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sports/basketball/ncaa/2016 NCAA basketball tourney odds for the title game

2017-04-03 20:42 ET rev. 2017-04-04 00:44:43 UT blog/sports/basketball/ncaa/2016/tourney_odds-championship-game.txt

Our updated title probabilities and odds by effective overall seed number, for the 2016-17 final:

 # Team       Prob     Odds
-- ------    -----   ------
 1 Gonzag     0.5309  0.9:1
 2 NCarol     0.4691  1.1:1

Our expected final score: Gonzaga 76, North Carolina 75.

sports/basketball/ncaa/2016 updated NCAA basketball tournament championship odds

2017-03-29 20:35 ET rev. 2017-03-30 00:37:51 UT blog/sports/basketball/ncaa/2016/tourney_odds-final-4.txt

Our updated title probabilities and odds by effective overall seed number, for teams in the Final Four 2016-17:

 # Team       Prob       Odds
-- ------    -----   --------
 1 SCarol    .0917      9.9:1
 2 Oregon    .1587      5.3:1
 3 NCarol    .3357      2.0:1
 4 Gonzag    .4139      1.4:1

sports/basketball/ncaa/2016 updated NCAA basketball tournament championship odds

2017-03-25 13:44 ET rev. 2017-03-25 23:05:27 UT blog/sports/basketball/ncaa/2016/tourney_odds-elite-8.txt

Our updated title probabilities and odds by effective overall seed number, for teams entering the Elite 8:

 # Team       Prob       Odds
-- ------    -----   --------
 1 Florid    .1445      5.9:1
 2 Kansas    .1622      5.2:1
 3 NCarol    .1679      5.0:1
 4 Gonzag    .2519      3.0:1
 5 Xavier    .0344     28.1:1
 6 Kentuc    .1390      6.2:1
 7 Oregon    .0634     14.8:1
 8 SCarol    .0368     26.2:1

sports/basketball/ncaa/2016 updated NCAA basketball tournament championship odds

2017-03-20 18:53 ET rev. 2017-03-25 23:03:57 UT blog/sports/basketball/ncaa/2016/tourney_odds-sweet-16.txt

Our updated title probabilities and odds by effective overall seed number, for teams entering the Sweet 16:

 # Team       Prob       Odds
-- ------    -----   --------
 1 Wiscon    .0488     19.5:1
 2 Kansas    .0975      9.3:1
 3 NCarol    .1361      6.3:1
 4 Gonzag    .1369      6.3:1
 5 Arizon    .0588     16.0:1
 6 Kentuc    .1134      7.8:1
 7 Michig    .0307     31.6:1
 8 SCarol    .0145     68.1:1
 9 Baylor    .0601     15.7:1
10 Oregon    .0444     21.5:1
11 UCLA      .0175     56.1:1
12 Xavier    .0154     63.8:1
13 WVirgi    .0786     11.7:1
14 Butler    .0214     45.6:1
15 Purdue    .0475     20.0:1
16 Florid    .0783     11.8:1

sports/basketball/ncaa/2016 updated NCAA basketball tournament championship odds

2017-03-18 10:56 ET rev. 2017-03-25 22:54:45 UT blog/sports/basketball/ncaa/2016/tourney_odds-round-of-32.txt

Our updated title probabilities and odds by effective overall seed number, for teams entering the round of 32:

 # Team       Prob       Odds
-- ------    -----   --------
 1 Villan    .0808     11.4:1
 2 Kansas    .0550     17.2:1
 3 NCarol    .1201      7.3:1
 4 Gonzag    .1141      7.8:1
 5 Arizon    .0292     33.3:1
 6 Kentuc    .0553     17.1:1
 7 Louisv    .0642     14.6:1
 8 Duke      .0512     18.5:1
 9 Baylor    .0340     28.4:1
10 Oregon    .0272     35.7:1
11 UCLA      .0078    127.9:1
12 FlorSt    .0131     75.2:1
13 WVirgi    .0496     19.2:1
14 Butler    .0157     62.7:1
15 Purdue    .0266     36.6:1
16 Florid    .0231     42.2:1
17 Virgin    .0595     15.8:1
18 IowaSt    .0181     54.1:1
19 MidTen    .0015    667.0:1
20 NotDam    .0108     91.8:1
21 Xavier    .0062    159.7:1
22 Cincin    .0196     49.9:1
23 RhoIsl    .0031    320.0:1
24 SerCal    .0010   1008.1:1
25 SCarol    .0044    223.8:1
26 Michig    .0130     76.1:1
27 WichSt    .0468     20.4:1
28 StMars    .0181     54.4:1
29 Nweste    .0019    518.7:1
30 Arkans    .0022    456.6:1
31 MichSt    .0102     97.5:1
32 Wiscon    .0165     59.6:1

sports/basketball/ncaa/2016 NCAA basketball tournament championship odds

2017-03-13 23:19 ET rev. 2017-03-25 22:54:15 UT blog/sports/basketball/ncaa/2016/tourney_odds.txt

Our title probabilities and odds by overall seed number:

 # Team       Prob          Odds
-- ------    -----  ------------
 1 Villan    .0928         9.8:1
 2 Kansas    .0522        18.2:1
 3 NCarol    .1173         7.5:1
 4 Gonzag    .1097         8.1:1
 5 Arizon    .0303        32.0:1
 6 Kentuc    .0687        13.6:1
 7 Louisv    .0689        13.5:1
 8 Duke      .0476        20.0:1
 9 Baylor    .0204        48.0:1
10 Oregon    .0230        42.5:1
11 UCLA      .0079       125.3:1
12 FlorSt    .0128        77.3:1
13 WVirgi    .0495        19.2:1
14 Butler    .0145        67.7:1
15 Purdue    .0242        40.3:1
16 Florid    .0220        44.5:1
17 Virgin    .0575        16.4:1
18 IowaSt    .0162        60.8:1
19 Minnes    .0014       716.0:1
20 NotDam    .0090       109.8:1
21 Maryla    .0025       397.8:1
22 Cincin    .0126        78.7:1
23 Creigh    .0053       186.9:1
24 SMU       .0252        38.6:1
25 SCarol    .0021       473.1:1
26 Michig    .0081       121.8:1
27 Dayton    .0011       900.4:1
28 StMars    .0128        77.0:1
29 Nweste    .0010       959.9:1
30 Arkans    .0013       756.3:1
31 MiaFla    .0052       190.6:1
32 Wiscon    .0124        79.9:1
33 VirTec    .0004      2388.5:1
34 MichSt    .0053       188.3:1
35 SetHal    .0017       599.2:1
36 Vander    .0030       337.5:1
37 VCU       .0018       543.6:1
38 WichSt    .0363        26.5:1
39 OklaSt    .0040       252.1:1
40 Marque    .0014       696.8:1
41 SerCal    .0003      3730.1:1
42 RhoIsl    .0015       682.1:1
43 KansSt    .0026       378.5:1
44 Xavier    .0040       252.1:1
45 Prince    .0007      1450.3:1
46 MidTen    .0008      1311.7:1
47 Nevada    .0002      4864.5:1
48 NC-Wil    .0001      9382.4:1
49 ETenSt    .0000     24057.4:1
50 Vermon    .0002      5391.7:1
51 Winthr    .0000     82187.3:1
52 Buckne    .0001     18674.7:1
53 FloGul    .0000     21641.3:1
54 KentSt    .0000    191859.5:1
55 Iona      .0000     82442.9:1
56 NMexSt    .0001     13863.7:1
57 Troy      .0000    586157.0:1
58 JacvSt    .0000   1117009.3:1
59 NerKen    .0000    888178.2:1
60 NDakot    .0000    680162.6:1
61 SDakSt    .0000    199469.3:1
62 TexSer    .0000   1767340.0:1
63 UCDavi    .0000   2425342.7:1
64 MouStM    .0000   3763781.9:1

math/alg rational exponents

2017-03-13 23:08 ET rev. 2018-09-18 00:21:44 UT blog/math/alg/rational_exponents.txt

For integers :(n\ge2):, we say real number :(x): is an :(n):th root of real number :(y): iff :[x^n=y.]:

Unless :(n): is even and :(x<0):, we also write :[x=\root n \of y=y^\frac1n]: and say :(x): is the (principal real) :(n):th root of :(y):.

This leads to :[y^\frac{m}{n} = (y^m)^\frac1n = (y^\frac1n)^m]: for integer :(m):.

Every real number :(y\neq0): has :(n): :(n):th roots, of which none, one, or two are real; the others are complex.

math/geo perimeter and area of regular polygon

2017-03-13 09:10 ET rev. 2017-03-13 13:15:15 UT blog/math/geo/ngon.txt

For a regular :(n):-gon with side length :(s):, apothem :(a):, or center-to-vertex distance :(d):, the perimeter :(p): and area :(A): can be found to be, respectively,

:[p=ns=2na\tan\frac{180^\circ}{n}=2nd\sin\frac{180^\circ}{n}]:

and

:[A=\frac{ns^2}{4\tan\frac{180^\circ}{n}}=na^2\tan\frac{180^\circ}{n}=\frac{nd^2}{2}\sin\frac{360^\circ}{n}.]:

math/mat gerrymandering case at U.S. Supreme Court

2017-03-04 20:11 ET rev. 2017-03-05 01:13:21 UT blog/math/mat/gerrymandering.txt

From SCOTUSblog: Court sends majority-minority districts back for another look in Virginia gerrymandering case.

misc I.F. Stone then and now

2017-02-26 11:14 ET rev. 2017-02-26 16:36:09 UT blog/misc/ifstone.txt

A modern-day I.F. Stone writes about I.F. Stone. And an I.F. Stone is almost always worth reading.

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