IowaHawkBlogs Degrees of Separation through Conference Championships

Here are this weeks Degrees of Separation Rankings based on the three different weighting systems we are playing with.  I am copying and pasting the description of this ranking technique as I wrote it few weeks ago:

"In this system, a team's rank is based solely on who they have defeated, and who those teams have defeated, and who those teams have defeated, down 5 levels.   I think the easiest way to explain this is with an example.  Let's say Team A defeated Team B and Team C.  Team A will get 5 points for each of those wins.  Let's then assume Team B has beaten D and E while C has only beaten F.  While B and C will get their points for those respective wins, Team A will also get 4 points for each of those three "Linked Wins."  This process continues down to give 3 points, and 2 points, and 1 point for each successive "Degree of Separation" of the linked wins."

"That's it. Teams can't get points for a linked win over themselves, and can only get credit for each of the other FBS teams once---at whatever the fewest degrees of separation is that gives them that linked win."

"We have played around with what weights to use for each win at each degree of separation.  In the example above I used {5,4,3,2,1} for the weights at each degree, but below I am also including rankings based on other weight vectors.  First though, the linear one using {5,4,3,2,1}:"

Rank	Team	W	L	Conf	Linked Wins	Score
1	LSU	13	0	SEC	121	399
2	Georgia	11	2	SEC	124	390
3	Ohio State	13	0	B10	121	385
4	Michigan	9	3	B10	120	370
5	Notre Dame	10	2	IND	121	369
6	Penn State	10	2	B10	124	366
7	Auburn	9	3	SEC	122	365
8	Wisconsin	10	3	B10	121	364
9	Florida	10	2	SEC	124	360
10	BYU	7	5	IND	121	345
11	Cincinnati	10	3	AAC	113	339
12	Clemson	13	0	ACC	116	338
13	Minnesota	10	2	B10	123	338
14	SMU	10	2	AAC	116	338
15	Memphis	12	1	AAC	115	336
16	Iowa	9	3	B10	117	335
17	Boise State	12	1	MWC	116	333
18	Kentucky	7	5	SEC	124	332
19	Utah	11	2	PAC	118	327
20	UCF	9	3	AAC	118	325
21	Oklahoma St.	8	4	B12	116	321
22	Navy	9	2	AAC	116	315
23	App. St.	12	1	SUN	114	309
24	Pittsburgh	7	5	ACC	114	309
25	Toledo	6	6	MID	121	308
26	Oklahoma	12	1	B12	111	306
27	Kansas St.	8	4	B12	113	304
28	Tennessee	7	5	SEC	123	303
29	Buffalo	7	5	MID	119	302
30	Wake Forest	8	4	ACC	112	302
31	Arizona St.	7	5	PAC	113	301
32	Temple	8	4	AAC	112	300
33	Baylor	11	2	B12	112	299
34	San Diego St.	9	3	MWC	116	299
35	Wash.	7	5	PAC	115	297
36	Alabama	10	2	SEC	115	296
37	S. Carolina	4	8	SEC	120	296
38	Mich. St.	6	6	B10	115	291
39	Texas	7	5	B12	111	291
40	Miami (FL)	6	6	ACC	113	290
41	Oregon	11	2	PAC	109	287
42	USC	8	4	PAC	111	287
43	Colorado	5	7	PAC	113	286
44	Virginia	9	4	ACC	111	285
45	Miss. St.	6	6	SEC	116	283
46	Virginia Tech	8	4	ACC	112	282
47	Tulsa	4	8	AAC	116	281
48	Illinois	6	6	B10	117	280
49	Missouri	6	6	SEC	116	280
50	Air Force	10	2	MWC	112	278
51	Louisville	7	5	ACC	104	275
52	Syracuse	5	7	ACC	108	270
53	N. Carolina	6	6	ACC	113	267
54	Hawaii	9	5	MWC	104	265
55	California	7	5	PAC	107	263
56	E. Mich.	6	6	MID	114	259
57	W. Virginia	5	7	B12	108	256
58	Wyoming	7	5	MWC	113	255
59	Texas A&M	7	5	SEC	110	253
60	Florida St.	6	6	ACC	99	252
61	Iowa State	7	5	B12	106	252
62	Nebraska	5	7	B10	108	251
63	BC	6	6	ACC	106	250
64	Georgia St.	7	5	SUN	107	250
65	Florida Atl.	10	3	USA	103	249
66	Stanford	4	8	PAC	106	249
67	UL Lafayette	10	3	SUN	107	248
68	W. Michigan	7	5	MID	113	247
69	Ball State	5	7	MID	112	242
70	Nevada	7	5	MWC	105	242
71	Wash. St.	6	6	PAC	105	241
72	Oregon St.	5	7	PAC	103	240
73	TCU	5	7	B12	109	239
74	Georgia Tech	3	9	ACC	104	238
75	Indiana	8	4	B10	104	238
76	S. Florida	4	8	AAC	109	238
77	C. Mich.	8	5	MID	107	237
78	Tulane	6	6	AAC	103	237
79	Utah State	7	5	MWC	106	236
80	Duke	5	7	ACC	101	235
81	Georgia So.	7	5	SUN	96	233
82	UCLA	4	8	PAC	100	233
83	Arizona	4	8	PAC	106	229
84	Kent State	6	6	MID	107	225
85	N. Illinois	5	7	MID	105	224
86	Texas Tech	4	8	B12	107	224
87	Arkansas St.	7	5	SUN	102	221
88	Marshall	8	4	USA	87	217
89	Vanderbilt	3	9	SEC	110	217
90	NC State	4	8	ACC	99	216
91	Purdue	4	8	B10	99	216
92	UNLV	4	8	MWC	99	212
93	Kansas	3	9	B12	105	210
94	LA Tech	9	3	USA	93	208
95	Northwestern	3	9	B10	100	208
96	Florida Int.	6	6	USA	87	206
97	Miami (OH)	8	5	MID	99	202
98	W. Kentucky	8	4	USA	81	202
99	Houston	4	8	AAC	97	198
100	Liberty	7	5	IND	99	196
101	Ohio	6	6	MID	99	195
102	Bowling Grn	3	9	MID	98	191
103	Coastal Caro.	5	7	SUN	90	180
104	Fresno St.	4	8	MWC	83	179
105	Maryland	3	9	B10	80	171
106	UL Monroe	5	7	SUN	82	167
107	UAB	9	4	USA	73	163
108	Mid. Tenn.	4	8	USA	70	161
109	Troy	5	7	SUN	76	152
110	Texas State	3	9	SUN	74	146
111	Charlotte	7	5	USA	64	143
112	S. Miss.	7	5	USA	62	140
113	Colorado St.	4	8	MWC	72	138
114	Ole Miss	4	8	SEC	69	134
115	San Jose St.	5	7	MWC	61	130
116	S. Alabama	2	10	SUN	65	121
117	Rutgers	2	10	B10	56	103
118	North Texas	4	8	USA	48	100
119	Rice	3	9	USA	48	100
120	Arkansas	2	10	SEC	38	69
121	Army	5	7	IND	28	65
122	UTSA	4	8	USA	28	57
123	E. Carolina	4	8	AAC	4	17
124	Connecticut	2	10	AAC	2	9
125	New Mexico	2	10	MWC	2	9
126	UMASS	1	11	MID	1	5
127	NM St.	2	10	IND	1	5
128	Akron	0	12	MID	0	0
129	Old Dominion	1	11	USA	0	0
130	UTEP	1	11	USA	0	0

Here is the rankings using weights of {256,16,4,2,1}:

Rank	Team	W	L	Conf	Linked Wins	Score
1	LSU	13	0	SEC	121	3906
2	Ohio State	13	0	B10	121	3890
3	Clemson	13	0	ACC	116	3721
4	Georgia	11	2	SEC	124	3361
5	Notre Dame	10	2	IND	121	3327
6	Wisconsin	10	3	B10	121	3262
7	Cincinnati	10	3	AAC	113	3203
8	SMU	10	2	AAC	116	3183
9	Boise State	12	1	MWC	116	3171
10	Memphis	12	1	AAC	115	3152
11	Utah	11	2	PAC	118	3139
12	App. St.	12	1	SUN	114	3106
13	Oklahoma	12	1	B12	111	3052
14	Oregon	11	2	PAC	109	3050
15	Michigan	9	3	B10	120	3040
16	Baylor	11	2	B12	112	3009
17	Penn State	10	2	B10	124	3005
18	Iowa	9	3	B10	117	2963
19	Minnesota	10	2	B10	123	2898
20	Alabama	10	2	SEC	115	2791
21	Auburn	9	3	SEC	122	2791
22	Air Force	10	2	MWC	112	2755
23	Florida Atl.	10	3	USA	103	2717
24	Florida	10	2	SEC	124	2697
25	UL Lafayette	10	3	SUN	107	2668
26	UCF	9	3	AAC	118	2622
27	Navy	9	2	AAC	116	2588
28	San Diego St.	9	3	MWC	116	2564
29	USC	8	4	PAC	111	2531
30	Virginia	9	4	ACC	111	2515
31	Hawaii	9	5	MWC	104	2501
32	W. Kentucky	8	4	USA	81	2368
33	Wake Forest	8	4	ACC	112	2332
34	Oklahoma St.	8	4	B12	116	2328
35	LA Tech	9	3	USA	93	2326
36	Kansas St.	8	4	B12	113	2303
37	Temple	8	4	AAC	112	2296
38	Texas	7	5	B12	111	2269
39	UAB	9	4	USA	73	2253
40	BYU	7	5	IND	121	2228
41	Marshall	8	4	USA	87	2179
42	Indiana	8	4	B10	104	2147
43	Arizona St.	7	5	PAC	113	2128
44	C. Mich.	8	5	MID	107	2121
45	Pittsburgh	7	5	ACC	114	2103
46	Kentucky	7	5	SEC	124	2098
47	Wash.	7	5	PAC	115	2085
48	Tennessee	7	5	SEC	123	2068
49	Louisville	7	5	ACC	104	2064
50	Miami (OH)	8	5	MID	99	2044
51	Mich. St.	6	6	B10	115	2044
52	Buffalo	7	5	MID	119	2034
53	Illinois	6	6	B10	117	1993
54	Virginia Tech	8	4	ACC	112	1990
55	California	7	5	PAC	107	1977
56	Georgia St.	7	5	SUN	107	1957
57	Wyoming	7	5	MWC	113	1948
58	W. Michigan	7	5	MID	113	1928
59	Iowa State	7	5	B12	106	1927
60	Texas A&M	7	5	SEC	110	1927
61	Nevada	7	5	MWC	105	1925
62	Georgia So.	7	5	SUN	96	1905
63	Utah State	7	5	MWC	106	1885
64	Arkansas St.	7	5	SUN	102	1863
65	Toledo	6	6	MID	121	1837
66	Miami (FL)	6	6	ACC	113	1830
67	Miss. St.	6	6	SEC	116	1817
68	Colorado	5	7	PAC	113	1790
69	Charlotte	7	5	USA	64	1754
70	S. Miss.	7	5	USA	62	1740
71	E. Mich.	6	6	MID	114	1729
72	Missouri	6	6	SEC	116	1721
73	N. Carolina	6	6	ACC	113	1718
74	Florida St.	6	6	ACC	99	1717
75	Nebraska	5	7	B10	108	1689
76	BC	6	6	ACC	106	1687
77	Wash. St.	6	6	PAC	105	1662
78	Tulane	6	6	AAC	103	1656
79	Kent State	6	6	MID	107	1596
80	Florida Int.	6	6	USA	87	1592
81	Syracuse	5	7	ACC	108	1544
82	Ohio	6	6	MID	99	1535
83	Tulsa	4	8	AAC	116	1520
84	Stanford	4	8	PAC	106	1426
85	W. Virginia	5	7	B12	108	1423
86	Duke	5	7	ACC	101	1408
87	UCLA	4	8	PAC	100	1408
88	Ball State	5	7	MID	112	1398
89	TCU	5	7	B12	109	1397
90	Oregon St.	5	7	PAC	103	1391
91	N. Illinois	5	7	MID	105	1365
92	Purdue	4	8	B10	99	1334
93	Liberty	7	5	IND	99	1299
94	Coastal Caro.	5	7	SUN	90	1270
95	UL Monroe	5	7	SUN	82	1256
96	S. Carolina	4	8	SEC	120	1242
97	Troy	5	7	SUN	76	1238
98	San Jose St.	5	7	MWC	61	1228
99	Georgia Tech	3	9	ACC	104	1135
100	Arizona	4	8	PAC	106	1114
101	NC State	4	8	ACC	99	1112
102	S. Florida	4	8	AAC	109	1103
103	UNLV	4	8	MWC	99	1093
104	Northwestern	3	9	B10	100	1089
105	Texas Tech	4	8	B12	107	1078
106	Houston	4	8	AAC	97	1066
107	Fresno St.	4	8	MWC	83	1055
108	Mid. Tenn.	4	8	USA	70	1038
109	Colorado St.	4	8	MWC	72	960
110	Ole Miss	4	8	SEC	69	945
111	North Texas	4	8	USA	48	908
112	Rice	3	9	USA	48	908
113	Army	5	7	IND	28	880
114	Vanderbilt	3	9	SEC	110	847
115	UTSA	4	8	USA	28	836
116	Kansas	3	9	B12	105	826
117	Bowling Grn	3	9	MID	98	771
118	Maryland	3	9	B10	80	753
119	Texas State	3	9	SUN	74	722
120	Rutgers	2	10	B10	56	659
121	E. Carolina	4	8	AAC	4	532
122	S. Alabama	2	10	SUN	65	453
123	Arkansas	2	10	SEC	38	361
124	Connecticut	2	10	AAC	2	272
125	New Mexico	2	10	MWC	2	272
126	UMASS	1	11	MID	1	256
127	NM St.	2	10	IND	1	256
128	Akron	0	12	MID	0	0
129	Old Dominion	1	11	USA	0	0
130	UTEP	1	11	USA	0	0

Here is the rankings using weights of {1000,100,10,1,0}:

Rank	Team	W	L	Conf	Linked Wins	Score
1	LSU	13	0	SEC	121	16227
2	Ohio State	13	0	B10	121	16198
3	Clemson	13	0	ACC	116	15170
4	Georgia	11	2	SEC	124	13948
5	Notre Dame	10	2	IND	121	13826
6	Wisconsin	10	3	B10	121	13336
7	Cincinnati	10	3	AAC	113	13044
8	SMU	10	2	AAC	116	12887
9	Boise State	12	1	MWC	116	12825
10	Memphis	12	1	AAC	115	12651
11	Utah	11	2	PAC	118	12607
12	Michigan	9	3	B10	120	12532
13	App. St.	12	1	SUN	114	12472
14	Penn State	10	2	B10	124	12274
15	Oregon	11	2	PAC	109	12181
16	Iowa	9	3	B10	117	12162
17	Oklahoma	12	1	B12	111	12060
18	Baylor	11	2	B12	112	11761
19	Minnesota	10	2	B10	123	11609
20	Auburn	9	3	SEC	122	11586
21	Alabama	10	2	SEC	115	11050
22	Air Force	10	2	MWC	112	10890
23	Florida	10	2	SEC	124	10859
24	Florida Atl.	10	3	USA	103	10798
25	UCF	9	3	AAC	118	10508
26	UL Lafayette	10	3	SUN	107	10405
27	Navy	9	2	AAC	116	10306
28	San Diego St.	9	3	MWC	116	10226
29	USC	8	4	PAC	111	10049
30	Hawaii	9	5	MWC	104	9970
31	Virginia	9	4	ACC	111	9934
32	Wake Forest	8	4	ACC	112	9366
33	W. Kentucky	8	4	USA	81	9365
34	BYU	7	5	IND	121	9244
35	Oklahoma St.	8	4	B12	116	9194
36	Kansas St.	8	4	B12	113	9116
37	Temple	8	4	AAC	112	9089
38	LA Tech	9	3	USA	93	8971
39	Texas	7	5	B12	111	8936
40	Marshall	8	4	USA	87	8758
41	Arizona St.	7	5	PAC	113	8756
42	UAB	9	4	USA	73	8720
43	Pittsburgh	7	5	ACC	114	8496
44	Wash.	7	5	PAC	115	8435
45	Louisville	7	5	ACC	104	8432
46	Indiana	8	4	B10	104	8333
47	Kentucky	7	5	SEC	124	8282
48	Tennessee	7	5	SEC	123	8247
49	Mich. St.	6	6	B10	115	8146
50	C. Mich.	8	5	MID	107	8127
51	Buffalo	7	5	MID	119	7983
52	California	7	5	PAC	107	7811
53	Illinois	6	6	B10	117	7810
54	Virginia Tech	8	4	ACC	112	7776
55	Miami (OH)	8	5	MID	99	7761
56	Georgia St.	7	5	SUN	107	7742
57	Wyoming	7	5	MWC	113	7628
58	Nevada	7	5	MWC	105	7542
59	W. Michigan	7	5	MID	113	7523
60	Iowa State	7	5	B12	106	7486
61	Texas A&M	7	5	SEC	110	7475
62	Miami (FL)	6	6	ACC	113	7458
63	Georgia So.	7	5	SUN	96	7453
64	Miss. St.	6	6	SEC	116	7400
65	Toledo	6	6	MID	121	7379
66	Utah State	7	5	MWC	106	7260
67	Arkansas St.	7	5	SUN	102	7193
68	Colorado	5	7	PAC	113	7163
69	Charlotte	7	5	USA	64	6903
70	E. Mich.	6	6	MID	114	6861
71	Florida St.	6	6	ACC	99	6828
72	S. Miss.	7	5	USA	62	6813
73	N. Carolina	6	6	ACC	113	6716
74	Missouri	6	6	SEC	116	6645
75	Nebraska	5	7	B10	108	6600
76	BC	6	6	ACC	106	6593
77	Wash. St.	6	6	PAC	105	6456
78	Tulane	6	6	AAC	103	6438
79	Syracuse	5	7	ACC	108	6326
80	Florida Int.	6	6	USA	87	6156
81	Tulsa	4	8	AAC	116	6046
82	Kent State	6	6	MID	107	6034
83	Ohio	6	6	MID	99	5762
84	Stanford	4	8	PAC	106	5523
85	UCLA	4	8	PAC	100	5497
86	Duke	5	7	ACC	101	5482
87	W. Virginia	5	7	B12	108	5447
88	TCU	5	7	B12	109	5357
89	Ball State	5	7	MID	112	5341
90	Oregon St.	5	7	PAC	103	5307
91	N. Illinois	5	7	MID	105	5209
92	Purdue	4	8	B10	99	5021
93	Liberty	7	5	IND	99	4880
94	San Jose St.	5	7	MWC	61	4812
95	Coastal Caro.	5	7	SUN	90	4768
96	UL Monroe	5	7	SUN	82	4755
97	Troy	5	7	SUN	76	4722
98	S. Carolina	4	8	SEC	120	4721
99	Georgia Tech	3	9	ACC	104	4284
100	NC State	4	8	ACC	99	4259
101	Arizona	4	8	PAC	106	4176
102	UNLV	4	8	MWC	99	4134
103	Northwestern	3	9	B10	100	4129
104	Mid. Tenn.	4	8	USA	70	4080
105	Fresno St.	4	8	MWC	83	4077
106	S. Florida	4	8	AAC	109	4020
107	Houston	4	8	AAC	97	4017
108	Texas Tech	4	8	B12	107	3920
109	Colorado St.	4	8	MWC	72	3611
110	Army	5	7	IND	28	3526
111	Ole Miss	4	8	SEC	69	3521
112	North Texas	4	8	USA	48	3484
113	Rice	3	9	USA	48	3484
114	UTSA	4	8	USA	28	3227
115	Vanderbilt	3	9	SEC	110	3132
116	Kansas	3	9	B12	105	3017
117	Maryland	3	9	B10	80	2728
118	Bowling Grn	3	9	MID	98	2714
119	Texas State	3	9	SUN	74	2661
120	Rutgers	2	10	B10	56	2475
121	E. Carolina	4	8	AAC	4	2110
122	S. Alabama	2	10	SUN	65	1706
123	Arkansas	2	10	SEC	38	1358
124	Connecticut	2	10	AAC	2	1100
125	New Mexico	2	10	MWC	2	1100
126	UMASS	1	11	MID	1	1000
127	NM St.	2	10	IND	1	1000
128	Akron	0	12	MID	0	0
129	Old Dominion	1	11	USA	0	0
130	UTEP	1	11	USA	0	0