Characterizing Schedules

January 25, 2015

I've published a presumptive schedule strength report using the traditional average-opponents' values (of the ISR in this case) but there are lots of ways to characterize schedules other than average opponent rating. In that report I included the median opponent rank as a comparison, and in this article I'll compare that to other rank-based schedule categorizations.

Generally one would prefer to use ratings rather than rankings for characerization because ratings account for the fact that there's a larger absolute difference between #1 and #10 than between #101 and #110. This analysis uses opponent rankings because
• whole-number rankings are easier to present/understand, and
• the same analysis can be applied to any rating system that ranks teams.

There are as many ways to calculate a schedule's strength as there are opinions, and like the latter there isn't a moral notion of "right" and "wrong." I'll look at different ways to summarize opponents' ranks and talk a little about what each tells us. Ultimately I'll argue that it is probably better to compare schedules in whole, and ignore any such summation!

Here are the top 25 schedules according to four varieties of "average" non-conference SOS.

Ix	Harm	Team	Rank
1	7.1	Texas-San Antonio	81
2	7.4	Alabama	34
3	7.7	Jackson State	224
4	7.8	Southern	297
5	8.4	Fresno State	75
6	8.5	Stony Brook	130
7	10.0	Grambling State	287
8	10.2	McNeese State	141
9	10.9	Northwestern State	125
10	11.2	Nicholls State	128
11	11.2	Southeastern Louisiana	76
12	12.7	Santa Clara	127
13	12.8	San Jose State	163
14	13.1	Portland	234
15	13.3	Cal Poly	3
16	13.3	Southern California	43
17	15.2	Pacific	105
18	15.4	Stanford	24
19	15.9	Rice	19
20	16.5	New Mexico	40
21	16.6	Grand Canyon	117
22	17.8	Oregon State	2
23	17.9	Baylor	73
24	17.9	New Orleans	271
25	18.1	Texas Christian	6

Ix	Geom	Team	Rank
1	27.4	Fresno State	75
2	29.6	Stanford	24
3	32.4	Rice	19
4	35.1	Pacific	105
5	36.9	San Diego	37
6	37.0	Cal State Fullerton	28
7	40.2	Southern California	43
8	42.4	Arizona State	31
9	43.5	Portland	234
10	43.6	Texas-San Antonio	81
11	44.2	Grand Canyon	117
12	44.2	Baylor	73
13	45.6	Santa Clara	127
14	45.8	Cal Poly	3
15	45.8	Wichita State	71
16	47.5	Long Beach State	27
17	47.5	Loyola Marymount	57
18	48.6	UCLA	62
19	50.3	New Mexico	40
20	50.5	San Jose State	163
21	51.6	San Francisco	106
22	54.0	Texas Christian	6
23	54.1	Texas	5
24	55.8	Minnesota	120
25	56.4	Nebraska	35

Ix	Arith	Team	Rank
1	52.6	Cal State Fullerton	28
2	55.2	Stanford	24
3	59.6	Pacific	105
4	59.7	San Diego	37
5	61.9	Fresno State	75
6	62.1	Rice	19
7	65.0	Loyola Marymount	57
8	67.0	Long Beach State	27
9	69.0	Wichita State	71
10	69.6	San Francisco	106
11	70.7	Baylor	73
12	75.2	Texas	5
13	77.3	Portland	234
14	77.3	Arizona State	31
15	78.7	UCLA	62
16	79.0	UC Santa Barbara	30
17	80.4	Cal Poly	3
18	81.4	UC Irvine	22
19	84.0	Texas State	78
20	84.3	Nebraska	35
21	85.2	Coastal Carolina	191
22	87.1	Texas-San Antonio	81
23	87.3	New Mexico	40
24	87.4	Indiana	9
25	88.2	Houston	14

Harm	The Harmonic Mean is the inverse of the average of inverses of opponents' ranks. This gives the most weight to playing games against highly-ranked opponents. It takes only a few games against a top-5 opponent to wind up high on this list: Jackson State's NC schedule has a harmonic opponents' rank mean of 7.7, despite playing only five games against the top half of the field.
Geom	The Geometric Mean is the anti-logarithm of the average of logarithms of opponents' ranks. Like the harmonic mean this gives more weight to better opponents' rankings but the effect is less extreme than the harmonic mean. An argument could be made that it is better measure of schedule difficulty than the usual average.
Arith	The Arithmentic Mean is just the usual average of opponents' ranks. It gives equal weight to extreme values, so will give an equal result to teams whose opponents are all ranked between 100 and 200 as teams who play an equivalent number of top 100 and bottom 100 teams. By itself, it isn't all that informative.

A histogram is a better schedule description. In this version I count the number of games where the opponents' ISR ranks fall into the same rank ranges used for the NCAA "Nitty Gritty" report.

Ix	Wtd	Team	Rank	Conf	1 - 25	26 - 50	51 - 75	76 - 100	101 - 150	151 - 301	NonD1
1	4.724	Cal State Fullerton	28	BigW	11	9	5	0	2	2	0
2	4.462	San Diego	37	WCC	8	10	2	2	0	4	0
2	4.462	Fresno State	75	MW	9	9	2	0	3	3	0
4	4.333	Rice	19	CUSA	12	3	0	1	6	2	0
4	4.333	Pacific	105	WCC	9	5	2	3	3	2	0
6	4.292	Stanford	24	P12	11	4	0	1	6	2	0
7	4.148	Long Beach State	27	BigW	6	7	7	0	6	1	0
8	4.138	San Francisco	106	WCC	8	7	4	2	7	1	0
9	4.000	Wichita State	71	MVC	5	14	1	8	5	2	0
9	4.000	Texas	5	B12	8	7	2	4	5	3	0
9	4.000	Loyola Marymount	57	WCC	4	11	2	0	5	3	0
12	3.957	Arizona State	31	P12	6	7	1	3	1	5	0
13	3.929	Grand Canyon	117	WAC	8	9	1	0	3	7	0
14	3.880	UCLA	62	P12	7	7	0	3	3	5	0
15	3.857	Baylor	73	B12	5	8	2	5	7	1	0
16	3.844	UC Santa Barbara	30	BigW	5	5	14	0	4	4	0
17	3.840	Southern California	43	P12	9	5	2	0	0	9	0
18	3.750	Portland	234	WCC	9	0	8	1	6	4	0
19	3.719	Nebraska	35	B10	4	8	6	5	7	2	0
20	3.688	UC Irvine	22	BigW	3	11	6	3	3	6	0
21	3.625	Cal Poly	3	BigW	8	3	8	0	8	5	0
22	3.615	New Mexico	40	MW	7	4	3	1	6	5	0
22	3.615	San Diego State	25	MW	6	4	7	0	1	8	0
24	3.609	Sam Houston State	33	SLC	5	2	8	1	1	6	0
24	3.609	California	47	P12	4	4	3	6	3	3	0
Full list

The histogram gives a better "picture" of the teams' schedules, but turning that into a #1 to #n list requires using a weighted average and the weights are arbitrary. To produce this list I just used a simple 6-5-4-3-2-1 weighting for the counts. It would not be difficult to define "better" ones, but not without resorting to an ad hoc approach intended to produce a desired result.

And that's the point to which I alluded above. If you have arepresentation of the whole (non-conference) schedule, you can form independent jusgements or comparisons using whatever criteria mean the most to you. The following list is ordered by the opponent rank that represents at least half of the teams' games.

Arith	Geom	Harm	Int	Team	Rank	Conf	Opponents' 2014 ISR Ranks
62.1	32.4	15.9	3.0010	Rice	19	CUSA	5	5	5	5	6	14	14	14	24	24	24	24	33	33	36	78	121	135	135	136	136	136	173	175
55.2	29.6	15.4	3.0445	Stanford	24	P12	5	5	5	5	9	9	9	19	19	19	19	28	28	28	37	79	105	105	106	106	127	127	163	163
61.9	27.4	8.4	2.9666	Fresno State	75	MW	2	2	2	2	3	3	22	22	22	30	30	30	30	43	43	47	47	47	70	70	132	132	132	156	245	245
98.2	40.2	13.3	2.7460	Southern California	43	P12	3	3	3	4	6	16	16	22	22	26	28	28	30	30	75	75	181	181	181	243	243	243	265	265	265
59.7	36.9	21.7	2.9228	San Diego	37	WCC	5	5	5	22	22	24	25	25	27	27	28	28	32	32	32	42	42	42	64	64	79	92	197	197	197	197
65.0	47.5	33.8	2.7920	Loyola Marymount	57	WCC	6	22	25	25	27	27	29	29	29	30	30	35	35	35	38	64	64	113	113	113	117	131	163	163	163
52.6	37.0	26.9	2.9553	Cal State Fullerton	28	BigW	9	9	9	16	17	17	17	21	24	24	24	35	35	37	37	39	39	39	43	43	62	62	73	73	73	138	143	184	184
75.2	54.1	40.9	2.7742	Texas	5	B12	19	19	19	19	24	24	24	24	33	35	35	35	37	37	37	69	71	78	78	78	81	120	120	120	120	121	180	239	284
59.6	35.1	15.2	2.8343	Pacific	105	WCC	3	3	3	15	15	15	15	24	24	38	38	38	38	47	70	70	79	79	79	132	132	132	161	180
77.3	42.4	21.5	2.8312	Arizona State	31	P12	6	6	6	11	11	11	27	27	27	38	38	40	40	74	89	89	89	104	184	184	212	215	251
88.4	44.2	16.6	2.6235	Grand Canyon	117	WAC	3	3	3	11	11	11	17	17	38	38	40	40	41	41	44	44	44	57	127	127	149	156	170	235	252	252	252	252
69.0	45.8	25.6	2.7691	Wichita State	71	MVC	5	6	6	6	11	27	27	27	30	30	30	33	33	33	40	40	40	41	41	74	78	78	78	91	91	96	96	99	123	123	123	137	149	236	236
69.6	51.6	37.2	2.6649	San Francisco	106	WCC	13	13	17	17	17	17	24	24	40	40	42	42	42	47	47	64	64	64	70	79	79	132	132	145	145	146	146	146	163
78.7	48.6	25.9	2.7336	UCLA	62	P12	4	6	16	16	22	22	25	27	27	28	28	49	49	49	97	97	97	104	104	104	156	156	228	228	228
87.4	61.8	45.9	2.6941	Indiana	9	B10	21	24	24	24	26	27	27	27	28	28	28	46	46	51	51	51	77	77	87	87	113	134	160	179	187	195	206	242	263
67.0	47.5	32.1	2.8235	Long Beach State	27	BigW	9	9	9	16	25	25	31	31	31	37	37	38	38	57	57	62	62	71	71	71	107	107	107	145	145	145	266
103.9	84.8	71.9	2.4220	Georgia Southern	88	SBC	45	45	45	48	48	51	51	53	53	54	54	54	60	60	72	72	72	186	186	189	189	194	194	209	209	209
99.6	58.7	22.3	2.6758	Pepperdine	16	WCC	3	3	15	15	15	27	28	30	30	43	43	62	62	131	131	131	131	146	146	146	156	156	195	248	248	248
91.1	62.4	43.1	2.6668	San Diego State	25	MW	17	17	17	22	22	22	27	27	37	37	57	57	62	64	64	64	64	140	156	156	206	206	206	207	207	207
81.4	67.7	57.1	2.6750	UC Irvine	22	BigW	25	25	25	37	37	43	43	44	44	44	47	47	47	47	57	62	62	75	75	75	81	81	81	120	120	120	163	163	163	184	184	184
85.2	65.4	46.7	2.2968	Coastal Carolina	191	BigS	12	12	12	20	39	45	48	49	49	51	51	54	55	56	59	65	66	66	66	87	97	98	98	102	107	111	126	129	194	200	214	288
95.1	74.2	46.6	2.5623	Liberty	50	BigS	7	7	39	39	45	48	49	55	55	58	58	60	66	66	66	66	82	84	84	107	118	129	129	129	129	151	154	194	218	218	238
109.8	62.2	23.8	2.2510	Cal State Bakersfield	184	WAC	3	3	22	22	22	28	28	30	30	31	31	64	64	67	67	67	104	156	156	215	245	245	245	255	255	255	255
84.3	56.4	28.2	2.6829	Nebraska	35	B10	5	5	5	10	28	28	36	38	38	38	46	46	57	57	57	67	67	67	85	85	85	91	91	131	140	140	140	140	149	149	289	289
70.7	44.2	17.9	2.7796	Baylor	73	B12	3	3	3	10	14	28	28	28	33	33	36	42	42	69	69	78	78	78	81	81	125	125	129	129	129	131	135	239
full list

The Interest column is a bit different - it takes into account the team's rank as well as that of its opponents. It's a scale from 0 (non-D1 opponent) to 4.5 (#1 vs #1). It increases with better ranks and decreases with larger differences between team ranks. This may be a more meaningful measurement than absolute schedule strength but what is reported here is the arithmetic average of the games' interest factors so it is pretty coarse.

Why Bother?

Other than providing fodder for pointless-but-fun "mine is bigger than yours" bar debates, any measure of absolute schedule strength provides is information that by itself doesn't improve our knowledge. Teams outside of the top five or six conferences must schedule tougher non-conference opponents (and do well against them) to improve their post-season probabilities. And if top-50 teams only scheduled other top-50 teams we'd have no way to find out which of the latter group ought to be top-50.

I find the most "telling" observations from schedule analysis are:

Median Opponent Rank: The context for this is how that compares to the overall schedule. Teams from the Big West, Pac 12 and SEC are likely to have top-25 toughest schedules regardless of their non-conference scheduling, and for those teams...
Number of NC games against "better-ranked" teams: Context again must be taken into account. Obviously the higher ranked the team the fewer potential opponents' there are. For teams "in the middle" more better-ranked opponents may mean the coach expects the team to be better than the year before.

By the Numbers

The top 25 teams (by 2014 ISR) have 677 nonconference scheduling opportunities and spend 104 of them (15.4 percent) on games vs other top 25 teams.
406 (29.7 percent) of the 1369 top-50 scheduling opportunities are top 50 vs top 50 matchups.
There are 4140 non-conference games between D1 opponents, not including 12 games vs "TBA."
There are 126 games against 82 non-D1 teams.
10 non-D1 teams have 13 home games against D1 opponents.

As always, schedules are subject to change.

In memory of
SEBaseball.com