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NCAA Tourney Bayesian Ratings and Odds

March 16, 2011
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Okay, ready for the tournament?

I’ve put together some adjustments based on the work I teased yesterday.  The theory behind the adjustments may be found on STATS @ MTSU and Dr. Winner @ Florida.  Basically, I’m adjusting for teams that raise their game to a higher level against good foes (or vise-versa).  For instance, Long Island plays much better against good teams–probably because they got bored against the bad teams/pulled their starters.  Now, we can’t just take a simple linear regression; the slope doesn’t continue infinitely.  So I construct the Prediction Interval to estimate the mean and standard deviation at any point along the regression line, and regress based on the REGRESSED standard deviation of the team’s adjusted efficiency differentials.

For example, let’s see what Hampton looks like.  They raise their game more than just about anyone in the field; they’ve played a very easy schedule.  Here’s what their regressed curves look like:

Hampton's Regressed Efficiency Differential Curve

Hampton's Regressed Efficiency Differential Curve

To simplify the math, I presumed that all games in the tournament were against +25 level foes: I estimate that this is “the best” that each team can play with it all on the line.  Of course, a few teams have played worse with it all on the line (see Duke).

To incorporate this into the Bayesian ratings, I simply took the latest Bayesian rating and added in the projected differential at +25, minus the average efficiency differential for the team.

Next, I set about estimating the standard deviation for each team.  We can easily calculate the team’s standard deviation of performances; I estimated that the standard deviation of the Bayesian efficiency was 1 less than that.  Next, I looked at the standard deviation of the curve above at the +25 mark.  I decided the best way to combine the two was to take the geometric mean of the Bayesian-based Stdev and the stdev of the non-regressed efficiency differential curve.  I’m not totally sure how to do this here, so this is my best guess; I’m a little over my head mathematically.  Anyway, the results look about right intuitively.

So now we’ve got a new “Tourmament Power Rating” and a standard deviation… so it’s easy to calculate odds for each game.

First, here’s the ratings in tabular form:

OSdReTeamConfW-LBayesianRk25DeltaTourneyRkStdev
11EOhio St.B1032-233.471-0.2233.25114.81
216EAlabama St.SWAC17-17-13.90299-0.77-14.666816.34
216ETexas San AntonioSlnd19-13-6.582324.22-2.366610.69
39EVillanovaBE21-1118.9025-1.1417.763715.51
48EGeorge MasonCAA26-615.6244-1.1614.464615.71
55EWest VirginiaBE20-1121.74160.0821.821814.12
612EClemsonACC22-1120.68191.9422.621713.05
612EUABCUSA22-912.1365-0.9511.185014.09
713EPrincetonIvy25-66.121000.546.665513.87
84EKentuckySEC25-827.056-0.2026.85614.35
93ESyracuseBE26-725.529-0.3525.171117.45
1014EIndiana St.MVC20-135.52104-0.884.645816.16
1111EMarquetteBE20-1418.70280.9719.672413.97
126EXavierA1024-718.76272.8021.572017.24
137EWashingtonP1023-1022.8215-2.3620.462315.76
1410EGeorgiaSEC21-1113.09611.8714.964514.89
1515ELong IslandNEC27-51.301482.984.285913.05
162ENorth CarolinaACC26-723.04140.2623.301515.95
191WDukeACC30-432.262-3.0629.20312.23
2016WHamptonMEAC24-8-5.842249.844.006012.99
219WTennesseeSEC19-1415.58463.2118.792813.65
228WMichiganB1020-1316.25421.5317.783613.71
235WArizonaP1027-718.4333-3.1715.264413.94
2412WMemphisCUSA25-910.0573-0.349.725315.05
2513WOaklandSum25-910.7570-0.4310.325112.65
264WTexasB1227-727.4241.3028.72414.29
273WConnecticutBE26-921.70171.6423.351413.34
2814WBucknellPat25-84.401151.105.505714.78
2911WMissouriB1223-1018.20350.6818.882714.36
306WCincinnatiBE25-818.4731-0.4218.053517.60
317WTempleA1025-717.29370.7718.063413.40
3210WPenn St.B1019-1415.58451.3816.964017.06
3315WNorthern ColoradoBSky21-102.87128-2.700.176212.14
342WSan Diego St.MWC32-224.10122.6126.72714.10
361SWKansasB1232-231.423-1.4230.00215.24
3716SWBoston UniversityAE21-13-0.25160-0.77-1.026414.23
389SWIllinoisB1019-1320.18210.4120.592212.90
398SWNevada Las VegasMWC24-819.3724-0.8418.532914.53
405SWVanderbiltSEC23-1018.5830-0.1218.453013.52
4112SWRichmondA1027-715.1049-0.8114.294715.02
4213SWMorehead St.OVC24-95.971024.1210.095215.10
434SWLouisvilleBE25-924.14110.2724.411314.67
443SWPurdueB1025-725.7980.4026.19814.51
4514SWSt. Peter'sMAAC20-132.57131-1.670.906116.04
4611SWSouthern CaliforniaP1019-1415.40472.6818.083316.55
4611SWVirginia CommonwealthCAA23-119.32763.7413.064914.06
476SWGeorgetownBE21-1019.5222-0.4519.072615.06
487SWTexas A&MB1224-817.34360.0017.343912.76
4910SWFlorida St.ACC21-1016.6639-1.1615.504310.01
5015SWAkronMAC23-124.81112-4.810.006315.78
512SWNotre DameBE26-625.37100.2125.581016.26
531SEPittsburghBE27-527.265-0.3526.92512.13
5416SEArkansas Little RockSB19-17-5.36220-8.35-13.706714.98
5416SENC AshevilleBSth20-13-0.93167-0.53-1.466517.12
559SEOld DominionCAA27-614.9250-0.9114.014813.56
568SEButlerHorz23-916.32413.0319.352517.75
575SEKansas St.B1222-1019.41231.5020.912114.77
5812SEUtah St.WAC30-320.35201.4421.791915.45
5913SEBelmontASun30-418.6029-2.6815.924216.76
604SEWisconsinB1023-826.797-0.6426.15916.88
613SEBrigham YoungMWC30-423.40131.3524.751215.71
6214SEWoffordSC21-128.0987-1.266.845417.07
6311SEGonzagaWCC24-918.4632-2.2216.244114.68
646SESt. John'sBE21-1116.66401.7618.423117.79
657SEUCLAP1022-1014.61523.5818.183214.67
6610SEMichigan St.B1019-1417.09380.4617.553816.02
6715SEUC Santa BarbaraBW18-132.191373.565.745614.84
682SEFloridaSEC26-721.50181.7423.241616.39

A few notes:

  • Teams to watch out for: Clemson, Utah St., Marquette, Missouri, Illinois, and Texas.
  • Overseeded teams: Arizona, George Mason, ODU, Cincinnati, Texas A&M, and Vanderbilt.
  • Hampton raises its game a lot, but it’s still not good.  San Diego does quite a bit also, and they are good.
  • Duke and Arizona got their great efficiencies by beating up on the little guys.

And here are my directly calculated odds for each team to reach each level in the tournament:

OSdReTeam643216Elite 8Final 4FinalChamp1 in
11EOhio St.10099.7486.26561.97146.491831.099121.395324.67
84EKentucky10092.3759.22522.99113.99566.98103.6878827.1
93ESyracuse10088.9053.93632.03412.44455.69662.7658136.2
162ENorth Carolina10090.4256.02728.6469.73023.96111.7344457.7
126EXavier10054.8225.49513.0044.00861.48100.59137169
137EWashington10064.0030.13813.3483.68871.23820.45524220
55EWest Virginia10053.5921.4305.8422.81311.01610.40160249
612EClemson80.041.9117.4924.9572.49060.94130.38895257
1111EMarquette10045.1818.8218.6842.15550.65910.22431446
39EVillanova10058.369.0792.9291.12360.30550.092831077
1410EGeorgia10036.0012.2593.8330.64380.13470.032353091
48EGeorge Mason10041.644.6361.1610.35920.07410.017505714
612EUAB20.04.500.7780.0810.01870.00260.00042236328
1014EIndiana St.10011.101.7480.2730.01630.00120.00011872170
713EPrinceton1007.631.0750.0670.01010.00080.000081261187
1515ELong Island1009.581.5760.1780.00730.00040.000033684929
216ETexas San Antonio81.40.240.0170.0000.00000.00000.0000032042448855
216EAlabama St.18.60.020.0010.0000.00000.00000.0000092485855933097
191WDuke10097.7178.07246.44230.574516.02429.5489110.47
264WTexas10091.3678.14342.89027.298313.94768.0571112.41
342WSan Diego St.10097.8271.86246.69421.896210.06795.2857118.92
273WConnecticut10089.7656.49926.85410.01053.73361.6183861.8
2911WMissouri10052.0721.8447.8772.10440.57940.18736534
306WCincinnati10047.9319.6236.9781.90100.52750.16976589
219WTennessee10052.9511.9703.9391.45470.39160.12428805
317WTemple10052.8514.7296.1021.47270.37150.11084902
3210WPenn St.10047.1513.1845.2531.29490.32830.097051030
228WMichigan10047.059.6332.9511.01360.25180.073931353
235WArizona10064.8813.6992.7930.79240.15980.038292612
2412WMemphis10035.124.5990.5620.10120.01260.0018853133
2513WOakland1008.643.5600.3960.06810.00790.0011189988
2814WBucknell10010.242.0340.2260.01480.00120.00011935504
2016WHampton1002.290.3250.0270.00230.00010.0000111921993
3315WNorthern Colorado1002.180.2250.0150.00030.00000.00000283924556
361SWKansas10098.2374.80853.80734.875522.701212.196128.20
443SWPurdue10095.0967.15839.79319.964311.11694.8564020.6
512SWNotre Dame10094.4869.82338.34318.657010.05404.2760923.4
434SWLouisville10083.2058.05324.60512.52456.38752.4997740.0
389SWIllinois10055.9714.8227.2332.93171.18710.34145293
476SWGeorgetown10057.5219.7168.1162.64920.99040.26462378
405SWVanderbilt10061.4624.6376.7732.38410.83850.20407490
398SWNevada Las Vegas10044.0310.2474.4541.59500.57130.14397695
487SWTexas A&M10056.3718.0245.9861.64080.52530.11272887
4611SWSouthern California62.829.839.7943.8351.19660.42690.10962912
4112SWRichmond10038.5411.8942.3910.63060.16660.029213424
4910SWFlorida St.10043.6311.5103.1220.67390.17440.027663615
4611SWVirginia Commonwealth37.212.652.6460.7000.13660.03170.0047021274
4213SWMorehead St.10016.805.4150.7290.13380.02470.0028335298
4514SWSt. Peter's1004.910.6860.0590.00350.00030.000019254589
5015SWAkron1005.520.6430.0450.00230.00020.0000118342534
3716SWBoston University1001.770.1230.0090.00040.00000.00000187954430
531SEPittsburgh10097.8072.99644.33428.302114.81126.6989714.93
613SEBrigham Young10086.2558.30635.20317.66958.23993.3226630.1
604SEWisconsin10072.8344.94524.05914.51867.27973.2077931.2
682SEFlorida10086.8454.88029.75913.80635.93852.1920545.6
5812SEUtah St.10052.3324.14410.1665.09661.99990.66136151
575SEKansas St.10047.6720.9538.2893.97091.46270.44823223
568SEButler10063.2220.3578.4923.77861.30350.37840264
646SESt. John's10055.3222.53310.1943.60461.17220.31870314
657SEUCLA10051.6422.1539.2833.08330.93520.22991435
6610SEMichigan St.10048.3620.1968.2302.67330.79390.19261519
6311SEGonzaga10044.6815.5336.1121.75310.45680.094731056
5913SEBelmont10027.179.9582.8711.04590.27970.060731647
559SEOld Dominion10036.786.3601.7690.54150.11240.017905585
6214SEWofford10013.753.6280.7590.10460.01280.0011884838
6715SEUC Santa Barbara10013.162.7710.4600.04940.00460.00031320919
5416SENC Asheville77.72.170.2860.0210.00180.00010.0000033535383
5416SEArkansas Little Rock22.30.030.0010.0000.00000.00000.0000057507213911169

That’s a bit hard to follow, so perhaps a pretty chart would be easier:

Tourney Flow 2011

This helps us visualize which parts of the bracket are harder and which are easier.  In particular, Pitt’s bracket is really weak.  Ohio State is a solid favorite.

EDIT: Spreadsheets NOW AVAILABLE:

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3 Responses to NCAA Tourney Bayesian Ratings and Odds

  1. Nathan Walker on March 16, 2011 at 5:19 pm

    Super-thorough as always…maybe update it after all the opening round games are done?

  2. taylor on March 17, 2011 at 8:31 am

    Thanks for this!

    Question – if I’m filling out 3 brackets for the same pool, how do you balance your picks out? Any recommendations using this data?

    • DanielM on March 17, 2011 at 10:49 am

      See my new post!

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