur (all other maps are after the subtraction step). The primary effect of the win percentage scaling is to blur the differences between the schools; the map becomes more uniform with the northwest not looking quite so bad and the southeast's dominance being more dispersed. In some sense Figure 7 begins to approach Figure 8; when winning percentage highly skews the competitive effect many schools almost "disappear" and it is almost as if these schools weren't even subtracted. One interesting comparison between Figures 7 and 8 lies in the northwest--the solid performance by these schools ends up leaving this region "in the red" (or white, for these saturation images) when it comes to surplus of recruits (i.e. I wouldn't want to establish a new program in this region).

	Dilution Factor = 0.0				Dilution Factor = 1.0				Dilution Factor = 2.0				Dilution Factor = 4.0				Dilution Factor = 8.0
Rank	School	Effective Pop.		Rank	School	Effective Pop.		Rank	School	Effective Pop.		Rank	School	Effective Pop.		Rank	School	Effective Pop.
1	Georgia Tech	152		1	Florida State	106		1	UCF	94		1	South Florida	85		1	South Florida	79
2	Auburn	148		2	UCF	106		2	South Florida	94		2	UCF	85		2	UCF	79
3	Georgia	146		3	South Florida	105		3	Florida State	92		3	Florida State	82		3	Florida	75
4	Florida State	146		4	Florida	104		4	Florida	91		4	Florida	82		4	Florida Atlantic	75
5	Troy	145		5	Georgia Tech	102		5	Florida Atlantic	88		5	Florida Atlantic	80		5	Florida State	75
6	UAB	143		6	Auburn	101		6	FIU	86		6	FIU	78		6	FIU	73
7	South Carolina	140		7	Troy	99		7	Georgia Tech	86		7	Miami	76		7	Miami	72
8	Clemson	140		8	Georgia	98		8	Auburn	85		8	Georgia Tech	73		8	Auburn	64
9	UCF	140		9	Florida Atlantic	97		9	Troy	84		9	Auburn	72		9	Georgia Tech	64
10	Florida	140		10	FIU	95		10	Miami	84		10	Troy	71		10	Troy	63
11	Alabama	138		11	South Carolina	94		11	Georgia	81		11	Georgia	68		11	Georgia	60
12	South Florida	138		12	Miami	93		12	South Carolina	78		12	South Carolina	66		12	South Carolina	58
13	Mississippi State	133		13	UAB	92		13	UAB	74		13	UAB	60		13	Tulane	52
14	Southern Miss	132		14	Clemson	90		14	Clemson	73		14	Clemson	60		14	Southern Miss	52
15	Tulane	127		15	Alabama	88		15	Southern Miss	72		15	Tulane	60		15	Clemson	51
16	Louisiana-Monroe	126		16	Southern Miss	87		16	Alabama	71		16	Southern Miss	60		16	UAB	51
17	Florida Atlantic	126		17	Tulane	85		17	Tulane	71		17	Alabama	58		17	LSU	49
18	Tennessee	126		18	LSU	81		18	LSU	67		18	LSU	56		18	Alabama	49
19	Ole Miss	125		19	Mississippi State	81		19	Louisiana-Lafayette	66		19	Louisiana-Lafayette	55		19	Louisiana-Lafayette	47
20	FIU	124		20	Louisiana-Lafayette	80		20	Mississippi State	64		20	Mississippi State	50		20	Louisiana-Monroe	41
21	Middle Tennessee	124		21	Louisiana-Monroe	79		21	Louisiana-Monroe	63		21	Louisiana-Monroe	50		21	Mississippi State	41
22	Wake Forest	124		22	Louisiana Tech	77		22	Louisiana Tech	61		22	Louisiana Tech	49		22	Louisiana Tech	40
23	LSU	123		23	SMU	74		23	SMU	59		23	SMU	48		23	SMU	40
24	Louisiana Tech	123		24	Wake Forest	74		24	Wake Forest	57		24	Texas A&M	46		24	Texas A&M	39
25	Louisiana-Lafayette	122		25	Tennessee	73		25	Texas A&M	56		25	Houston	44		25	Houston	37
26	Duke	122		26	Ole Miss	73		26	North Carolina	55		26	Rice	44		26	Rice	37
27	North Carolina	121		27	Duke	72		27	Duke	55		27	Wake Forest	43		27	Baylor	35
28	Vanderbilt	121		28	North Carolina	72		28	Ole Miss	55		28	Baylor	43		28	TCU	35
29	Miami	119		29	NC State	70		29	Houston	55		29	North Carolina	42		29	Wake Forest	35
30	Memphis	118		30	Texas A&M	69		30	Rice	55		30	TCU	42		30	ECU	34
31	NC State	118		31	Houston	69		31	Tennessee	55		31	Duke	42		31	North Carolina	34
32	SMU	118		32	Rice	69		32	NC State	55		32	NC State	42		32	NC State	34
33	Western Kentucky	116		33	Middle Tennessee	68		33	Baylor	54		33	ECU	42		33	North Texas	33
34	Virginia Tech	113		34	ECU	68		34	ECU	53		34	Ole Miss	41		34	Duke	33
35	Virginia	112		35	Baylor	67		35	TCU	53		35	North Texas	41		35	Ole Miss	32
36	ECU	111		36	North Texas	67		36	North Texas	53		36	Tennessee	41		36	Tennessee	31
37	Maryland	111		37	TCU	67		37	Maryland	51		37	Maryland	39		37	Maryland	31
38	Arkansas State	110		38	Memphis	66		38	Navy	50		38	Navy	38		38	Navy	31
39	North Texas	110		39	Maryland	66		39	Middle Tennessee	49		39	Texas	36		39	Texas	30
40	Houston	109		40	Navy	65		40	Memphis	48		40	Virginia	35		40	Virginia	27
41	Rice	109		41	Virginia	64		41	Virginia	48		41	Memphis	34		41	Memphis	25
42	Navy	109		42	Vanderbilt	64		42	Virginia Tech	46		42	Middle Tennessee	34		42	Temple	25
43	Texas A&M	109		43	Virginia Tech	63		43	Texas	46		43	Virginia Tech	33		43	Middle Tennessee	24
44	Baylor	108		44	Arkansas State	58		44	Vanderbilt	45		44	Temple	33		44	San Diego State	24
45	Kentucky	108		45	Temple	58		45	Temple	44		45	Vanderbilt	30		45	Virginia Tech	24
46	TCU	107		46	Western Kentucky	58		46	Arkansas State	41		46	San Diego State	28		46	Rutgers	20
47	Marshall	106		47	Texas	57		47	Western Kentucky	38		47	Arkansas State	27		47	Vanderbilt	20
48	West Virginia	104		48	West Virginia	54		48	Rutgers	38		48	Rutgers	27		48	UCLA	19
49	Ohio	104		49	Pittsburgh	53		49	West Virginia	37		49	Penn State	25		49	USC	19
50	Pittsburgh	103		50	Penn State	52		50	Penn State	37		50	West Virginia	24		50	Arkansas State	18
51	Louisville	102		51	Marshall	52		51	Pittsburgh	36		51	Pittsburgh	23		51	Penn State	17
52	Cincinnati	102		52	Rutgers	51		52	San Diego State	34		52	UCLA	23		52	West Virginia	15
53	Temple	100		53	Kentucky	51		53	Marshall	33		53	USC	23		53	Pittsburgh	14
54	Kent State	99		54	Ohio	49		54	Arkansas	33		54	Western Kentucky	23		54	Army	13
55	Miami (OH)	99		55	Arkansas	48		55	Kentucky	31		55	Arkansas	20		55	Western Kentucky	12
56	Ohio State	98		56	Kent State	46		56	Ohio	31		56	Army	19		56	Arkansas	12
57	Akron	98		57	Louisville	46		57	Army	30		57	Marshall	19		57	Oklahoma	11
58	Indiana	97		58	Akron	45		58	UCLA	29		58	Oklahoma	18		58	Marshall	9
59	Penn State	97		59	Cincinnati	44		59	USC	29		59	Kentucky	16		59	Tulsa	8
60	Arkansas	94		60	Ohio State	44		60	Oklahoma	29		60	Ohio	16		60	Ohio	6
61	Ball State	93		61	Oklahoma	43		61	Kent State	29		61	Tulsa	15		61	Kentucky	6
62	Texas	92		62	Army	42		62	Akron	28		62	Kent State	15		62	Connecticut	5
63	Rutgers	90		63	Tulsa	42		63	Tulsa	27		63	Akron	14		63	Kent State	5
64	Bowling Green	88		64	Miami (OH)	42		64	Louisville	27		64	Oklahoma State	12		64	Akron	5
65	Tulsa	87		65	San Diego State	41		65	Cincinnati	25		65	Louisville	12		65	Oklahoma State	4
66	Toledo	86		66	Indiana	40		66	Ohio State	25		66	Connecticut	11		66	Syracuse	3
67	Illinois	86		67	Oklahoma State	37		67	Oklahoma State	23		67	Ohio State	11		67	Buffalo	2
68	Purdue	86		68	UCLA	37		68	Miami (OH)	22		68	Cincinnati	10		68	Louisville	2
69	Eastern Michigan	85		69	USC	37		69	Buffalo	21		69	Syracuse	10		69	Texas Tech	2
70	Oklahoma	83		70	Buffalo	36		70	Indiana	21		70	Buffalo	10		70	Boston College	2
71	Michigan	81		71	Ball State	36		71	Syracuse	20		71	Texas Tech	7		71	Fresno State	1
72	Army	81		72	Bowling Green	34		72	Connecticut	19		72	Miami (OH)	7		72	Ohio State	1
73	Missouri	80		73	Missouri	33		73	Missouri	17		73	Boston College	7		73	UNLV	1
74	Oklahoma State	80		74	Toledo	33		74	Ball State	17		74	Indiana	5		74	Arizona State	1
75	Buffalo	79		75	Syracuse	33		75	Texas Tech	16		75	UNLV	5		75	Cincinnati	0
76	Notre Dame	79		76	Illinois	33		76	Bowling Green	16		76	Fresno State	5		76	Hawaii	0
77	Western Michigan	77		77	Eastern Michigan	32		77	Toledo	15		77	Arizona State	5		77	Arizona	-2
78	Michigan State	76		78	Purdue	31		78	Illinois	15		78	Missouri	5		78	Miami (OH)	-3
79	Northwestern	76		79	Connecticut	30		79	Eastern Michigan	14		79	Arizona	3		79	Missouri	-4
80	Northern Illinois	72		80	Michigan	30		80	Boston College	14		80	Ball State	2		80	Indiana	-5
81	Syracuse	71		81	Texas Tech	27		81	Purdue	13		81	Bowling Green	2		81	UTEP	-5
82	Central Michigan	69		82	Notre Dame	27		82	Michigan	13		82	Toledo	1		82	San Jose State	-6
83	Kansas	68		83	Northwestern	26		83	UNLV	12		83	Illinois	1		83	New Mexico State	-7
84	Iowa	64		84	Michigan State	26		84	Arizona State	12		84	Eastern Michigan	0		84	Stanford	-7
85	San Diego State	63		85	Western Michigan	25		85	Fresno State	11		85	Hawaii	0		85	California	-8
86	Connecticut	62		86	Kansas	24		86	Kansas	10		86	UTEP	0		86	Bowling Green	-8
87	Wisconsin	61		87	Northern Illinois	24		87	Arizona	9		87	Michigan	-1		87	Ball State	-8
88	UCLA	60		88	Boston College	23		88	Northwestern	9		88	Purdue	-1		88	Toledo	-8
89	USC	60		89	Central Michigan	23		89	Michigan State	9		89	New Mexico State	-2		89	Illinois	-9
90	Kansas State	60		90	UNLV	20		90	Notre Dame	9		90	Kansas	-2		90	Eastern Michigan	-9
91	Texas Tech	60		91	Arizona State	20		91	Western Michigan	8		91	San Jose State	-2		91	Kansas	-10
92	Iowa State	57		92	Iowa	19		92	Central Michigan	8		92	Stanford	-3		92	Michigan	-10
93	Boston College	52		93	Kansas State	19		93	Northern Illinois	8		93	California	-4		93	New Mexico	-11
94	Nebraska	51		94	Fresno State	18		94	UTEP	7		94	Northwestern	-4		94	Purdue	-11
95	UTEP	45		95	Wisconsin	18		95	New Mexico State	6		95	Michigan State	-4		95	Nevada	-12
96	UNLV	45		96	Arizona	18		96	Kansas State	6		96	Central Michigan	-5		96	Kansas State	-13
97	New Mexico State	45		97	UTEP	17		97	Iowa	4		97	Notre Dame	-5		97	Central Michigan	-13
98	Arizona State	45		98	New Mexico State	16		98	San Jose State	3		98	Kansas State	-5		98	Northwestern	-13
99	Minnesota	44		99	Iowa State	15		99	Wisconsin	3		99	Northern Illinois	-5		99	Michigan State	-13
100	Arizona	43		100	Nebraska	13		100	Stanford	3		100	Western Michigan	-6		100	Northern Illinois	-14
101	New Mexico	41		101	New Mexico	12		101	New Mexico	2		101	New Mexico	-6		101	Notre Dame	-14
102	Fresno State	40		102	San Jose State	11		102	California	2		102	Iowa	-7		102	Western Michigan	-15
103	Air Force	37		103	Minnesota	10		103	Iowa State	2		103	Wisconsin	-8		103	Iowa	-15
104	Colorado	33		104	Stanford	10		104	Nebraska	1		104	Nevada	-8		104	Washington	-16
105	San Jose State	33		105	California	9		105	Hawaii	0		105	Nebraska	-9		105	Wisconsin	-16
106	Stanford	32		106	Air Force	6		106	Minnesota	-1		106	Iowa State	-9		106	Minnesota	-16
107	Colorado State	30		107	Nevada	5		107	Nevada	-3		107	Minnesota	-10		107	Nebraska	-16
108	California	30		108	Colorado	2		108	Air Force	-5		108	Washington	-13		108	Iowa State	-17
109	Wyoming	28		109	Hawaii	0		109	Washington	-8		109	Air Force	-13		109	Air Force	-18
110	Nevada	26		110	Colorado State	0		110	Colorado	-9		110	Oregon State	-17		110	Oregon State	-20
111	BYU	24		111	Wyoming	-2		111	BYU	-10		111	Oregon	-17		111	Oregon	-20
112	Utah State	22		112	BYU	-2		112	Colorado State	-11		112	Colorado	-17		112	BYU	-22
113	Utah	22		113	Washington	-3		113	Wyoming	-12		113	BYU	-17		113	Colorado	-23
114	Washington	13		114	Utah	-4		114	Utah	-12		114	Utah	-19		114	Utah	-23
115	Idaho	11		115	Utah State	-4		115	Oregon State	-12		115	Colorado State	-19		115	Boise State	-24
116	Boise State	11		116	Oregon State	-7		116	Oregon	-13		116	Wyoming	-20		116	Colorado State	-24
117	Oregon State	10		117	Oregon	-7		117	Utah State	-13		117	Utah State	-20		117	Utah State	-24
118	Washington State	10		118	Boise State	-8		118	Boise State	-15		118	Boise State	-20		118	Wyoming	-25
119	Oregon	10		119	Idaho	-9		119	Idaho	-16		119	Idaho	-21		119	Idaho	-25
120	Hawaii	0		120	Washington State	-10		120	Washington State	-16		120	Washington State	-22		120	Washington State	-25

Teams Sorted Alphabetically

School	0	1	2	4	8		School	0	1	2	4	8		School	0	1	2	4	8
Air Force	103	106	108	109	109		Kansas	83	86	86	90	91		Purdue	68	78	81	88	94
Akron	57	58	62	63	64		Kansas State	90	93	96	98	96		Rice	41	32	30	26	26
Alabama	11	15	16	17	18		Kent State	54	56	61	62	63		Rutgers	63	52	48	48	46
Arizona	100	96	87	79	77		Kentucky	45	53	55	59	61		San Diego State	85	65	52	46	44
Arizona State	98	91	84	77	74		Louisiana Tech	24	22	22	22	22		San Jose State	105	102	98	91	82
Arkansas	60	55	54	55	56		Louisiana-Lafayette	25	20	19	19	19		SMU	32	23	23	23	23
Arkansas State	38	44	46	47	50		Louisiana-Monroe	16	21	21	21	20		South Carolina	7	11	12	12	12
Army	72	62	57	56	54		Louisville	51	57	64	65	68		South Florida	12	3	2	1	1
Auburn	2	6	8	9	8		LSU	23	18	18	18	17		Southern Miss	14	16	15	16	14
Ball State	61	71	74	80	87		Marshall	47	51	53	57	58		Stanford	106	104	100	92	84
Baylor	44	35	33	28	27		Maryland	37	39	37	37	37		Syracuse	81	75	71	69	66
Boise State	116	118	118	118	115		Memphis	30	38	40	41	41		TCU	46	37	35	30	28
Boston College	93	88	80	73	70		Miami	29	12	10	7	7		Temple	53	45	45	44	42
Bowling Green	64	72	76	81	86		Miami (OH)	55	64	68	72	78		Tennessee	18	25	31	36	36
Buffalo	75	70	69	70	67		Michigan	71	80	82	87	92		Texas	62	47	43	39	39
BYU	111	112	111	113	112		Michigan State	78	84	89	95	99		Texas A&M	43	30	25	24	24
California	108	105	102	93	85		Middle Tennessee	21	33	39	42	43		Texas Tech	91	81	75	71	69
Central Michigan	82	89	92	96	97		Minnesota	99	103	106	107	106		Toledo	66	74	77	82	88
Cincinnati	52	59	65	68	75		Mississippi State	13	19	20	20	21		Troy	5	7	9	10	10
Clemson	8	14	14	14	15		Missouri	73	73	73	78	79		Tulane	15	17	17	15	13
Colorado	104	108	110	112	113		Navy	42	40	38	38	38		Tulsa	65	63	63	61	59
Colorado State	107	110	112	115	116		NC State	31	29	32	32	32		UAB	6	13	13	13	16
Connecticut	86	79	72	66	62		Nebraska	94	100	104	105	107		UCF	9	2	1	2	2
Duke	26	27	27	31	34		Nevada	110	107	107	104	95		UCLA	88	68	58	52	48
Eastern Michigan	69	77	79	84	90		New Mexico	101	101	101	101	93		UNLV	96	90	83	75	73
ECU	36	34	34	33	30		New Mexico State	97	98	95	89	83		USC	89	69	59	53	49
FIU	20	10	6	6	6		North Carolina	27	28	26	29	31		Utah	113	114	114	114	114
Florida	10	4	4	4	3		North Texas	39	36	36	35	33		Utah State	112	115	117	117	117
Florida Atlantic	17	9	5	5	4		Northern Illinois	80	87	93	99	100		UTEP	95	97	94	86	81
Florida State	4	1	3	3	5		Northwestern	79	83	88	94	98		Vanderbilt	28	42	44	45	47
Fresno State	102	94	85	76	71		Notre Dame	76	82	90	97	101		Virginia	35	41	41	40	40
Georgia	3	8	11	11	11		Ohio	49	54	56	60	60		Virginia Tech	34	43	42	43	45
Georgia Tech	1	5	7	8	9		Ohio State	56	60	66	67	72		Wake Forest	22	24	24	27	29
Hawaii	120	109	105	85	76		Oklahoma	70	61	60	58	57		Washington	114	113	109	108	104
Houston	40	31	29	25	25		Oklahoma State	74	67	67	64	65		Washington State	118	120	120	120	120
Idaho	115	119	119	119	119		Ole Miss	19	26	28	34	35		West Virginia	48	48	49	50	52
Illinois	67	76	78	83	89		Oregon	119	117	116	111	111		Western Kentucky	33	46	47	54	55
Indiana	58	66	70	74	80		Oregon State	117	116	115	110	110		Western Michigan	77	85	91	100	102
Iowa	84	92	97	102	103		Penn State	59	50	50	49	51		Wisconsin	87	95	99	103	105
Iowa State	92	99	103	106	108		Pittsburgh	50	49	51	51	53		Wyoming	109	111	113	116	118

Tom Brennan, © 2009