IowaHawkBlog's Degrees of Separation Ranking - Week 11

Welcome everyone to the newest ranking system proposed by the great David Burge.  In this system, a teams 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.

In a situation where a linked win would be a team defeating itself, those do not result in any points being awarded to the primary team.  Say team E manages to beat Team A in the example above, thus meaning A has a linked win over itself, Team A does not get points for beating itself.

I think that's basically it.  Losses do nothing other than prevent teams from getting points or any linked wins.  This inherently accounts for quality of schedule, as the better the teams are that you beat, the more linked wins they will deliver to your count.

The rankings are tabulated below.

EDIT (11/10/19 11:00):  After discussion with David, he clarified a couple things on how this should work, and I've updated my code accordingly.  Essentially, you only get credit for a linked win over another team once. Whatever the fewest number of degrees is to get to that linked win is the one that gets counted, regardless of whether you have other paths of victory over that team at farther degrees of separation. The updated rankings are below.

EDIT (11/11/19 18:00): I am adding in a couple additional tables where we are using the exact same procedure, but changing up the weightings for the respective degrees of separation.  The top table here still uses weights of {5,4,3,2,1} for the first five degrees.  Below I have included tables using {256,16,4,2,1} (power) and using {1000,100,10,1,0} (logarithmic).

Rank	Team	W	L	Conf	Linked Wins	Score
1	LSU	9	0	SEC	116	359
2	Georgia	8	1	SEC	112	315
3	Penn State	8	1	B10	114	313
4	SMU	9	1	AAC	113	313
5	BYU	5	4	IND	114	312
6	Florida	8	2	SEC	112	310
7	Ohio State	9	0	B10	112	308
8	Wisconsin	7	2	B10	112	305
9	Michigan	7	2	B10	107	301
10	Minnesota	9	0	B10	113	300
11	Boise State	8	1	MWC	107	296
12	Notre Dame	7	2	IND	106	290
13	Auburn	7	2	SEC	102	286
14	Clemson	10	0	ACC	100	281
15	Memphis	8	1	AAC	108	278
16	Oklahoma St.	6	3	B12	108	278
17	Utah	8	1	PAC	105	278
18	Cincinnati	8	1	AAC	101	272
19	Toledo	6	3	MID	106	272
20	Kansas St.	6	3	B12	107	269
21	Oklahoma	8	1	B12	105	267
22	UCF	7	3	AAC	105	267
23	Temple	6	3	AAC	109	265
24	App. St.	8	1	SUN	101	263
25	Wash.	6	4	PAC	107	263
26	Texas	6	3	B12	106	261
27	Miami (FL)	6	4	ACC	103	260
28	Pittsburgh	6	3	ACC	104	259
29	Wake Forest	7	2	ACC	99	256
30	Baylor	9	0	B12	102	254
31	USC	6	4	PAC	100	248
32	Oregon	8	1	PAC	97	247
33	Alabama	8	1	SEC	96	246
34	Illinois	6	4	B10	105	246
35	Navy	7	1	AAC	100	246
36	Virginia	7	3	ACC	101	241
37	S. Carolina	4	6	SEC	110	240
38	Tulsa	3	7	AAC	99	240
39	Kentucky	4	5	SEC	104	239
40	Mich. St.	4	5	B10	97	239
41	Iowa	6	3	B10	92	236
42	Buffalo	5	4	MID	106	235
43	N. Carolina	4	5	ACC	102	235
44	Miss. St.	4	5	SEC	99	231
45	Virginia Tech	6	3	ACC	97	229
46	Louisville	5	4	ACC	90	227
47	Tennessee	5	5	SEC	103	226
48	Arizona St.	5	4	PAC	91	224
49	E. Mich.	4	5	MID	96	224
50	Florida St.	5	5	ACC	89	221
51	TCU	4	5	B12	102	219
52	Colorado	4	6	PAC	92	217
53	California	5	4	PAC	91	216
54	W. Michigan	6	4	MID	96	216
55	Georgia Tech	2	7	ACC	98	215
56	S. Florida	4	5	AAC	98	215
57	San Diego St.	7	2	MWC	86	212
58	UL Lafayette	7	2	SUN	91	211
59	Ball State	4	5	MID	98	210
60	UCLA	4	5	PAC	91	203
61	Iowa State	5	4	B12	92	201
62	Stanford	4	5	PAC	93	201
63	Air Force	7	2	MWC	79	200
64	Wyoming	6	3	MWC	86	200
65	Texas Tech	4	5	B12	96	199
66	Missouri	5	4	SEC	92	197
67	Arizona	4	5	PAC	89	191
68	BC	5	5	ACC	86	191
69	Georgia St.	6	3	SUN	81	191
70	Oregon St.	4	5	PAC	89	188
71	Hawaii	6	4	MWC	79	187
72	Georgia So.	5	4	SUN	82	185
73	Kansas	3	6	B12	95	183
74	Duke	4	5	ACC	84	182
75	Nevada	6	4	MWC	73	176
76	C. Mich.	6	4	MID	85	174
77	Texas A&M	6	3	SEC	72	174
78	Florida Atl.	7	3	USA	77	173
79	Indiana	7	2	B10	77	173
80	Tulane	6	3	AAC	77	173
81	Bowling Grn	3	6	MID	87	170
82	Ohio	4	5	MID	87	170
83	Nebraska	4	5	B10	76	163
84	LA Tech	8	1	USA	72	159
85	Utah State	5	4	MWC	68	158
86	Wash. St.	4	5	PAC	72	156
87	NC State	4	5	ACC	76	152
88	Marshall	6	3	USA	64	150
89	Miami (OH)	5	4	MID	74	149
90	Syracuse	3	6	ACC	69	148
91	Purdue	4	6	B10	63	144
92	Liberty	6	4	IND	72	143
93	W. Virginia	3	6	B12	72	138
94	Fresno St.	4	5	MWC	63	135
95	Coastal Caro.	4	5	SUN	69	131
96	Vanderbilt	2	7	SEC	65	129
97	UL Monroe	4	5	SUN	53	116
98	Texas State	3	6	SUN	53	114
99	Troy	4	5	SUN	58	109
100	Arkansas St.	5	4	SUN	49	108
101	S. Miss.	6	3	USA	43	101
102	Colorado St.	4	5	MWC	49	97
103	Mid. Tenn.	3	6	USA	40	97
104	W. Kentucky	6	4	USA	33	97
105	Maryland	3	7	B10	44	90
106	Ole Miss	4	6	SEC	43	90
107	N. Illinois	3	6	MID	49	87
108	Kent State	3	6	MID	53	86
109	Rutgers	2	7	B10	41	77
110	Charlotte	5	5	USA	27	71
111	UNLV	2	7	MWC	36	69
112	North Texas	4	6	USA	27	68
113	San Jose St.	4	6	MWC	20	59
114	Houston	3	6	AAC	21	55
115	Arkansas	2	8	SEC	27	52
116	Florida Int.	5	5	USA	19	52
117	Northwestern	1	8	B10	21	38
118	UAB	6	3	USA	6	29
119	Army	4	6	IND	6	27
120	UTSA	4	5	USA	3	15
121	Connecticut	2	8	AAC	2	9
122	E. Carolina	3	7	AAC	1	5
123	UMASS	1	9	MID	1	5
124	New Mexico	2	7	MWC	1	5
125	Akron	0	9	MID	0	0
126	NM St.	0	9	IND	0	0
127	Old Dominion	1	9	USA	0	0
128	Rice	0	9	USA	0	0
129	S. Alabama	1	8	SUN	0	0
130	UTEP	1	8	USA	0	0

Here is the same thing with weights of {256,16,4,2,1}:

Rank	Team	W	L	Conf	Linked Wins	Score
1	Ohio State	9	0	B10	112	2917
2	SMU	9	1	AAC	113	2846
3	Clemson	10	0	ACC	100	2844
4	LSU	9	0	SEC	116	2766
5	Minnesota	9	0	B10	113	2578
6	Cincinnati	8	1	AAC	101	2515
7	Alabama	8	1	SEC	96	2456
8	Baylor	9	0	B12	102	2431
9	Georgia	8	1	SEC	112	2373
10	Penn State	8	1	B10	114	2370
11	Michigan	7	2	B10	107	2358
12	Boise State	8	1	MWC	107	2351
13	Wisconsin	7	2	B10	112	2346
14	Auburn	7	2	SEC	102	2342
15	Notre Dame	7	2	IND	106	2309
16	Memphis	8	1	AAC	108	2291
17	Utah	8	1	PAC	105	2271
18	App. St.	8	1	SUN	101	2264
19	Oregon	8	1	PAC	97	2252
20	Oklahoma	8	1	B12	105	2231
21	Florida	8	2	SEC	112	2074
22	LA Tech	8	1	USA	72	2020
23	UCF	7	3	AAC	105	1993
24	Texas	6	3	B12	106	1972
25	Wake Forest	7	2	ACC	99	1970
26	USC	6	4	PAC	100	1968
27	Iowa	6	3	B10	92	1958
28	Illinois	6	4	B10	105	1942
29	Navy	7	1	AAC	100	1934
30	Virginia	7	3	ACC	101	1915
31	Air Force	7	2	MWC	79	1903
32	BYU	5	4	IND	114	1893
33	UL Lafayette	7	2	SUN	91	1888
34	San Diego St.	7	2	MWC	86	1884
35	Florida Atl.	7	3	USA	77	1810
36	Indiana	7	2	B10	77	1801
37	Toledo	6	3	MID	106	1751
38	Miami (FL)	6	4	ACC	103	1748
39	Oklahoma St.	6	3	B12	108	1748
40	Wash.	6	4	PAC	107	1726
41	Kansas St.	6	3	B12	107	1725
42	Pittsburgh	6	3	ACC	104	1723
43	W. Kentucky	6	4	USA	33	1715
44	Temple	6	3	AAC	109	1703
45	Florida St.	5	5	ACC	89	1647
46	W. Michigan	6	4	MID	96	1644
47	Georgia St.	6	3	SUN	81	1628
48	Wyoming	6	3	MWC	86	1616
49	Hawaii	6	4	MWC	79	1580
50	Nevada	6	4	MWC	73	1578
51	Texas A&M	6	3	SEC	72	1578
52	Tulane	6	3	AAC	77	1560
53	Marshall	6	3	USA	64	1526
54	C. Mich.	6	4	MID	85	1504
55	Louisville	5	4	ACC	90	1456
56	Miss. St.	4	5	SEC	99	1438
57	S. Miss.	6	3	USA	43	1433
58	Mich. St.	4	5	B10	97	1428
59	Colorado	4	6	PAC	92	1409
60	Tennessee	5	5	SEC	103	1405
61	Virginia Tech	6	3	ACC	97	1399
62	California	5	4	PAC	91	1398
63	Arizona St.	5	4	PAC	91	1397
64	N. Carolina	4	5	ACC	102	1397
65	Buffalo	5	4	MID	106	1395
66	Kentucky	4	5	SEC	104	1390
67	UCLA	4	5	PAC	91	1357
68	Missouri	5	4	SEC	92	1336
69	Iowa State	5	4	B12	92	1331
70	BC	5	5	ACC	86	1323
71	Stanford	4	5	PAC	93	1320
72	Georgia So.	5	4	SUN	82	1302
73	UAB	6	3	USA	6	1296
74	Utah State	5	4	MWC	68	1284
75	Nebraska	4	5	B10	76	1277
76	Purdue	4	6	B10	63	1244
77	Miami (OH)	5	4	MID	74	1235
78	Liberty	6	4	IND	72	1205
79	Arkansas St.	5	4	SUN	49	1179
80	Tulsa	3	7	AAC	99	1179
81	E. Mich.	4	5	MID	96	1168
82	Charlotte	5	5	USA	27	1128
83	S. Carolina	4	6	SEC	110	1126
84	TCU	4	5	B12	102	1124
85	Florida Int.	5	5	USA	19	1094
86	Ball State	4	5	MID	98	1080
87	S. Florida	4	5	AAC	98	1076
88	Arizona	4	5	PAC	89	1060
89	Oregon St.	4	5	PAC	89	1054
90	Texas Tech	4	5	B12	96	1052
91	Duke	4	5	ACC	84	1038
92	Ohio	4	5	MID	87	1018
93	Wash. St.	4	5	PAC	72	998
94	NC State	4	5	ACC	76	992
95	Fresno St.	4	5	MWC	63	971
96	Coastal Caro.	4	5	SUN	69	953
97	UL Monroe	4	5	SUN	53	940
98	Troy	4	5	SUN	58	905
99	Colorado St.	4	5	MWC	49	892
100	Ole Miss	4	6	SEC	43	887
101	San Jose St.	4	6	MWC	20	877
102	North Texas	4	6	USA	27	874
103	Georgia Tech	2	7	ACC	98	835
104	Army	4	6	IND	6	816
105	Kansas	3	6	B12	95	783
106	Syracuse	3	6	ACC	69	770
107	UTSA	4	5	USA	3	768
108	Bowling Grn	3	6	MID	87	746
109	Vanderbilt	2	7	SEC	65	714
110	W. Virginia	3	6	B12	72	710
111	Mid. Tenn.	3	6	USA	40	703
112	Texas State	3	6	SUN	53	688
113	Maryland	3	7	B10	44	637
114	N. Illinois	3	6	MID	49	630
115	Rutgers	2	7	B10	41	630
116	Houston	3	6	AAC	21	610
117	Kent State	3	6	MID	53	604
118	UNLV	2	7	MWC	36	350
119	Arkansas	2	8	SEC	27	342
120	Northwestern	1	8	B10	21	303
121	Connecticut	2	8	AAC	2	272
122	E. Carolina	3	7	AAC	1	256
123	UMASS	1	9	MID	1	256
124	New Mexico	2	7	MWC	1	256
125	Akron	0	9	MID	0	0
126	NM St.	0	9	IND	0	0
127	Old Dominion	1	9	USA	0	0
128	Rice	0	9	USA	0	0
129	S. Alabama	1	8	SUN	0	0
130	UTEP	1	8	USA	0	0

Here is the same procedure with [1000,100,10,1,0] for the weights of the 5 degrees:

Rank	Team	W	L	Conf	Linked Wins	Score
1	Ohio State	9	0	B10	112	11987
2	Clemson	10	0	ACC	100	11600
3	LSU	9	0	SEC	116	11432
4	SMU	9	1	AAC	113	11376
5	Minnesota	9	0	B10	113	10335
6	Cincinnati	8	1	AAC	101	10036
7	Alabama	8	1	SEC	96	9749
8	Georgia	8	1	SEC	112	9605
9	Penn State	8	1	B10	114	9593
10	Michigan	7	2	B10	107	9588
11	Auburn	7	2	SEC	102	9570
12	Boise State	8	1	MWC	107	9567
13	Baylor	9	0	B12	102	9484
14	Wisconsin	7	2	B10	112	9458
15	Notre Dame	7	2	IND	106	9271
16	Memphis	8	1	AAC	108	9209
17	Oregon	8	1	PAC	97	9125
18	App. St.	8	1	SUN	101	9104
19	Utah	8	1	PAC	105	9050
20	Oklahoma	8	1	B12	105	8805
21	Florida	8	2	SEC	112	8256
22	UCF	7	3	AAC	105	7914
23	LA Tech	8	1	USA	72	7899
24	Iowa	6	3	B10	92	7864
25	USC	6	4	PAC	100	7852
26	Wake Forest	7	2	ACC	99	7812
27	BYU	5	4	IND	114	7810
28	Texas	6	3	B12	106	7786
29	Air Force	7	2	MWC	79	7688
30	Illinois	6	4	B10	105	7651
31	Navy	7	1	AAC	100	7591
32	UL Lafayette	7	2	SUN	91	7477
33	Virginia	7	3	ACC	101	7472
34	San Diego St.	7	2	MWC	86	7442
35	Florida Atl.	7	3	USA	77	7130
36	Indiana	7	2	B10	77	7057
37	Miami (FL)	6	4	ACC	103	7018
38	Toledo	6	3	MID	106	6954
39	W. Kentucky	6	4	USA	33	6945
40	Oklahoma St.	6	3	B12	108	6885
41	Pittsburgh	6	3	ACC	104	6822
42	Wash.	6	4	PAC	107	6815
43	Kansas St.	6	3	B12	107	6764
44	Temple	6	3	AAC	109	6613
45	Georgia St.	6	3	SUN	81	6560
46	W. Michigan	6	4	MID	96	6497
47	Florida St.	5	5	ACC	89	6492
48	Wyoming	6	3	MWC	86	6394
49	Texas A&M	6	3	SEC	72	6285
50	Nevada	6	4	MWC	73	6270
51	Hawaii	6	4	MWC	79	6202
52	Tulane	6	3	AAC	77	6142
53	Marshall	6	3	USA	64	6043
54	Louisville	5	4	ACC	90	5938
55	Miss. St.	4	5	SEC	99	5755
56	C. Mich.	6	4	MID	85	5674
57	S. Miss.	6	3	USA	43	5660
58	Colorado	4	6	PAC	92	5627
59	Mich. St.	4	5	B10	97	5619
60	California	5	4	PAC	91	5546
61	Tennessee	5	5	SEC	103	5520
62	Arizona St.	5	4	PAC	91	5481
63	Virginia Tech	6	3	ACC	97	5456
64	N. Carolina	4	5	ACC	102	5392
65	Buffalo	5	4	MID	106	5372
66	UCLA	4	5	PAC	91	5307
67	Kentucky	4	5	SEC	104	5305
68	Missouri	5	4	SEC	92	5179
69	BC	5	5	ACC	86	5122
70	Iowa State	5	4	B12	92	5110
71	UAB	6	3	USA	6	5100
72	Utah State	5	4	MWC	68	5059
73	Stanford	4	5	PAC	93	5020
74	Georgia So.	5	4	SUN	82	4999
75	Nebraska	4	5	B10	76	4959
76	Purdue	4	6	B10	63	4840
77	Miami (OH)	5	4	MID	74	4721
78	E. Mich.	4	5	MID	96	4658
79	Tulsa	3	7	AAC	99	4630
80	Arkansas St.	5	4	SUN	49	4584
81	Liberty	6	4	IND	72	4523
82	Charlotte	5	5	USA	27	4456
83	TCU	4	5	B12	102	4332
84	Florida Int.	5	5	USA	19	4324
85	S. Carolina	4	6	SEC	110	4191
86	Ball State	4	5	MID	98	4044
87	Arizona	4	5	PAC	89	4026
88	Oregon St.	4	5	PAC	89	3999
89	S. Florida	4	5	AAC	98	3976
90	Duke	4	5	ACC	84	3917
91	Texas Tech	4	5	B12	96	3898
92	Ohio	4	5	MID	87	3838
93	Wash. St.	4	5	PAC	72	3790
94	NC State	4	5	ACC	76	3766
95	Fresno St.	4	5	MWC	63	3730
96	UL Monroe	4	5	SUN	53	3624
97	Coastal Caro.	4	5	SUN	69	3607
98	San Jose St.	4	6	MWC	20	3552
99	North Texas	4	6	USA	27	3457
100	Ole Miss	4	6	SEC	43	3390
101	Troy	4	5	SUN	58	3386
102	Colorado St.	4	5	MWC	49	3375
103	Army	4	6	IND	6	3300
104	Georgia Tech	2	7	ACC	98	3061
105	Syracuse	3	6	ACC	69	3040
106	UTSA	4	5	USA	3	3000
107	Mid. Tenn.	3	6	USA	40	2889
108	Kansas	3	6	B12	95	2871
109	Vanderbilt	2	7	SEC	65	2726
110	Bowling Grn	3	6	MID	87	2672
111	Texas State	3	6	SUN	53	2634
112	W. Virginia	3	6	B12	72	2623
113	Houston	3	6	AAC	21	2454
114	Rutgers	2	7	B10	41	2440
115	Maryland	3	7	B10	44	2401
116	N. Illinois	3	6	MID	49	2361
117	Kent State	3	6	MID	53	2154
118	Arkansas	2	8	SEC	27	1336
119	UNLV	2	7	MWC	36	1271
120	Northwestern	1	8	B10	21	1126
121	Connecticut	2	8	AAC	2	1100
122	E. Carolina	3	7	AAC	1	1000
123	UMASS	1	9	MID	1	1000
124	New Mexico	2	7	MWC	1	1000
125	Akron	0	9	MID	0	0
126	NM St.	0	9	IND	0	0
127	Old Dominion	1	9	USA	0	0
128	Rice	0	9	USA	0	0
129	S. Alabama	1	8	SUN	0	0
130	UTEP	1	8	USA	0	0