B10 vs SEC schedules 2020

What a Difference Two Games Make!

B10 vs SEC schedules 2020

24 September 2020

The 2020 college football season is a mess, but the Big Ten's decision to play an 8-conference-game-only schedule actually gives us an opportunity to measure some of the effects of schedule topology on ratings that depend upon the connectivity of the games graph. That the SEC and now Big 10 are playing only conference schedules the D1 field as a whole is not connected.

Both leagues have two 7-team divisions so the schedules are asymmetric.

Schedules

B10

	IN	MD	MI	MS	OS	PS	RU	IL	IA	MN	NE	NW	PU	WI
IN		1	1	1	1	1	1	0	0	0	0	0	1	1
MD	1		1	1	1	1	1	0	0	1	0	1	0	0
MI	1	1		1	1	1	1	0	0	1	0	0	0	1
MS	1	1	1		1	1	1	0	1	0	0	1	0	0
OS	1	1	1	1		1	1	1	0	0	1	0	0	0
PS	1	1	1	1	1		1	0	1	0	1	0	0	0
RU	1	1	1	1	1	1		1	0	0	0	0	1	0
IL	0	0	0	0	1	0	1		1	1	1	1	1	1
IA	0	0	0	1	0	1	0	1		1	1	1	1	1
MN	0	1	1	0	0	0	0	1	1		1	1	1	1
NE	0	0	0	0	1	1	0	1	1	1		1	1	1
NW	0	1	0	1	0	0	0	1	1	1	1		1	1
PU	1	0	0	0	0	0	1	1	1	1	1	1		1
WI	1	0	1	0	0	0	0	1	1	1	1	1	1

SEC

	UF	UG	UK	UM	SC	UT	VU	UA	AR	AU	LS	OM	MS	AM
UF		1	1	1	1	1	1	0	1	0	1	1	0	1
UG	1		1	1	1	1	1	1	1	1	0	0	1	0
UK	1	1		1	1	1	1	1	0	1	0	1	1	0
UM	1	1	1		1	1	1	1	1	0	1	0	1	0
SC	1	1	1	1		1	1	0	0	1	1	1	0	1
UT	1	1	1	1	1		1	1	1	1	0	0	0	1
VU	1	1	1	1	1	1		0	0	0	1	1	1	1
UA	0	1	1	1	0	1	0		1	1	1	1	1	1
AR	1	1	0	1	0	1	0	1		1	1	1	1	1
AU	0	1	1	0	1	1	0	1	1		1	1	1	1
LS	1	0	0	1	1	0	1	1	1	1		1	1	1
OM	1	0	1	0	1	0	1	1	1	1	1		1	1
MS	0	1	1	1	0	0	1	1	1	1	1	1		1
AM	1	0	0	0	1	1	1	1	1	1	1	1	1

The SEC's two extra games make its schedule more tightly connected than the Big Ten's.

Number of Common Opponents

B10

	IN	MD	MI	MS	OS	PS	RU	IL	IA	MN	NE	NW	PU	WI
IN		5	6	5	5	5	6	4	4	4	4	4	2	2
MD	5		6	6	5	5	5	4	4	2	4	2	4	4
MI	6	6		5	5	5	5	4	4	2	4	4	4	2
MS	5	6	5		5	6	5	4	2	4	4	2	4	4
OS	5	5	5	5		6	6	2	4	4	2	4	4	4
PS	5	5	5	6	6		5	4	2	4	2	4	4	4
RU	6	5	5	5	6	5		2	4	4	4	4	2	4
IL	4	4	4	4	2	4	2		5	5	6	5	6	5
IA	4	4	4	2	4	2	4	5		5	6	6	5	5
MN	4	2	2	4	4	4	4	5	5		5	6	5	6
NE	4	4	4	4	2	2	4	6	6	5		5	5	5
NW	4	2	4	2	4	4	4	5	6	6	5		5	5
PU	2	4	4	4	4	4	2	6	5	5	5	5		6
WI	2	4	2	4	4	4	4	5	5	6	5	5	6

SEC

	UF	UG	UK	UM	SC	UT	VU	UA	AR	AU	LS	OM	MS	AM
UF		6	6	7	8	7	8	8	6	8	6	6	8	6
UG	6		8	8	6	8	6	6	6	6	8	8	6	8
UK	6	8		7	7	7	7	6	8	6	8	6	6	8
UM	7	8	7		6	7	7	6	6	8	6	8	6	8
SC	8	6	7	6		7	8	8	8	6	6	6	8	6
UT	7	8	7	7	7		6	6	6	6	8	8	8	6
VU	8	6	7	7	8	6		8	8	8	6	6	6	6
UA	8	6	6	6	8	6	8		8	8	6	6	8	6
AR	6	6	8	6	8	6	8	8		7	7	6	7	7
AU	8	6	6	8	6	6	8	8	7		6	7	7	7
LS	6	8	8	6	6	8	6	6	7	6		8	7	8
OM	6	8	6	8	6	8	6	6	6	7	8		7	8
MS	8	6	6	6	8	8	6	8	7	7	7	7		6
AM	6	8	8	8	6	6	6	6	7	7	8	8	6

Number of Paths 3 Edges Long

Diag	[3]	Team	_16	_17	_18	_19	_20	_21	_22	_23	_24	_25	_26	_27	_28	_29	_40	_41	_42	_43	_44	_45	_46	_47	_48	_49	_50	_51	_52	_53
36	_16	Indiana	36	43	40	43	43	43	40	31	30	31	30	30	36	36	0	0	0	0	0	0	0	0	0	0	0	0	0	0
36	_17	Maryland	43	36	40	40	43	43	43	30	31	36	30	36	30	31	0	0	0	0	0	0	0	0	0	0	0	0	0	0
36	_18	Michigan	40	40	36	43	43	43	43	30	30	36	30	31	31	36	0	0	0	0	0	0	0	0	0	0	0	0	0	0
36	_19	Michigan State	43	40	43	36	43	40	43	30	36	31	31	36	30	30	0	0	0	0	0	0	0	0	0	0	0	0	0	0
36	_20	Ohio State	43	43	43	43	36	40	40	36	31	30	36	30	31	30	0	0	0	0	0	0	0	0	0	0	0	0	0	0
36	_21	Penn State	43	43	43	40	40	36	43	31	36	30	36	31	30	30	0	0	0	0	0	0	0	0	0	0	0	0	0	0
36	_22	Rutgers	40	43	43	43	40	43	36	36	30	30	31	30	36	31	0	0	0	0	0	0	0	0	0	0	0	0	0	0
36	_23	Illinois	31	30	30	30	36	31	36	36	43	43	40	43	40	43	0	0	0	0	0	0	0	0	0	0	0	0	0	0
36	_24	Iowa	30	31	30	36	31	36	30	43	36	43	40	40	43	43	0	0	0	0	0	0	0	0	0	0	0	0	0	0
36	_25	Minnesota	31	36	36	31	30	30	30	43	43	36	43	40	43	40	0	0	0	0	0	0	0	0	0	0	0	0	0	0
36	_26	Nebraska	30	30	30	31	36	36	31	40	40	43	36	43	43	43	0	0	0	0	0	0	0	0	0	0	0	0	0	0
36	_27	Northwestern	30	36	31	36	30	31	30	43	40	40	43	36	43	43	0	0	0	0	0	0	0	0	0	0	0	0	0	0
36	_28	Purdue	36	30	31	30	31	30	36	40	43	43	43	43	36	40	0	0	0	0	0	0	0	0	0	0	0	0	0	0
36	_29	Wisconsin	36	31	36	30	30	30	31	43	43	40	43	43	40	36	0	0	0	0	0	0	0	0	0	0	0	0	0	0
66	_40	Florida	0	0	0	0	0	0	0	0	0	0	0	0	0	0	66	76	76	73	70	73	70	66	72	67	75	74	67	75
66	_41	Georgia	0	0	0	0	0	0	0	0	0	0	0	0	0	0	76	66	70	70	76	70	76	76	74	74	66	66	74	66
66	_42	Kentucky	0	0	0	0	0	0	0	0	0	0	0	0	0	0	76	70	66	73	73	73	73	74	68	74	67	72	74	67
66	_43	Missouri	0	0	0	0	0	0	0	0	0	0	0	0	0	0	73	70	73	66	76	73	73	74	74	68	72	67	74	67
66	_44	South Carolina	0	0	0	0	0	0	0	0	0	0	0	0	0	0	70	76	73	76	66	73	70	66	67	72	74	75	67	75
66	_45	Tennessee	0	0	0	0	0	0	0	0	0	0	0	0	0	0	73	70	73	73	73	66	76	74	74	74	67	67	68	72
66	_46	Vanderbilt	0	0	0	0	0	0	0	0	0	0	0	0	0	0	70	76	73	73	70	76	66	66	67	67	75	75	72	74
66	_47	Alabama	0	0	0	0	0	0	0	0	0	0	0	0	0	0	66	76	74	74	66	74	66	66	70	70	76	76	70	76
66	_48	Arkansas	0	0	0	0	0	0	0	0	0	0	0	0	0	0	72	74	68	74	67	74	67	70	66	73	73	76	73	73
66	_49	Auburn	0	0	0	0	0	0	0	0	0	0	0	0	0	0	67	74	74	68	72	74	67	70	73	66	76	73	73	73
66	_50	LSU	0	0	0	0	0	0	0	0	0	0	0	0	0	0	75	66	67	72	74	67	75	76	73	76	66	70	73	70
66	_51	Mississippi	0	0	0	0	0	0	0	0	0	0	0	0	0	0	74	66	72	67	75	67	75	76	76	73	70	66	73	70
66	_52	Mississippi State	0	0	0	0	0	0	0	0	0	0	0	0	0	0	67	74	74	74	67	68	72	70	73	73	73	73	66	76
66	_53	Texas A&M	0	0	0	0	0	0	0	0	0	0	0	0	0	0	75	66	67	67	75	72	74	76	73	73	70	70	76	66

Number of Paths 4 Edges Long

Diag	[4]	Team	_16	_17	_18	_19	_20	_21	_22	_23	_24	_25	_26	_27	_28	_29	_40	_41	_42	_43	_44	_45	_46	_47	_48	_49	_50	_51	_52	_53
324	_16	Indiana	324	306	315	305	306	305	315	276	280	276	280	280	264	264	0	0	0	0	0	0	0	0	0	0	0	0	0	0
324	_17	Maryland	306	324	315	315	305	306	305	280	276	264	280	264	280	276	0	0	0	0	0	0	0	0	0	0	0	0	0	0
324	_18	Michigan	315	315	324	306	305	305	306	280	280	264	280	276	276	264	0	0	0	0	0	0	0	0	0	0	0	0	0	0
324	_19	Michigan State	305	315	306	324	306	315	305	280	264	276	276	264	280	280	0	0	0	0	0	0	0	0	0	0	0	0	0	0
324	_20	Ohio State	306	305	305	306	324	315	315	264	276	280	264	280	276	280	0	0	0	0	0	0	0	0	0	0	0	0	0	0
324	_21	Penn State	305	306	305	315	315	324	306	276	264	280	264	276	280	280	0	0	0	0	0	0	0	0	0	0	0	0	0	0
324	_22	Rutgers	315	305	306	305	315	306	324	264	280	280	276	280	264	276	0	0	0	0	0	0	0	0	0	0	0	0	0	0
324	_23	Illinois	276	280	280	280	264	276	264	324	306	305	315	305	315	306	0	0	0	0	0	0	0	0	0	0	0	0	0	0
324	_24	Iowa	280	276	280	264	276	264	280	306	324	306	315	315	305	305	0	0	0	0	0	0	0	0	0	0	0	0	0	0
324	_25	Minnesota	276	264	264	276	280	280	280	305	306	324	305	315	306	315	0	0	0	0	0	0	0	0	0	0	0	0	0	0
324	_26	Nebraska	280	280	280	276	264	264	276	315	315	305	324	306	306	305	0	0	0	0	0	0	0	0	0	0	0	0	0	0
324	_27	Northwestern	280	264	276	264	280	276	280	305	315	315	306	324	305	306	0	0	0	0	0	0	0	0	0	0	0	0	0	0
324	_28	Purdue	264	280	276	280	276	280	264	315	305	306	306	305	324	315	0	0	0	0	0	0	0	0	0	0	0	0	0	0
324	_29	Wisconsin	264	276	264	280	280	280	276	306	305	315	305	306	315	324	0	0	0	0	0	0	0	0	0	0	0	0	0	0
734	_40	Florida	0	0	0	0	0	0	0	0	0	0	0	0	0	0	734	700	702	711	725	711	725	728	712	724	700	704	724	700
736	_41	Georgia	0	0	0	0	0	0	0	0	0	0	0	0	0	0	700	736	724	724	700	724	700	696	704	704	728	728	704	728
732	_42	Kentucky	0	0	0	0	0	0	0	0	0	0	0	0	0	0	702	724	732	714	711	714	711	704	720	704	724	712	704	724
732	_43	Missouri	0	0	0	0	0	0	0	0	0	0	0	0	0	0	711	724	714	732	702	714	711	704	704	720	712	724	704	724
734	_44	South Carolina	0	0	0	0	0	0	0	0	0	0	0	0	0	0	725	700	711	702	734	711	725	728	724	712	704	700	724	700
732	_45	Tennessee	0	0	0	0	0	0	0	0	0	0	0	0	0	0	711	724	714	714	711	732	702	704	704	704	724	724	720	712
734	_46	Vanderbilt	0	0	0	0	0	0	0	0	0	0	0	0	0	0	725	700	711	711	725	702	734	728	724	724	700	700	712	704
736	_47	Alabama	0	0	0	0	0	0	0	0	0	0	0	0	0	0	728	696	704	704	728	704	728	736	724	724	700	700	724	700
732	_48	Arkansas	0	0	0	0	0	0	0	0	0	0	0	0	0	0	712	704	720	704	724	704	724	724	732	714	711	702	714	711
732	_49	Auburn	0	0	0	0	0	0	0	0	0	0	0	0	0	0	724	704	704	720	712	704	724	724	714	732	702	711	714	711
734	_50	LSU	0	0	0	0	0	0	0	0	0	0	0	0	0	0	700	728	724	712	704	724	700	700	711	702	734	725	711	725
734	_51	Mississippi	0	0	0	0	0	0	0	0	0	0	0	0	0	0	704	728	712	724	700	724	700	700	702	711	725	734	711	725
732	_52	Mississippi State	0	0	0	0	0	0	0	0	0	0	0	0	0	0	724	704	704	704	724	720	712	724	714	714	711	711	732	702
734	_53	Texas A&M	0	0	0	0	0	0	0	0	0	0	0	0	0	0	700	728	724	724	700	712	704	700	711	711	725	725	702	734

Number of Paths 5 Edges Long

Diag	[5]	Team	_16	_17	_18	_19	_20	_21	_22	_23	_24	_25	_26	_27	_28	_29	_40	_41	_42	_43	_44	_45	_46	_47	_48	_49	_50	_51	_52	_53
2380	_16	Indiana	2380	2426	2401	2431	2426	2431	2401	2265	2250	2265	2251	2251	2295	2295	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2380	_17	Maryland	2426	2380	2401	2401	2431	2426	2431	2250	2265	2295	2251	2295	2251	2265	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2380	_18	Michigan	2401	2401	2380	2426	2431	2431	2426	2251	2251	2295	2250	2265	2265	2295	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2380	_19	Michigan State	2431	2401	2426	2380	2426	2401	2431	2251	2295	2265	2265	2295	2250	2251	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2380	_20	Ohio State	2426	2431	2431	2426	2380	2401	2401	2295	2265	2250	2295	2251	2265	2251	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2380	_21	Penn State	2431	2426	2431	2401	2401	2380	2426	2265	2295	2251	2295	2265	2251	2250	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2380	_22	Rutgers	2401	2431	2426	2431	2401	2426	2380	2295	2251	2251	2265	2250	2295	2265	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2380	_23	Illinois	2265	2250	2251	2251	2295	2265	2295	2380	2426	2431	2401	2431	2401	2426	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2380	_24	Iowa	2250	2265	2251	2295	2265	2295	2251	2426	2380	2426	2401	2401	2431	2431	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2380	_25	Minnesota	2265	2295	2295	2265	2250	2251	2251	2431	2426	2380	2431	2401	2426	2401	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2380	_26	Nebraska	2251	2251	2250	2265	2295	2295	2265	2401	2401	2431	2380	2426	2426	2431	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2380	_27	Northwestern	2251	2295	2265	2295	2251	2265	2250	2431	2401	2401	2426	2380	2431	2426	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2380	_28	Purdue	2295	2251	2265	2250	2265	2251	2295	2401	2431	2426	2426	2431	2380	2401	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2380	_29	Wisconsin	2295	2265	2295	2251	2251	2250	2265	2426	2431	2401	2431	2426	2401	2380	0	0	0	0	0	0	0	0	0	0	0	0	0	0
7090	_40	Florida	0	0	0	0	0	0	0	0	0	0	0	0	0	0	7090	7196	7186	7161	7111	7161	7111	7088	7136	7106	7187	7174	7106	7187
7080	_41	Georgia	0	0	0	0	0	0	0	0	0	0	0	0	0	0	7196	7080	7116	7116	7196	7116	7196	7204	7172	7172	7088	7088	7172	7088
7100	_42	Kentucky	0	0	0	0	0	0	0	0	0	0	0	0	0	0	7186	7116	7100	7146	7161	7146	7161	7172	7126	7169	7106	7136	7169	7106
7100	_43	Missouri	0	0	0	0	0	0	0	0	0	0	0	0	0	0	7161	7116	7146	7100	7186	7146	7161	7172	7169	7126	7136	7106	7169	7106
7090	_44	South Carolina	0	0	0	0	0	0	0	0	0	0	0	0	0	0	7111	7196	7161	7186	7090	7161	7111	7088	7106	7136	7174	7187	7106	7187
7100	_45	Tennessee	0	0	0	0	0	0	0	0	0	0	0	0	0	0	7161	7116	7146	7146	7161	7100	7186	7172	7169	7169	7106	7106	7126	7136
7090	_46	Vanderbilt	0	0	0	0	0	0	0	0	0	0	0	0	0	0	7111	7196	7161	7161	7111	7186	7090	7088	7106	7106	7187	7187	7136	7174
7080	_47	Alabama	0	0	0	0	0	0	0	0	0	0	0	0	0	0	7088	7204	7172	7172	7088	7172	7088	7080	7116	7116	7196	7196	7116	7196
7100	_48	Arkansas	0	0	0	0	0	0	0	0	0	0	0	0	0	0	7136	7172	7126	7169	7106	7169	7106	7116	7100	7146	7161	7186	7146	7161
7100	_49	Auburn	0	0	0	0	0	0	0	0	0	0	0	0	0	0	7106	7172	7169	7126	7136	7169	7106	7116	7146	7100	7186	7161	7146	7161
7090	_50	LSU	0	0	0	0	0	0	0	0	0	0	0	0	0	0	7187	7088	7106	7136	7174	7106	7187	7196	7161	7186	7090	7111	7161	7111
7090	_51	Mississippi	0	0	0	0	0	0	0	0	0	0	0	0	0	0	7174	7088	7136	7106	7187	7106	7187	7196	7186	7161	7111	7090	7161	7111
7100	_52	Mississippi State	0	0	0	0	0	0	0	0	0	0	0	0	0	0	7106	7172	7169	7169	7106	7126	7136	7116	7146	7146	7161	7161	7100	7186
7090	_53	Texas A&M	0	0	0	0	0	0	0	0	0	0	0	0	0	0	7187	7088	7106	7106	7187	7136	7174	7196	7161	7161	7111	7111	7186	7090

The remainder of the D1 field is connected by paths no more than 5 edges long. By this time there are more than three times the number of connections between pairs of SEC teams than between pairs of Big Ten teams – an average of 7146.7 to 2337.5.

Another difference is evident when we compare the size and number of scheduled round-robins. There are 29 subsets of SEC teams where each member plays all of the others, with orders 4, 5, 6 and 7. All of the 14 interdivisional round robins in the Big Ten schedule are order 3.

#	Teams
7	{ Illinois; Iowa; Minnesota; Nebraska; Northwestern; Purdue; Wisconsin }
7	{ Indiana; Maryland; Michigan; Michigan State; Ohio State; Penn State; Rutgers }
3	{ Penn State; Iowa; Nebraska }
3	{ Indiana; Purdue; Wisconsin }
3	{ Ohio State; Rutgers; Illinois }
3	{ Michigan State; Penn State; Iowa }
3	{ Indiana; Michigan; Wisconsin }
3	{ Indiana; Rutgers; Purdue }
3	{ Michigan State; Iowa; Northwestern }
3	{ Rutgers; Illinois; Purdue }
3	{ Ohio State; Illinois; Nebraska }
3	{ Ohio State; Penn State; Nebraska }
3	{ Maryland; Minnesota; Northwestern }
3	{ Maryland; Michigan State; Northwestern }
3	{ Michigan; Minnesota; Wisconsin }
3	{ Maryland; Michigan; Minnesota }

#	Teams
7	{ Florida; Georgia; Kentucky; Missouri; South Carolina; Tennessee; Vanderbilt }
7	{ Alabama; Arkansas; Auburn; LSU; Mississippi; Mississippi State; Texas A&M }
6	{ Florida; South Carolina; Vanderbilt; LSU; Mississippi; Texas A&M }
5	{ South Carolina; Auburn; LSU; Mississippi; Texas A&M }
5	{ Georgia; Kentucky; Missouri; Vanderbilt; Mississippi State }
5	{ Florida; Missouri; South Carolina; Vanderbilt; LSU }
5	{ Tennessee; Alabama; Arkansas; Auburn; Texas A&M }
5	{ Florida; South Carolina; Tennessee; Vanderbilt; Texas A&M }
5	{ Georgia; Kentucky; Missouri; Alabama; Mississippi State }
5	{ Georgia; Kentucky; Missouri; Tennessee; Alabama }
5	{ Florida; Arkansas; LSU; Mississippi; Texas A&M }
5	{ Florida; Kentucky; South Carolina; Vanderbilt; Mississippi }
5	{ Vanderbilt; LSU; Mississippi; Mississippi State; Texas A&M }
5	{ Missouri; Alabama; Arkansas; LSU; Mississippi State }
5	{ Kentucky; Alabama; Auburn; Mississippi; Mississippi State }
5	{ Georgia; Kentucky; Alabama; Auburn; Mississippi State }
5	{ Georgia; Kentucky; Tennessee; Alabama; Auburn }
5	{ Georgia; Kentucky; South Carolina; Tennessee; Auburn }
5	{ Georgia; Alabama; Arkansas; Auburn; Mississippi State }
5	{ Georgia; Tennessee; Alabama; Arkansas; Auburn }
5	{ Georgia; Missouri; Alabama; Arkansas; Mississippi State }
5	{ Georgia; Missouri; Tennessee; Alabama; Arkansas }
5	{ Florida; Georgia; Missouri; Tennessee; Arkansas }
4	{ Florida; Tennessee; Arkansas; Texas A&M }
4	{ Florida; Missouri; Arkansas; LSU }
4	{ Kentucky; Vanderbilt; Mississippi; Mississippi State }
4	{ South Carolina; Tennessee; Auburn; Texas A&M }
4	{ Missouri; Vanderbilt; LSU; Mississippi State }
4	{ Kentucky; South Carolina; Auburn; Mississippi }

It will be interesting to see how rating systems treat these two disconnected islands in D1. After the (ir)regular season I'll compare the range and standard deviation of the ratings available to me for the connected part of the field to the same for these separately. That may give us an estimate for the cost of playing non-1A opponents and playing extra conference games.