Inequitable NCAA Tournament Brackets -- Seeding by AP Rank

One of the few things the 2011 NCAA tournament selection committee got right about seeding is that the top four seeds in each bracket do correspond with the AP top sixteen. But the assignments are hardly equitable. The West (not the East as has been widely decried) is the toughest. The East and Southwest, though, are not too far behind. The Southeast region, however, is bizarrely out-of whack -- absurdly less challenging.

In Table 1, I've listed AP rank and points; these ranks and points are placed in column groups to the right corresponding to NCAA tournament region. If the regional brackets were equal, the sum of the AP ranks would be roughly equal, but as indicated in the bottom rows, they're far from it. West ranks accumulate to 25½, far, far, below the Southeast's 45 cumulative. AP points is a more nuanced indicator of cumulative perceived strength because it accounts for differentials between ranks (120 voting points separate #7 and #8; only 6 separate #11 and #12). But, still the West is the toughest, and the Southeast, by far the easiest.

Table	AP		wins-	AP	Region					AP Rank					AP Points
1	rank		losses	pts	west	sw	se	east		west	sw	se	east		west	sw	se	east
---	1	Ohio State (51)	32-2	1,611				1					1					1,611
	2	Kansas (14)	32-2	1,574		1					2					1,574
AP	3	Duke	30-4	1,472	1					3					1,472
rank	4	Pittsburgh	27-5	1,406			1					4					1,406
vs.	5½	Notre Dame	26-6	1,332		2					5.5					1,332
bracket	5½	San Diego State	32-2	1,322	2					5.5					1,322
and	7	North Carolina	26-7	1,189				2					7					1,189
seed	8	Texas	27-7	1,069	4					8					1,069
	9	Connecticut	26-9	1,019	3					9					1,019
	10	Brigham Young U	30-4	977			3					10					977
	11	Kentucky	25-8	928				4					11					928
	12	Syracuse	26-7	922				3					12					922
	13	Purdue	25-7	903		3					13					903
	14	Louisville	25-9	874		4					14					874
	15	Florida	26-7	840			2					15					840
	16	Wisconsin	23-8	619			4					16					619
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
		West Region Total ............................................								25½					4,882
		Southwest Region ............................................									34½					4,683
		Southeast Region ............................................										45					3,842
		East Region Total ............................................											31					4,650

The differential between West and Southeast is considerably worse yet when you look at the top 5 seeds with Arizona (#17, 516 pts) in the West and Kansas State (#21, 240pts) in the Southeast.

The top seven seeds are worth considering because this year, there's a sharp break in the AP voting between Cincinatti (#28, 115 pts) and Old Dominion (#29, 65 pts). Twenty-seven of the 28 #1-7 seeds are in the AP top 28. The exception is UCLA (#42, 3 pts), while Utah State, #19 overall, received only a #12 seed -- the standard non-major conference bias. Why UCLA was deemed worthy of a #7 seed is anyone's guess, but rather than put them in their natural West region, where they could balance an otherwise tough field, they've been placed in the Southeast in the same absurdly weak Southeast sub-bracket.

The Southeast region is especially weak in the lower half of the bracket. It would seem as though the committee was trying to rig a trip to the elite 8 for Florida. The two most outlandish high seeds of the tournament are #7 UCLA and #2 Florida and they'll play each other in the round of 32. in the round of 16, they'll face-off against whoever emerges from the tournament's version of the Paralympics, the sub-bracket of Brigham Young (#3) without their starting center and 2nd best player (dismissed for having had sex) is not remotely a top 10 team, and St. John's (#6) likewise crippled from the loss of their top player.

Are the NCAA Basketball Tournament seedings fair?

Whatever the criticism of the 2011 Men's NCAA Tournament Selection Committee selections, the seedings are far worse. Any team with even a remote chance of ultimately winning the overall championship, or even a regional, is in the field, but their chances are dramatically affected by their bracket and seeding. And this year at least, these placements are virtually inexplicable. For example, Florida and Kentucky entered the SEC championship with equivalent credentials.

		Florida	Kentucky
	Rank	11	15
	Record	26-5	24-7
	Strength of schedule	5	7

Florida did have a better SEC record, 13-3, compared to 10-6 for Kentucky. But that may well have been a series of fortunate bounces. In one possession games conference games, Florida was 5-0, whereas Kentucky went an unlucky 1-5, suggesting also that Kentucky may well have been better than it's record and Florida not as good. In the conference game at a neutral site, Kentucky seemed to clear any doubt with a convincing 70-54 win. Accordingly, AP reversed their rankings -- voting Kentucky #11 and Florida #15. But the NCAA selection committee rewarded Kentucky for their decisive victory a #4 seed, and not any old #4 but #4 in the same bracket as Ohio State, the clear overall #1. Florida for it's poor performance was given a #2 seed, and not just any old #2 seed, but in a South-East sub-bracket that presents BY FAR the easiest path to the sweet sixteen, elite eight and final, and with the first two rounds in Florida to boot.

Seedings which the committee really ought to (but, or course, cannot) justify include:

Committee Loves (or Owes) Them:

	Seed	Region		AP rank	Pomeroy rank	Should be seeded	Notes
	2	se	Florida	15	19	#5		also gets first two games in Florida
	7	se	UCLA	43	51	#12

So not only are Florida and UCLA rewarded with unjustifiable seeds, but they get to play each other for a freebe sweet 16 slot, and then go against the crippled sub-bracket (BYU, St. Johns) for a gimmee elite 8 berth, and then the easiest shot -- through Pittsburgh, by far the weakest #1 seed, for an unearned final four. They also must love Gonzaga, not because of it received an #11 seed, but because it's an #11 seed in the cripple sub-bracket of the Southeast Region.

Committee Dislikes (or Hates) Them:

	Seed	Region		AP rank	Pomeroy rank	Should be seeded	Notes
	4	west	Texas	8	4	#2
	4	east	Kentucky	11	6	#2	has to face overall #1 for sweet 16
	12	se	Utah State	19	17	#5 (maybe #4)	what else could they have done this season?
	7	east	Washington	23	15	#5 (maybe #4)
	12	sw	Richmond	30	42	#9 or better
	13	se	Belmont	35	18	#9 or better
	12½	se	Clemson	39	21	#9 or better	Has to first win play-in game Tuesday midnite in Ohio to compete in Florida for 12 noon Thursday game

Who knows what crimes Texas, Kentucky, Washington or Clemson might have committed, but those of Richmond, Utah State and Belmont are clear -- they're not in the major conferences.

In a word, no. Like most years, the 2011 Men's NCAA Tournament Selection Committee selections are not awful: no slam-dunk team was excluded and no team without anything going for it is in fact going. But like most years, the 2011 choices around the edges are suspect, or worse. This year, for example, half a dozen teams outperformed Virginia Commonwealth (23-11) on most conceivable criteria.

NCAA selection committee chair, Ohio State athletic director Gene Smith "explained" the selection decisions speaking obliquely about a team's "resume" and "overall body of work," but what does that mean? Probably that there were no reasonable, systematic criteria at all.

30 years ago, to help systematize selections to the tournament, the NCAA established a "Rating Percentage Index" to rank teams based upon a team's wins and losses and its strength of schedule. This year Harvard (21-6), which was neck-and-neck all season for the Ivy League title, losing on a buzzer beater in a playoff after it tied with Princeton for the league title, ranked #35 on this index, as compared to VA Commonwealth's #49. Many from major conferences were admitted with far worse records and far lower RPIs, including:

• Michigan (19-13 Big Ten, RPI #52)
• Marquette (20-14 Big East, RPI #64)
• USC (19-14 Pac Ten, RPI #67)

So, why are these teams in, while others analysts expected to be such as Colorado (21-13, five wins over top-40 teams) and Virginia Tech (21-11, 9-7 in ACC*) not? (No one really expected an Ivy League at-large bid.)

In two words, organizational politics. The committee is made up of conference commissioners and athletic directors, each there, no doubt, to represent certain interests. Indeed, the final answer for every exclusion, was "they didn't get enough votes."

Conferences are the organizational units that constitute the NCAA. This year, the Colonial Conference and Conference-USA managed to enhance their own interest and prestige, just as the major conferences virtually always put their own interests ahead of the sport and its athletes. Note the conference from which selection committee chair Gene Smith hails placed seven of its 11 teams in the tournament, most of them with seeds and brackets more favorable than their "resumes" would seem to warrant (more on that tomorrow).

Organizational politics are a fact of life, but arbitrariness and, especially, favoritism undermines the spirit of sport. The attraction of sport is that, unlike life in general which we understand to be fixed at every turn, on the court, performance rather than pedigree prevails. The RPI is an extremely imperfect rating index, but it is something. In the best interest of the athletes, the schools themselves, and the sport, the NCAA ought to replace the current ad-hoc "body of work" with systematic, coherent selection criteria so as to reward play by student-athletes on the basketball court, rather than behind-the-scenes manuevering by operatives of the NCAA royal court.

* 21-11, 9-7 in ACC is normally good enough to get in not even factoring a late-season win vs. Duke, two wins in the ACC Tournament  and a relatively challenging non-conference schedule, and an expanded at-large pool.

And the Olympics winner is … Jamaica!

On a per capita basis, the best performing nation in the 2008 Olympics was – by far – Jamaica. Despite a population of only 2.7 million people, Jamaicans won six gold medals. No other nation had close to one gold per million, except for Bahrain a small nation which won a single gold. #2 was Jamaica’s Caribbean neighbor, Bahamas. Among the medals leaders, Australia (46 total medals) did best at #7 per capita.

Although China won more gold than any other country, it earned only .04 gold medals per million people. Jamaicans traveling from the far side of the planet bested the home country by a ratio of 60:1! Overall, it came in at only #64. The US, despite the greatest combination of wealth and infrastructure was hardly outstanding either, ranking only #43 overall. Although the US won more medals (110) than any other country, its .36 medals per million people is not even in the same league as the per-capita leaders.

The prize for the best performing region goes to the Caribbean. In addition to Jamaica and Bahamas, the largest Caribbean country, Cuba, also did very well – #11 per capita (Cuba’s 41 medals represent 2.1 medals per million people, 6 times the US medals rate) and Trinidad and Tobago #15. The two other very strong regions were Australia (#7)/New Zealand (#10), and northernmost Europe (Iceland #3, Norway #5, Estonia #9 Latvia #14 Denmark # 16 and Lithuania #19, as well as the Netherlands #17, Great Britain #21 and Finland #27).

Final 2008 Per Capita National Olympic Performance

Rank	Country	Gold medal	Silver medal	Bronze medals	4-2-1 points	pop (mil)	421 points /mil	Gold medals /mil	Tot medals /mil
1	Jamaica	6	3	2	32	3	11.79	2.211	4.05
2	Bahamas	0	1	1	3	0	9.06	.000	6.04
3	Iceland	0	1	0	2	0	6.32	.000	3.16
4	Bahrain	1	0	0	4	1	5.26	1.315	1.32
5	Norway	3	5	2	24	5	5.02	.628	2.09
6	Slovenia	1	2	2	10	2	4.93	.493	2.46
7	Australia	14	15	17	103	21	4.81	.654	2.15
8	Mongolia	2	2	0	12	3	4.56	.761	1.52
9	Estonia	1	1	0	6	1	4.48	.746	1.49
10	New Zealand	3	1	5	19	4	4.45	.702	2.11
11	Cuba	2	11	11	41	11	3.64	.177	2.13
12	Georgia	3	0	3	15	4	3.41	.682	1.36
13	Slovakia	3	2	1	17	5	3.15	.555	1.11
14	Latvia	1	1	1	7	2	3.09	.441	1.32
15	Trinidad and Tobago	0	2	0	4	1	3.00	.000	1.50
16	Denmark	2	2	3	15	5	2.73	.364	1.28
17	Netherlands	7	5	4	42	16	2.55	.426	.97
18	Hungary	3	5	2	24	10	2.39	.299	1.00
19	Lithuania	0	2	3	7	3	2.08	.000	1.49
20	Armenia	0	0	6	6	3	2.00	.000	2.00
21	Great Britain	19	13	15	117	61	1.93	.314	.78
22	Belarus	1	3	7	17	10	1.75	.103	1.14
23	Czech Republic	3	3	0	18	10	1.73	.288	.58
24	South Korea	13	10	8	80	48	1.66	.270	.64
25	Switzerland	2	0	4	12	8	1.57	.262	.79
26	Croatia	0	2	3	7	5	1.54	.000	1.10
27	Finland	1	1	2	8	5	1.50	.188	.75
28	Kazakhstan	2	4	7	23	15	1.49	.130	.84
29	Azerbaijan	1	2	4	12	8	1.42	.118	.83
30	Germany	16	10	15	99	82	1.20	.195	.50
31	Panama	1	0	0	4	3	1.20	.299	.30
32	France	7	16	17	77	64	1.19	.109	.62
33	Bulgaria	1	1	3	9	8	1.18	.131	.65
34	Ukraine	7	5	15	53	46	1.15	.152	.59
35	Russia	23	21	28	162	142	1.14	.162	.51
36	Canada	3	9	6	36	33	1.08	.090	.54
37	Italy	8	10	10	62	60	1.04	.134	.47
38	Romania	4	1	3	21	21	.98	.187	.37
39	Sweden	0	4	1	9	9	.98	.000	.54
40	Spain	5	10	3	43	46	.93	.109	.39
41	Kenya	5	5	4	34	38	.91	.133	.37
42	Ireland	0	1	2	4	4	.90	.000	.68
43	United States	36	38	36	256	305	.84	.118	.36
44	Mauritius	0	0	1	1	1	.79	.000	.79
45	Zimbabwe	1	3	0	10	13	.75	.075	.30
46	Poland	3	6	1	25	38	.66	.079	.26
47	Belgium	1	1	0	6	10	.60	.100	.20
48	Portugal	1	1	0	6	11	.56	.094	.19
49	Kyrgyzstan	0	1	1	3	5	.56	.000	.38
50	North Korea	2	1	3	13	24	.55	.084	.25
51	Greece	0	2	2	6	11	.54	.000	.36
52	Austria	0	1	2	4	8	.48	.000	.36
53	Japan	9	6	10	58	128	.45	.070	.20
54	Tajikistan	0	1	1	3	7	.45	.000	.30
55	Singapore	0	1	0	2	5	.44	.000	.22
56	Serbia	0	1	2	4	10	.41	.000	.30
57	Uzbekistan	1	2	3	11	27	.40	.037	.22
58	Tunisia	1	0	0	4	10	.39	.097	.10
59	Argentina	2	0	4	12	40	.30	.050	.15
60	Moldova	0	0	1	1	4	.26	.000	.26
61	Ethiopia	4	1	2	20	79	.25	.050	.09
62	Cameroon	1	0	0	4	19	.22	.054	.05
63	Turkey	1	4	3	15	71	.21	.014	.11
64	China	51	21	28	274	1,326	.21	.038	.08
65	Thailand	2	2	0	12	64	.19	.031	.06
66	Chinese Taipei	0	0	4	4	23	.17	.000	.17
67	Togo	0	0	1	1	7	.15	.000	.15
68	Ecuador	0	1	0	2	13	.15	.000	.07
69	Brazil	3	4	8	28	187	.15	.016	.08
70	Israel	0	0	1	1	7	.14	.000	.14
71	Chile	0	1	0	2	17	.12	.000	.06
72	Morocco	0	1	1	3	31	.10	.000	.06
73	Algeria	0	1	1	3	34	.09	.000	.06
74	Mexico	2	0	1	9	107	.08	.019	.03
75	Malaysaia	0	1	0	2	27	.07	.000	.04
76	Iran	1	0	1	5	70	.07	.014	.03
77	Colombia	0	1	1	3	45	.07	.000	.04
78	Sudan	0	1	0	2	39	.05	.000	.03
79	South Africa	0	1	0	2	48	.04	.000	.02
80	Indonesia	1	1	3	9	232	.04	.004	.02
81	Afghanistan	0	0	1	1	27	.04	.000	.04
82	Venezuela	0	0	1	1	28	.04	.000	.04
83	Nigeria	0	1	3	5	148	.03	.000	.03
84	Vietnam	0	1	0	2	87	.02	.000	.01
85	Egypt	0	0	1	1	75	.01	.000	.01
86	India	1	0	2	6	1,137	.01	.001	.00
231	Totals	298	300	350	2110	6,671	.32	.045	.14

Per Capita National Olympic Performance

Standard Olympic medal standings neglect obvious comparative inequities. The most glaring of these are vast differences in national populations. Per capita, the US ranks only #35 in medal performance and China ranks only #53. China's 39 gold medals -- 21% of the Olympic total -- are impressive until you realize that China also has 20% of the world's population. Its 15% take of total medals is considerably less than its share of world population, even though it has all the advantages of being the home country (and may well have cheated).

Per-capita, Jamaica, Slovenia and Estonia are #1, 2 and 3 although given that a single medal puts them in or takes them out of the top ten, these positions are not in a sense statistically significant. Among overall medal leader, no country is close to Australia (#4) which has more than 6 times as many medals per capita as the US, and nearly 30 times as many medals per capita as China.

Moreover, these figures may understate smaller nation performance. Many US and Chinese medals come from "team" events, in which small countries are at an extreme disadvantage.

Rank	Country	Gold medals	Silver medals	Bronze medals	4-2-1 points	pop (mil)	Gold medals /mil	Tot medals /mil	421 points /mil
1	Jamaica	2	3	0	14	3	.737	1.84	5.16
2	Slovenia	1	2	2	10	2	.493	2.46	4.93
3	Estonia	1	1	0	6	1	.746	1.49	4.48
4	Australia	11	12	12	80	21	.514	1.64	3.74
5	New Zealand	2	1	3	13	4	.468	1.40	3.04
6	Slovakia	3	1	0	14	5	.555	.74	2.59
7	Denmark	2	1	3	13	5	.364	1.09	2.37
8	Mongolia	1	1	0	6	3	.380	.76	2.28
9	Norway	1	2	2	10	5	.209	1.05	2.09
10	Georgia	2	0	1	9	4	.455	.68	2.05
11	Netherlands	4	5	4	30	16	.243	.79	1.82
12	Belarus	1	3	7	17	10	.103	1.14	1.75
13	Cuba	1	5	5	19	11	.089	.98	1.69
14	Armenia	0	0	5	5	3	.000	1.67	1.67
15	Trinidad and Tobago	0	1	0	2	1	.000	.75	1.50
16	Great Britain	16	9	8	90	61	.264	.54	1.49
17	Switzerland	2	0	3	11	8	.262	.65	1.44
18	Czech Republic	2	3	0	14	10	.192	.48	1.35
19	Finland	1	1	1	7	5	.188	0.56	1.32
20	South Korea	8	10	6	58	48	.166	.50	1.20
21	Panama	1	0	0	4	3	.299	.30	1.20
22	Lithuania	0	1	2	4	3	.000	.89	1.19
23	Azerbaijan	1	2	2	10	8	.118	0.59	1.18
24	Bulgaria	1	1	2	8	8	.131	.52	1.05
25	Romania	4	1	3	21	21	.187	.37	.98
26	Kazakhstan	1	3	4	14	15	.065	.52	.91
27	Hungary	0	4	1	9	10	.000	.50	.90
28	Germany	11	8	9	69	82	.134	.34	.84
29	France	4	11	14	52	64	.062	.45	.81
30	Ukraine	5	4	8	36	46	.109	.37	.78
31	Canada	2	6	5	25	33	.060	0.39	.75
32	Zimbabwe	1	3	0	10	13	.075	.30	.75
33	Italy	6	6	7	43	60	.101	.32	.72
34	Croatia	0	1	1	3	5	.000	.44	.66
35	Sweden	0	3	0	6	9	.000	.33	.65
36	Russia	10	14	18	86	142	.070	.30	.61
37	United States	26	26	27	183	305	.085	.26	.60
38	North Korea	2	1	4	14	24	.084	.29	.59
39	Kyrgyzstan	0	1	1	3	5	.000	.38	.56
40	Poland	3	4	1	21	38	.079	.21	.55
41	Austria	0	1	2	4	8	.000	.36	.48
42	Spain	3	4	2	22	46	.065	.20	.48
43	Latvia	0	0	1	1	2	.000	.44	.44
44	Singapore	0	1	0	2	5	.000	.22	.44
45	Kenya	2	3	2	16	38	.053	.19	.43
46	Japan	8	6	8	52	128	.063	.17	.41
47	Tunisia	1	0	0	4	10	.097	.10	.39
48	Greece	0	1	2	4	11	.000	.27	.36
49	Serbia	0	1	1	3	10	.000	.20	.30
50	Cameroon	1	0	0	4	19	.054	.05	.22
51	Portugal	0	1	0	2	11	.000	.09	.19
52	Uzbekistan	0	1	3	5	27	.000	.15	.18
53	China	43	14	19	219	1,326	.032	.06	.17
54	Togo	0	0	1	1	7	.000	.15	.15
55	Ecuador	0	1	0	2	13	.000	.07	.15
56	Tajikistan	0	0	1	1	7	.000	.15	.15
57	Ethiopia	2	1	0	10	79	.025	.04	.13
58	Argentina	1	0	1	5	40	.025	.05	.12
59	Chile	0	1	0	2	17	.000	.06	.12
60	Algeria	0	1	1	3	34	.000	.06	.09
61	Chinese Taipei	0	0	2	2	23	.000	.09	.09
62	Malaysaia	0	1	0	2	27	.000	.04	.07
63	Turkey	0	2	1	5	71	.000	.04	.07
64	Colombia	0	1	1	3	45	.000	.04	.07
65	Thailand	1	0	0	4	64	.016	.02	.06
66	Brazil	1	0	5	9	187	.005	.03	.05
67	South Africa	0	1	0	2	48	.000	.02	.04
68	Indonesia	1	1	3	9	232	.004	.02	.04
69	Morocco	0	0	1	1	31	.000	.03	.03
70	Vietnam	0	1	0	2	87	.000	.01	.02
71	Iran	0	0	1	1	70	.000	.01	.01
72	Egypt	0	0	1	1	75	.000	.01	.01
73	Mexico	0	0	1	1	107	.000	.01	.01
74	India	1	0	0	4	1,137	.001	.00	.00
231	Totals	204	205	231	1457	6,671	.031	.10	.22