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:
Seed | R1 | R2 | R2 | R4 | R5 | R6 | R7 | R8 | R9 | R10 | R11 | R12 | R13 | R14 | R15 | R16 |
1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
2 | 32 | 31 | 30 | 29 | 28 | 27 | 26 | 25 | 24 | 23 | 22 | 21 | 20 | 19 | 18 | 17 |
3 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 |
4 | 64 | 63 | 62 | 61 | 60 | 59 | 58 | 57 | 56 | 55 | 54 | 53 | 52 | 51 | 50 | 49 |
|
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.
Rgn | Sd | — | S | RPI | ISR | Team | D(S,RPI) | D(S,ISR) | — | D(RPI,ISR) |
1 | 1 | | 1 | 4 | 1 | UCLA | 3 | 0 | | 3 |
2 | 1 | | 2 | 5 | 2 | Louisiana State | 3 | 0 | | 3 |
3 | 1 | | 3 | 12 | 12 | Louisville | 9 | 9 | | 2 |
4 | 1 | | 4 | 3 | 8 | Florida | 5 | 6 | | 7 |
5 | 1 | | 5 | 1 | 6 | Miami Florida | 4 | 5 | | 5 |
6 | 1 | | 6 | 13 | 7 | Illinois | 7 | 5 | | 6 |
7 | 1 | | 7 | 8 | 3 | Texas Christian | 5 | 4 | | 5 |
8 | 1 | | 8 | 7 | 5 | Missouri State | 5 | 5 | | 4 |
9 | 1 | | 9 | 11 | 11 | Oklahoma State | 6 | 4 | | 2 |
10 | 1 | | 10 | 6 | 4 | Texas A&M | 6 | 6 | | 4 |
11 | 1 | | 11 | 10 | 10 | Vanderbilt | 5 | 3 | | 2 |
12 | 1 | | 12 | 2 | 9 | Dallas Baptist | 10 | 3 | | 7 |
13 | 1 | | 13 | 9 | 13 | Florida State | 4 | 0 | | 4 |
14 | 1 | | 14 | 25 | 22 | Cal State Fullerton | 11 | 7 | | 8 |
15 | 1 | | 15 | 14 | 18 | Houston | 1 | 5 | | 4 |
16 | 1 | | 16 | 20 | 14 | UC Santa Barbara | 6 | 2 | | 6 |
Rgn | Sd | — | S | RPI | ISR | Team | D(S,RPI) | D(S,ISR) | — | D(RPI,ISR) |
16 | 2 | | 17 | 23 | 17 | Southern California | 8 | 4 | | 8 |
15 | 2 | | 18 | 32 | 26 | Rice | 13 | 7 | | 12 |
14 | 2 | | 19 | 34 | 23 | Arizona State | 14 | 5 | | 15 |
13 | 2 | | 20 | 16 | 20 | College of Charleston | 6 | 6 | | 6 |
12 | 2 | | 21 | 35 | 15 | Oregon State | 13 | 6 | | 19 |
11 | 2 | | 22 | 15 | 24 | Radford | 7 | 3 | | 8 |
10 | 2 | | 23 | 18 | 27 | Coastal Carolina | 7 | 3 | | 8 |
9 | 2 | | 24 | 36 | 28 | Arkansas | 11 | 3 | | 10 |
8 | 2 | | 25 | 29 | 25 | Iowa | 11 | 5 | | 10 |
7 | 2 | | 26 | 26 | 30 | North Carolina State | 10 | 3 | | 11 |
6 | 2 | | 27 | 40 | 29 | Notre Dame | 11 | 3 | | 10 |
5 | 2 | | 28 | 24 | 33 | East Carolina | 12 | 4 | | 12 |
4 | 2 | | 29 | 17 | 16 | Florida Atlantic | 12 | 13 | | 5 |
3 | 2 | | 30 | 19 | 46 | Bradley | 11 | 9 | | 20 |
2 | 2 | | 31 | 27 | 50 | North Carolina-Wilmington | 8 | 11 | | 15 |
1 | 2 | | 32 | 31 | 48 | Mississippi | 8 | 10 | | 14 |
Rgn | Sd | — | S | RPI | ISR | Team | D(S,RPI) | D(S,ISR) | — | D(RPI,ISR) |
1 | 3 | | 33 | 42 | 40 | Maryland | 6 | 9 | | 5 |
2 | 3 | | 34 | 43 | 49 | Tulane | 6 | 9 | | 5 |
3 | 3 | | 35 | 61 | 54 | Michigan | 10 | 9 | | 5 |
4 | 3 | | 36 | 30 | 55 | South Florida | 11 | 9 | | 16 |
5 | 3 | | 37 | 65 | 93 | Columbia | 10 | 15 | | 5 |
6 | 3 | | 38 | 46 | 41 | Wright State | 7 | 13 | | 6 |
7 | 3 | | 39 | 55 | 88 | Stony Brook | 8 | 13 | | 7 |
8 | 3 | | 40 | 62 | 35 | Oregon | 8 | 13 | | 13 |
9 | 3 | | 41 | 37 | 32 | Oral Roberts | 11 | 14 | | 9 |
10 | 3 | | 42 | 39 | 19 | California | 11 | 23 | | 18 |
11 | 3 | | 43 | 32 | 38 | Indiana | 15 | 11 | | 12 |
12 | 3 | | 44 | 85 | 62 | Texas | 7 | 7 | | 4 |
13 | 3 | | 45 | 22 | 31 | Auburn | 25 | 15 | | 12 |
14 | 3 | | 46 | 56 | 59 | Clemson | 6 | 6 | | 4 |
15 | 3 | | 47 | 49 | 53 | Louisiana-Lafayette | 7 | 8 | | 3 |
16 | 3 | | 48 | 21 | 39 | Virginia | 27 | 13 | | 16 |
Rgn | Sd | — | S | RPI | ISR | Team | D(S,RPI) | D(S,ISR) | — | D(RPI,ISR) |
16 | 4 | | 49 | 76 | 44 | San Diego State | 3 | 11 | | 12 |
15 | 4 | | 50 | 133 | 128 | Houston Baptist | 8 | 8 | | 0 |
14 | 4 | | 51 | 113 | 92 | Pepperdine | 6 | 4 | | 4 |
13 | 4 | | 52 | 107 | 108 | Mercer | 5 | 4 | | 3 |
12 | 4 | | 53 | 93 | 119 | Virginia Commonwealth | 5 | 6 | | 5 |
11 | 4 | | 54 | 71 | 74 | Lipscomb | 7 | 6 | | 5 |
10 | 4 | | 55 | 154 | 155 | Texas Southern | 5 | 5 | | 0 |
9 | 4 | | 56 | 67 | 81 | St John's | 8 | 7 | | 5 |
8 | 4 | | 57 | 195 | 188 | Canisius | 4 | 4 | | 0 |
7 | 4 | | 58 | 220 | 256 | Sacred Heart | 4 | 5 | | 1 |
6 | 4 | | 59 | 122 | 116 | Ohio | 5 | 7 | | 2 |
5 | 4 | | 60 | 142 | 129 | Florida International | 5 | 5 | | 0 |
4 | 4 | | 61 | 231 | 225 | Florida A&M | 2 | 3 | | 1 |
3 | 4 | | 62 | 112 | 110 | Morehead State | 8 | 9 | | 3 |
2 | 4 | | 63 | 239 | 270 | Lehigh | 1 | 1 | | 0 |
1 | 4 | | 64 | 127 | 103 | Cal State Bakersfield | 7 | 11 | | 4 |
| | | | | | | 255 | 221 | | 220 |
|
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 | Sd | RPI | Ranks | ISR | | 1 | 1.562 | 20 | 14 | 1.684 | UC Santa Barbara | 4 | 0.733 | 76 | 44 | 1.116 | San Diego State | 3 | 1.427 | 21 | 39 | 1.160 | Virginia | 2 | 1.404 | 23 | 17 | 1.544 | Southern California |
| | Los Angeles | Sd | RPI | Ranks | ISR | | 1 | 2.125 | 4 | 1 | 2.158 | UCLA {1} | 4 | 0.231 | 127 | 103 | 0.506 | Cal State Bakersfield | 3 | 1.159 | 42 | 40 | 1.154 | Maryland | 2 | 1.296 | 31 | 48 | 1.069 | Mississippi |
| | Springfield | Sd | RPI | Ranks | ISR | | 1 | 1.954 | 7 | 5 | 1.999 | Missouri State {8} | 4 | -0.455 | 195 | 188 | -0.413 | Canisius | 3 | 0.949 | 62 | 35 | 1.170 | Oregon | 2 | 1.311 | 29 | 25 | 1.309 | Iowa |
| | Stillwater | Sd | RPI | Ranks | ISR | | 1 | 1.782 | 11 | 11 | 1.751 | Oklahoma State | 4 | 0.847 | 67 | 81 | 0.710 | St John's | 3 | 1.239 | 37 | 32 | 1.196 | Oral Roberts | 2 | 1.249 | 36 | 28 | 1.256 | Arkansas |
|
|
Tallahassee | Sd | RPI | Ranks | ISR | | 1 | 1.935 | 9 | 13 | 1.707 | Florida State | 4 | 0.359 | 107 | 108 | 0.442 | Mercer | 3 | 1.421 | 22 | 31 | 1.222 | Auburn | 2 | 1.621 | 16 | 20 | 1.416 | College of Charleston |
| | Gainesville | Sd | RPI | Ranks | ISR | | 1 | 2.131 | 3 | 8 | 1.929 | Florida {4} | 4 | -0.775 | 231 | 225 | -0.728 | Florida A&M | 3 | 1.304 | 30 | 55 | 0.970 | South Florida | 2 | 1.617 | 17 | 16 | 1.562 | Florida Atlantic |
| | Coral Gables | Sd | RPI | Ranks | ISR | | 1 | 2.231 | 1 | 6 | 1.976 | Miami Florida {5} | 4 | 0.086 | 142 | 129 | 0.279 | Florida International | 3 | 0.870 | 65 | 93 | 0.588 | Columbia | 2 | 1.384 | 24 | 33 | 1.193 | East Carolina |
| | Dallas | Sd | RPI | Ranks | ISR | | 1 | 2.162 | 2 | 9 | 1.898 | Dallas Baptist | 4 | 0.535 | 93 | 119 | 0.358 | Virginia Commonwealth | 3 | 0.663 | 85 | 62 | 0.921 | Texas | 2 | 1.251 | 35 | 15 | 1.616 | Oregon State |
|
|
Fullerton | Sd | RPI | Ranks | ISR | | 1 | 1.372 | 25 | 22 | 1.380 | Cal State Fullerton | 4 | 0.306 | 113 | 92 | 0.591 | Pepperdine | 3 | 1.004 | 56 | 59 | 0.925 | Clemson | 2 | 1.266 | 34 | 23 | 1.378 | Arizona State |
| | Lousville | Sd | RPI | Ranks | ISR | | 1 | 1.772 | 12 | 12 | 1.717 | Louisville {3} | 4 | 0.310 | 112 | 110 | 0.437 | Morehead State | 3 | 0.955 | 61 | 54 | 0.979 | Michigan | 2 | 1.566 | 19 | 46 | 1.095 | Bradley |
| | Champaign | Sd | RPI | Ranks | ISR | | 1 | 1.762 | 13 | 7 | 1.964 | Illinois {6} | 4 | 0.259 | 122 | 116 | 0.402 | Ohio | 3 | 1.135 | 46 | 41 | 1.146 | Wright State | 2 | 1.223 | 40 | 29 | 1.245 | Notre Dame |
| | Nashville | Sd | RPI | Ranks | ISR | | 1 | 1.831 | 10 | 10 | 1.767 | Vanderbilt | 4 | 0.776 | 71 | 74 | 0.799 | Lipscomb | 3 | 1.268 | 32 | 38 | 1.165 | Indiana | 2 | 1.694 | 15 | 24 | 1.348 | Radford |
|
|
Houston | Sd | RPI | Ranks | ISR | | 1 | 1.749 | 14 | 18 | 1.541 | Houston | 4 | 0.188 | 133 | 128 | 0.290 | Houston Baptist | 3 | 1.119 | 49 | 53 | 0.985 | Louisiana-Lafayette | 2 | 1.268 | 32 | 26 | 1.304 | Rice |
| | Baton Rouge | Sd | RPI | Ranks | ISR | | 1 | 2.066 | 5 | 2 | 2.151 | Louisiana State {2} | 4 | -0.818 | 239 | 270 | -1.271 | Lehigh | 3 | 1.151 | 43 | 49 | 1.065 | Tulane | 2 | 1.339 | 27 | 50 | 1.062 | North Carolina-Wilmington |
| | Fort Worth | Sd | RPI | Ranks | ISR | | 1 | 1.949 | 8 | 3 | 2.046 | Texas Christian {7} | 4 | -0.686 | 220 | 256 | -1.068 | Sacred Heart | 3 | 1.006 | 55 | 88 | 0.608 | Stony Brook | 2 | 1.341 | 26 | 30 | 1.229 | North Carolina State |
| | College Station | Sd | RPI | Ranks | ISR | | 1 | 1.986 | 6 | 4 | 2.013 | Texas A&M | 4 | -0.035 | 154 | 155 | -0.038 | Texas Southern | 3 | 1.229 | 39 | 19 | 1.445 | California | 2 | 1.568 | 18 | 27 | 1.279 | Coastal 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