Analyzing the 2015 Tournament Part 2

March 27, 2015

Once the field is selected and the 16 number one seeds determined (only the top eight of which are actually "seeded", see below) the remaining teams are assigned to the sixteen regionals. One of the criteria for regional assignment is "competitive balance" and while that is not the most important one to the committee, it is the one that generates the most whining discussion on message boards.

It ought to help that there is a precise definition of what "competitive balance" means for a 64-team tournament that begins with 16 4-team "regionals." Suppose you have an ordered list of the 64 teams in "strongest to weakest" order. (Aside: that it is impossible to create such a list has been proven, but we can avoid that by including a qualifying "according to such-and-such.")

The regionals will be perfectly "balanced" if the region assignments and seeds within region are assigned based upon this table:

SeedR1R2R2R4R5R6R7R8R9R10R11R12R13R14R15R16
112345678910111213141516
232313029282726252423222120191817
333343536373839404142434445464748
464636261605958575655545352515049

This is called the "S-curve." To assign a team's regional and seed just find it's rank in the table and read off the column and row labels. The result is a "competitively balanced" field because the sum of participants' ranks is the same for all regionals. The best #1 faces the worst #4 and #2 along with the best #3. For the second round, the winner from R1 would meet the winner of R16, R2 would meet R15, and so on.

This is not what the committee does. Once the eight "national" seeds are determined the other eight #1 seeds are paired with them according to arbitrary criteria. The #1 seed in regional #16 is not necessarily the weakest #1, and assignments of #2, #3 and #4 seeds might best be called a matter of convenience.

Measuring Competitive Balance

Although the committee doesn't seed all 64 teams and use the teams' ranks to assign them to regions, we can use the actual region and seed assignments to assign the participant's "rank" using the same table (i.e. whatever team they made the third seed in region 13 is assigned "rank" 45.) Once that is done we can measure how different that is from the ordering of the same teams "according to such-and-such."

The measure of how different two ordered lists are is the distance, defined as the number of swaps required to make the lists the same. The field as defined is 255 swaps from the teams' order by RPI, and 221 from that defined by the ISR. Since there are 2016 total pairs, these correspond to about 87 and 89 percent. The distance between the RPI and ISR orderings is 220.

The majority of the differences are in the two and three seed area: 66.1 percent of the RPI distance and 63.8 percent of the ISR's are contributions from this range.

RgnSdSRPIISRTeamD(S,RPI)D(S,ISR)D(RPI,ISR)
11141UCLA303
21252Louisiana State303
3131212Louisville992
41438Florida567
51516Miami Florida455
616137Illinois756
71783Texas Christian545
81875Missouri State554
9191111Oklahoma State642
1011064Texas A&M664
111111010Vanderbilt532
1211229Dallas Baptist1037
13113913Florida State404
141142522Cal State Fullerton1178
151151418Houston154
161162014UC Santa Barbara626
RgnSdSRPIISRTeamD(S,RPI)D(S,ISR)D(RPI,ISR)
162172317Southern California848
152183226Rice13712
142193423Arizona State14515
132201620College of Charleston666
122213515Oregon State13619
112221524Radford738
102231827Coastal Carolina738
92243628Arkansas11310
82252925Iowa11510
72262630North Carolina State10311
62274029Notre Dame11310
52282433East Carolina12412
42291716Florida Atlantic12135
32301946Bradley11920
22312750North Carolina-Wilmington81115
12323148Mississippi81014
RgnSdSRPIISRTeamD(S,RPI)D(S,ISR)D(RPI,ISR)
13334240Maryland695
23344349Tulane695
33356154Michigan1095
43363055South Florida11916
53376593Columbia10155
63384641Wright State7136
73395588Stony Brook8137
83406235Oregon81313
93413732Oral Roberts11149
103423919California112318
113433238Indiana151112
123448562Texas774
133452231Auburn251512
143465659Clemson664
153474953Louisiana-Lafayette783
163482139Virginia271316
RgnSdSRPIISRTeamD(S,RPI)D(S,ISR)D(RPI,ISR)
164497644San Diego State31112
15450133128Houston Baptist880
1445111392Pepperdine644
13452107108Mercer543
1245393119Virginia Commonwealth565
114547174Lipscomb765
10455154155Texas Southern550
94566781St John's875
8457195188Canisius440
7458220256Sacred Heart451
6459122116Ohio572
5460142129Florida International550
4461231225Florida A&M231
3462112110Morehead State893
2463239270Lehigh110
1464127103Cal State Bakersfield7114
       255221220

That most of the discrepencies are in the two-three seed range is not surprising. There can be large rank differences in this area that have no effect on competitive balance, so we have to look a little harder.

Absolute Measurements

"The S-Curve leads to competitive balance because the sum of the ranks is the same for each region" is a simplification. To characterize the actual strength of teams in a regional requires using the teams' rating values. Since the #1 seeds are pre-determined and automatic qualifiers dominate the #4 seeds, we can characterize regions by the sum of the #2 and #3 teams' ratings.
2015 Bracket
Lake Elisnore
SdRPIRanksISR
11.56220141.684UC Santa Barbara
40.73376441.116San Diego State
31.42721391.160Virginia
21.40423171.544Southern California
    
Los Angeles
SdRPIRanksISR
12.125412.158UCLA {1}
40.2311271030.506Cal State Bakersfield
31.15942401.154Maryland
21.29631481.069Mississippi
    
Springfield
SdRPIRanksISR
11.954751.999Missouri State {8}
4-0.455195188-0.413Canisius
30.94962351.170Oregon
21.31129251.309Iowa
    
Stillwater
SdRPIRanksISR
11.78211111.751Oklahoma State
40.84767810.710St John's
31.23937321.196Oral Roberts
21.24936281.256Arkansas
 
Tallahassee
SdRPIRanksISR
11.9359131.707Florida State
40.3591071080.442Mercer
31.42122311.222Auburn
21.62116201.416College of Charleston
    
Gainesville
SdRPIRanksISR
12.131381.929Florida {4}
4-0.775231225-0.728Florida A&M
31.30430550.970South Florida
21.61717161.562Florida Atlantic
    
Coral Gables
SdRPIRanksISR
12.231161.976Miami Florida {5}
40.0861421290.279Florida International
30.87065930.588Columbia
21.38424331.193East Carolina
    
Dallas
SdRPIRanksISR
12.162291.898Dallas Baptist
40.535931190.358Virginia Commonwealth
30.66385620.921Texas
21.25135151.616Oregon State
 
Fullerton
SdRPIRanksISR
11.37225221.380Cal State Fullerton
40.306113920.591Pepperdine
31.00456590.925Clemson
21.26634231.378Arizona State
    
Lousville
SdRPIRanksISR
11.77212121.717Louisville {3}
40.3101121100.437Morehead State
30.95561540.979Michigan
21.56619461.095Bradley
    
Champaign
SdRPIRanksISR
11.7621371.964Illinois {6}
40.2591221160.402Ohio
31.13546411.146Wright State
21.22340291.245Notre Dame
    
Nashville
SdRPIRanksISR
11.83110101.767Vanderbilt
40.77671740.799Lipscomb
31.26832381.165Indiana
21.69415241.348Radford
 
Houston
SdRPIRanksISR
11.74914181.541Houston
40.1881331280.290Houston Baptist
31.11949530.985Louisiana-Lafayette
21.26832261.304Rice
    
Baton Rouge
SdRPIRanksISR
12.066522.151Louisiana State {2}
4-0.818239270-1.271Lehigh
31.15143491.065Tulane
21.33927501.062North Carolina-Wilmington
    
Fort Worth
SdRPIRanksISR
11.949832.046Texas Christian {7}
4-0.686220256-1.068Sacred Heart
31.00655880.608Stony Brook
21.34126301.229North Carolina State
    
College Station
SdRPIRanksISR
11.986642.013Texas A&M
4-0.035154155-0.038Texas Southern
31.22939191.445California
21.56818271.279Coastal Carolina
 
In this bracket the RPI and ISR values are reported in their normalized form: how much above or below the average value for all teams the team's value is. The numbers are therefore in the same "units" and can be directly compared.

The {2}-{7} brackets are interesting. Despite including the toughest overall regional, the set as a whole is the weakest of the CWS day one pairings. Coral Gables and Fort Worth basically have two #4 seeds while Lake Elisnore and College Station have two #3s and no #4. Other than those the field is pretty balanced, especially from the ISR perspective.

© Copyright 2015 Paul Kislanko