/* ]]> */

2015 March Madness – Bracket based on experimental utility function

 2015, basketball, March Madness, Tournament  Comments Off on 2015 March Madness – Bracket based on experimental utility function
Mar 172015
 

robust_bracket

The image above is an attempt at a recommended bracket using a utility function that minimizes your regret of being wrong. Fan distributions count almost as much as win probabilities with this utility function (which is not peer reviewed). So how much you regret an incorrect pick depends both on the probability of you being wrong (based in win probability) and on the number of other entries likely to get it correct (based on fan distributions). The resulting bracket is mostly robust to the size of your pool (beyond a dozen other entries) and to most common scoring methods.

One of the problems with the utility function used to generate the “which team to pick” widget, is it assumes all you care about is getting the champ right and not having too many other entries also get the champ right. It ignores the possibility of hedging popular picks (eg, Kentucky and Duke), and can recommend some quite improbable champions.

The approach depicted above reflects the mindset of a quantitative portfolio manager. The portfolio manager might choose to minimize his regret of not picking popular picks that turn out to win. He won’t always pick the team most likely to win, because he would really regret being wrong if so many other entrants pick the underdog and the underdog wins. If nobody in your pool picks Northern Iowa, then not picking Northern Iowa either really can’t hurt you.

 Posted by on March 17, 2015 at 10:09 am

2015 March Madness – Which Team to Pick (other than Kentucky)

 2015, March Madness, Office pool, Tournament  Comments Off on 2015 March Madness – Which Team to Pick (other than Kentucky)
Mar 162015
 

Widget for identifying which team to pick as champion, based on the size of your pool

Use this widget to decide which team(s) to pick for your entry champion(s), then fill in the rest of your bracket(s) using the most likely bracket below.

If you don’t see the widget, you may download the Excel workbook yourself.

 Posted by on March 16, 2015 at 8:57 pm

2015 March Madness Expected Survival Rates by Region

 2015, basketball, March Madness, Office pool, Tournament  Comments Off on 2015 March Madness Expected Survival Rates by Region
Mar 152015
 

Update, March 16, 2015, 5:10p PDT
Corrected “Alabama” to read “Albany” in East region. Oklahoma’s survival rates are improved, so other teams’ survival rates in that region are slightly reduced. TMA

Midwest region

SeedTeamRound 1Round 2Round 3Round 4Round 5Round 6
1Kentucky0.97530.89380.81120.67710.45930.3368
16Manhattan0.02470.00540.00110.000100
8Cincinnati0.56540.0620.03130.01080.00220.0005
9Purdue0.43460.03880.01710.0050.00080.0002
5West Virginia0.63020.37260.06110.02430.00570.0016
12Buffalo0.36980.17050.0190.00540.00080.0002
4Maryland0.61960.31080.04460.01580.00320.0008
13Valparaiso0.38040.1460.01460.00370.00050.0001
6Butler0.47750.20460.08660.01780.00440.0013
11Texas0.52250.23450.10430.02270.0060.0018
3Notre Dame0.87650.53830.2940.08260.02840.0113
14Northeastern0.12350.02260.00350.000300
7Wichita St.0.73090.39040.2080.05490.01770.0066
10Indiana0.26910.08450.02540.00350.00060.0001
2Kansas0.83810.48860.27080.07530.02570.0101
15New Mexico St.0.16190.03650.00730.00070.00010

West region

SeedTeamRound 1Round 2Round 3Round 4Round 5Round 6
1Wisconsin0.9550.81560.64430.36170.17180.1027
16Coastal Carolina0.0450.00970.00190.000100
8Oregon0.47210.07890.03290.00660.00110.0002
9Oklahoma St.0.52790.09570.04220.00920.00160.0004
5Arkansas Little Rock0.22460.01910.0008000
12Wofford0.77540.17870.02170.00250.00020
4North Carolina0.79420.67680.23830.08330.02360.0087
13Harvard0.20580.12540.01790.00250.00030
6Xavier0.52440.2340.05250.01520.00320.0009
11BYU0.47560.20150.04220.01150.00220.0006
3Baylor0.7750.48960.15210.05890.01690.0063
14Georgia St.0.2250.07490.00960.00170.00020
7VCU0.43540.07080.03030.00810.00160.0004
10Ohio St.0.56460.11170.05490.01720.00390.0012
2Arizona0.97720.81510.65810.42160.21790.1399
15Texas Southern0.02280.00240.0002000

East region

SeedTeamRound 1Round 2Round 3Round 4Round 5Round 6
1Villanova0.96780.81570.60250.3590.23040.1001
16Lafayette0.03220.00490.0005000
8North Carolina St.0.51650.09490.03470.00840.00230.0003
9LSU0.48350.08460.02970.00690.00180.0002
5Northern Iowa0.84910.54040.20510.08360.03750.0099
12Wyoming0.15090.03890.00450.00050.00010
4Louisville0.78810.37490.11730.03940.01460.0031
13UC Irvine0.21190.04570.00560.00070.00010
6Providence0.56040.21740.05690.01640.00520.0009
11Dayton0.43960.14820.03280.0080.00220.0003
3Oklahoma0.89220.61180.24260.10450.04920.0139
14Albany0.10780.02260.00190.000200
7Michigan St.0.62160.16810.08170.02840.01080.0024
10Georgia0.37840.07260.02690.00680.00190.0003
2Virginia0.9530.75170.55610.3370.21930.0973
15Belmont0.0470.00760.0010.000100

South region

SeedTeamRound 1Round 2Round 3Round 4Round 5Round 6
1Duke0.91960.70070.4460.26010.12460.0442
16North Florida0.08040.01780.00260.000300
8San Diego St.0.57560.17530.06910.02370.00610.0011
9St. John's0.42440.10620.03480.00980.0020.0003
5Utah0.74140.5210.2790.150.0650.0205
12Stephen F. Austin0.25860.12070.03670.0110.00240.0004
4Georgetown0.83740.33820.12930.04920.01420.0028
13Eastern Washington0.16260.02020.00240.000300
6SMU0.60740.27770.09880.03670.01050.002
11UCLA0.39260.14190.03820.01070.00220.0003
3Iowa St.0.86580.55130.24480.11330.04150.0108
14UAB0.13420.02910.00360.000500
7Iowa0.55440.16780.0770.02780.00770.0015
10Davidson0.44560.11710.04770.0150.00360.0006
2Gonzaga0.93850.70480.48850.29140.14470.0537
15North Dakota St.0.06150.01020.00140.000100

Survival rates are derived from a composite of strength ratings from Ken Pomoroy and LRMC. Any errors are mine.

 Posted by on March 15, 2015 at 5:15 pm

Whether to pick upsets in your bracket depends on the pool’s scoring method

 2015, basketball, March Madness, Office pool, Office pool strategy, Tournament  Comments Off on Whether to pick upsets in your bracket depends on the pool’s scoring method
Mar 132015
 

The traditional NCAA bracket entry is scored in progressive powers of two, such that each round offers 32 points. First round games are worth 1 point, second round 2, etc., and the final game is worth 32.

The leverage of the championship game – worth 32 points out of a possible 192 – is why so many entries pick the overall favorite. This year that favorite will be Kentucky. I predict your pool, if it uses traditional scoring, will have over 40% of the entries picking Kentucky as the champ.

The problem with picking the overall favorite yourself is it is what is known as a “crowded trade.” You already know nearly half the other entries are picking Kentucky. So whether you win the pool, with Kentucky as your champ, is a different matter from whether Kentucky wins the tournament. If Kentucky wins, your pool’s champ will probably be determined by a handful of early round games.

The corollary to this is that if you’re confident in your picking ability, you SHOULD pick Kentucky, because you expect other entries to have worse records than yours in the earlier rounds.

I prefer to look for low hanging fruit in terms of strong teams being underpicked by fans in pools. I predict schools like Virginia, Arizona, Wisconsin, and Villanova will all be underrepresented in pool entries to win it all relative to their probability of winning the whole tournament. Imagine you’re the only one in your pool who picks Wisconsin – that’s a wide margin of error for any earlier round games that you missed. Compare that to if you pick Kentucky – your early round picks had better be nearly perfect.

Scoring method matters. Some pools score rounds in a linearly increasing sequence (1, 2, 3, 4, 5, 6); in this case the final game counts for a mere 6 out of 120 points. Some pools now use Fibonacci (1, 2, 3, 5, 8, 13); here the final is worth only 13 out of 137. In both cases, getting the champ wrong hurts you less than it does in a traditional power-two pool, so you can afford to take more chances.

 Posted by on March 13, 2015 at 4:05 pm

Q: What’s Wrong With Selecting Kansas in Your Pool? A: You’ve Probably Already Been Eliminated

 basketball, March Madness, Tournament  Comments Off on Q: What’s Wrong With Selecting Kansas in Your Pool? A: You’ve Probably Already Been Eliminated
Mar 192010
 

Depending on your predictive model, Kansas had somewhere between a 20% and a 25% chance of winning the tournament, and so did Duke.  By winning last night, Kansas’ odds didn’t really change much, since they were supposed to beat Lehigh with near certainty, and the same goes for Duke vs. Ar-PB.

Meanwhile, in whatever pool you’re playing some 40% to 50% of its entries picked Kansas to win the championship, but only 6% picked Duke.  While you didn’t know the exact number prior to yesterday, you had pretty strong clues.  Since Monday night,  ESPN had been showing over 40% of its entries had picked Kansas as the champ, and Yahoo! had nearly half!  In other words, the probability that someone actually picked Kansas was twice as much as the probability that Kansas might actually win.

Let’s say you’re in a 20-entry pool and 10 have picked Kansas, 2 picked Duke.  Ex ante, each Kansas entry has a 2.5% shot at winning, while each Duke pick has a 12.5% shot.  Picking Kansas, in effect, was picking the early round upset lottery:  if you didn’t get many of yesterday’s upsets, you’re already screwed.

 Posted by on March 19, 2010 at 11:19 am