The math behind region races and playoff seeding

With just a few regular season weeks left, many region races are a complicated mess, especially those that are only a few games into region play.

Here I’d like to look at the math behind the region races and the playoff seeding and how the Monte Carlo season simulation helps us answer some of those questions. I’ll only focus on the top six classifications since the Class A playoffs are seeded differently. I’m excluding teams playing non-region schedules (Clarkston and Cross Keys in 5-AAAAA, Forest Park in 4-AAAAAA, and Osborne in 6-AAAAAA) and for simplicity’s sake I’m ignoring the AAAAAAA at-large bid.

First, let’s consider the sheer number of possible region standings. Since the order of the four playoff teams matters, we’ll be working with permutations (as opposed to combinations). Calculating permutations is fairly simple, but requires a math function referred to as a factorial, denoted by a “!”.

If each region sends four teams to the playoffs, then the possible permutations are:
(# of Members)! / (# of Members – 4)!

So for a region with six members, there are:
(6)! / (6 – 4)!
= (6 x 5 x 4 x 3 x 2 x 1) / (2 x 1)
= 720 / 2
= 360 possible permutations of four teams.

Here’s how Class AAAA breaks down:

Region Members Permutations
1-AAAA 8 1,680
2-AAAA 6 360
3-AAAA 6 360
4-AAAA 7 840
5-AAAA 7 840
6-AAAA 7 840
7-AAAA 5 120
8-AAAA 6 360

We can see that Region 1-AAAA has 1,680 permutations while even Region 7-AAAA has 120 with just five teams.

Using this information, we can then determine the surprisingly large number of ways to seed the Class AAAA bracket:
1680 x 360 x 360 x 840 x 840 x 840 x 120 x 360 = 5,574,884,681,318,400,000,000

Here’s the number of possible brackets for the top six classifications:

Classification Possible Brackets
AAAAAAA 102,395,841,085,440,000,000
AAAAAA 48,167,003,646,591,000,000,000
AAAAA 56,194,837,587,689,500,000,000
AAAA 5,574,884,681,318,400,000,000
AAA† 59,465,436,600,729,600,000,000
AA 364,225,799,179,469,000,000,000
† – Region 6-AAA has 10 teams but only 1,920 permutations because of its two five-team subregions and 1-4, 2-3 elimination format for seeding.

For reference, Class AA has 3.64 x 10^23 possibilities while there are “only” about 5.6 x 10^21 grains of sand on the entire Earth.

In short, there are a lot of possible brackets.

However the outcomes of the games are probabilistic, meaning that, using the ratings, we can assign a probability that a particular team will win a particular contest. Since the outcomes of the games are probabilistic, by extension the region standings are probabilistic, and by extension again the playoff brackets are probabilistic.

But because there are too many possible brackets to simply calculate the odds associated with them all, the Monte Carlo method becomes a practical way to estimate them. The Monte Carlo method is a well-accepted method for solving complex combinatorial problems through simulation. So, the program essentially simulates the season many times over by simulating the remaining regular season games, constructing region standings, seeding the playoff brackets, and finally simulating the playoffs. As the program executes the simulations, it counts, among many other things, how often each team wins the championship. The program conducts 1,000,000 simulations in about five hours, or roughly 50 seasons a second, although as the season progresses it gets down to about three hours because it uses the results of games already played instead of simulating their outcomes.

Among the items the program counts are the number of times each permutation of playoff teams occurs for each region. For example, Region 1-AAAAAA has five teams and 120 possible permutations of playoff teams, so the program counts how often each one of those 120 permutations occurs after simulating the remaining regular season games and constructing the region standings. The output then looks something like:

Occurrences No 1 Seed No 2 Seed No 3 Seed No 4 Seed
83,078 Valdosta Northside (Warner Robins) Lee County Houston County
59,730 Northside (Warner Robins) Valdosta Lee County Houston County
57,632 Valdosta Lee County Northside (Warner Robins) Houston County
49,205 Valdosta Northside (Warner Robins) Lee County Coffee
46,097 Northside (Warner Robins) Lee County Valdosta Houston County
42,943 Valdosta Northside (Warner Robins) Houston County Lee County
41,650 Valdosta Lee County Northside (Warner Robins) Coffee
40,640 Northside (Warner Robins) Valdosta Lee County Coffee
37,681 Lee County Valdosta Northside (Warner Robins) Houston County
31,578 Northside (Warner Robins) Lee County Valdosta Coffee

Here we see that out of the 1,000,000 simulations, Valdosta, Northside (Warner Robins), Lee County, and Houston County finished in that exact order 83,078 times, or roughly 8.3% of the time. Since it is the most common occurring of the 120 permutations, it is the modal playoff seeding for Region 1-AAAAAA.

The modal bracket is then constructed by simply starting with the modal playoff seeding from each region and assuming the favored team wins each game, which is the most likely outcome of all the possible outcomes.

However the modal bracket, while useful, is still extremely limited. After all, while it represents the most likely outcome of the season it is still highly unlikely to exactly occur. For example, while there is an 8.3% chance the playoff seeding for Region 1-AAAAAA will be the modal playoff seeding, there is a 91.7% chance some other scenario will unfold.

The Monte Carlo simulation takes into account the modal playoff seeding plus all the other possible outcomes as well. That’s why occasionally there will appear to be some discrepancies between the modal bracket and the table of odds.

For example, in 7-AAAAAA, the modal playoff seeding is Johns Creek, Centennial, Alpharetta, and Cambridge with a 23.0% chance of occurring. However, because of their remaining region games, Centennial actually fares slightly better in the full simulation. Overall they have a 45.5% of winning the region as compared to Johns Creek’s 42.3% chance, Centennial has a 99.5% chance of making the playoffs whereas Johns Creek has a 98.2% chance, and ultimately Centennial’s odds to win the title are 4,544.45 to one while Johns Creek’s are 5,616.98 to one.

So again, while the modal bracket is useful and entertaining, there is much more to consider than the one “most-likely-but-still-highly-unlikely” outcome it represents.

Below is every region playoff permutation with greater than a 3% chance of occurring:

Classification Region Occurrences Pct No 1 Seed No 2 Seed No 3 Seed No 4 Seed
AAAAAAA 1 – AAAAAAA 329,334 32.9% Colquitt County Lowndes Tift County Camden County
AAAAAAA 1 – AAAAAAA 183,637 18.4% Lowndes Colquitt County Tift County Camden County
AAAAAAA 1 – AAAAAAA 154,422 15.4% Colquitt County Lowndes Camden County Tift County
AAAAAAA 1 – AAAAAAA 94,472 9.4% Colquitt County Tift County Lowndes Camden County
AAAAAAA 1 – AAAAAAA 70,393 7.0% Lowndes Colquitt County Camden County Tift County
AAAAAAA 1 – AAAAAAA 68,569 6.9% Lowndes Tift County Colquitt County Camden County
AAAAAAA 2 – AAAAAAA 176,261 17.6% Westlake East Coweta Wheeler Newnan
AAAAAAA 2 – AAAAAAA 115,877 11.6% Westlake East Coweta Newnan Wheeler
AAAAAAA 2 – AAAAAAA 101,313 10.1% East Coweta Westlake Wheeler Newnan
AAAAAAA 2 – AAAAAAA 69,066 6.9% Westlake Wheeler East Coweta Newnan
AAAAAAA 2 – AAAAAAA 61,570 6.2% East Coweta Westlake Newnan Wheeler
AAAAAAA 2 – AAAAAAA 56,338 5.6% Westlake East Coweta Wheeler Pebblebrook
AAAAAAA 2 – AAAAAAA 30,687 3.1% East Coweta Westlake Wheeler Pebblebrook
AAAAAAA 2 – AAAAAAA 30,662 3.1% Westlake Newnan East Coweta Wheeler
AAAAAAA 3 – AAAAAAA 191,151 19.1% McEachern North Cobb North Paulding Hillgrove
AAAAAAA 3 – AAAAAAA 86,022 8.6% McEachern North Cobb Hillgrove North Paulding
AAAAAAA 3 – AAAAAAA 80,986 8.1% McEachern North Cobb North Paulding Marietta
AAAAAAA 3 – AAAAAAA 69,820 7.0% McEachern North Paulding North Cobb Hillgrove
AAAAAAA 3 – AAAAAAA 58,627 5.9% McEachern Hillgrove North Cobb North Paulding
AAAAAAA 3 – AAAAAAA 42,529 4.3% McEachern North Paulding Hillgrove North Cobb
AAAAAAA 3 – AAAAAAA 40,232 4.0% McEachern North Paulding North Cobb Marietta
AAAAAAA 3 – AAAAAAA 39,701 4.0% North Cobb McEachern Hillgrove North Paulding
AAAAAAA 3 – AAAAAAA 36,287 3.6% North Cobb McEachern North Paulding Hillgrove
AAAAAAA 3 – AAAAAAA 33,425 3.3% North Cobb North Paulding McEachern Hillgrove
AAAAAAA 3 – AAAAAAA 30,599 3.1% McEachern Hillgrove North Paulding North Cobb
AAAAAAA 4 – AAAAAAA 125,768 12.6% Roswell Lassiter Woodstock Cherokee
AAAAAAA 4 – AAAAAAA 81,575 8.2% Roswell Lassiter Cherokee Woodstock
AAAAAAA 4 – AAAAAAA 79,198 7.9% Roswell Lassiter Cherokee Etowah
AAAAAAA 4 – AAAAAAA 74,952 7.5% Roswell Lassiter Cherokee Walton
AAAAAAA 4 – AAAAAAA 71,909 7.2% Roswell Lassiter Walton Cherokee
AAAAAAA 4 – AAAAAAA 69,834 7.0% Roswell Lassiter Woodstock Walton
AAAAAAA 4 – AAAAAAA 43,537 4.4% Roswell Cherokee Lassiter Woodstock
AAAAAAA 4 – AAAAAAA 37,027 3.7% Roswell Cherokee Lassiter Etowah
AAAAAAA 4 – AAAAAAA 31,803 3.2% Roswell Lassiter Walton Woodstock
AAAAAAA 4 – AAAAAAA 31,451 3.1% Roswell Lassiter Etowah Woodstock
AAAAAAA 5 – AAAAAAA 70,324 7.0% West Forsyth Lambert South Forsyth Milton
AAAAAAA 5 – AAAAAAA 50,796 5.1% West Forsyth Lambert South Forsyth North Forsyth
AAAAAAA 5 – AAAAAAA 49,179 4.9% West Forsyth South Forsyth Lambert North Forsyth
AAAAAAA 5 – AAAAAAA 45,810 4.6% South Forsyth West Forsyth Lambert Milton
AAAAAAA 5 – AAAAAAA 45,127 4.5% South Forsyth West Forsyth Lambert North Forsyth
AAAAAAA 5 – AAAAAAA 40,412 4.0% West Forsyth South Forsyth Lambert Milton
AAAAAAA 5 – AAAAAAA 40,306 4.0% West Forsyth South Forsyth Milton Lambert
AAAAAAA 6 – AAAAAAA 312,644 31.3% Mill Creek North Gwinnett Mountain View Peachtree Ridge
AAAAAAA 6 – AAAAAAA 253,084 25.3% Mill Creek North Gwinnett Peachtree Ridge Mountain View
AAAAAAA 6 – AAAAAAA 131,625 13.2% Mill Creek Peachtree Ridge North Gwinnett Mountain View
AAAAAAA 6 – AAAAAAA 110,564 11.1% Mill Creek Mountain View North Gwinnett Peachtree Ridge
AAAAAAA 6 – AAAAAAA 55,096 5.5% Mill Creek North Gwinnett Mountain View Collins Hill
AAAAAAA 6 – AAAAAAA 31,873 3.2% Mill Creek North Gwinnett Peachtree Ridge Collins Hill
AAAAAAA 7 – AAAAAAA 492,045 49.2% Norcross Parkview Brookwood Central Gwinnett
AAAAAAA 7 – AAAAAAA 274,539 27.5% Norcross Brookwood Parkview Central Gwinnett
AAAAAAA 7 – AAAAAAA 72,203 7.2% Norcross Parkview Central Gwinnett Brookwood
AAAAAAA 7 – AAAAAAA 53,595 5.4% Brookwood Norcross Parkview Central Gwinnett
AAAAAAA 7 – AAAAAAA 38,491 3.8% Norcross Brookwood Central Gwinnett Parkview
AAAAAAA 8 – AAAAAAA 308,177 30.8% Grayson Archer Newton South Gwinnett
AAAAAAA 8 – AAAAAAA 119,046 11.9% Grayson Newton Archer South Gwinnett
AAAAAAA 8 – AAAAAAA 92,923 9.3% Grayson South Gwinnett Newton Archer
AAAAAAA 8 – AAAAAAA 74,580 7.5% Grayson Archer Newton Shiloh
AAAAAAA 8 – AAAAAAA 68,825 6.9% Archer Grayson Newton South Gwinnett
AAAAAAA 8 – AAAAAAA 57,116 5.7% Grayson Archer South Gwinnett Newton
AAAAAAA 8 – AAAAAAA 46,749 4.7% Grayson Newton South Gwinnett Archer
AAAAAA 1 – AAAAAA 83,078 8.3% Valdosta Northside (Warner Robins) Lee County Houston County
AAAAAA 1 – AAAAAA 59,730 6.0% Northside (Warner Robins) Valdosta Lee County Houston County
AAAAAA 1 – AAAAAA 57,632 5.8% Valdosta Lee County Northside (Warner Robins) Houston County
AAAAAA 1 – AAAAAA 49,205 4.9% Valdosta Northside (Warner Robins) Lee County Coffee
AAAAAA 1 – AAAAAA 46,097 4.6% Northside (Warner Robins) Lee County Valdosta Houston County
AAAAAA 1 – AAAAAA 42,943 4.3% Valdosta Northside (Warner Robins) Houston County Lee County
AAAAAA 1 – AAAAAA 41,650 4.2% Valdosta Lee County Northside (Warner Robins) Coffee
AAAAAA 1 – AAAAAA 40,640 4.1% Northside (Warner Robins) Valdosta Lee County Coffee
AAAAAA 1 – AAAAAA 37,681 3.8% Lee County Valdosta Northside (Warner Robins) Houston County
AAAAAA 1 – AAAAAA 31,578 3.2% Northside (Warner Robins) Lee County Valdosta Coffee
AAAAAA 2 – AAAAAA 170,794 17.1% Glynn Academy Effingham County Brunswick Richmond Hill
AAAAAA 2 – AAAAAA 140,095 14.0% Glynn Academy Brunswick Effingham County Richmond Hill
AAAAAA 2 – AAAAAA 103,154 10.3% Glynn Academy Richmond Hill Effingham County Brunswick
AAAAAA 2 – AAAAAA 94,459 9.4% Glynn Academy Richmond Hill Brunswick Effingham County
AAAAAA 2 – AAAAAA 87,387 8.7% Glynn Academy Effingham County Richmond Hill Brunswick
AAAAAA 2 – AAAAAA 61,096 6.1% Glynn Academy Brunswick Richmond Hill Effingham County
AAAAAA 2 – AAAAAA 34,533 3.5% Effingham County Glynn Academy Brunswick Richmond Hill
AAAAAA 2 – AAAAAA 30,189 3.0% Brunswick Glynn Academy Effingham County Richmond Hill
AAAAAA 3 – AAAAAA 65,336 6.5% Heritage (Conyers) Evans Grovetown Lakeside (Evans)
AAAAAA 3 – AAAAAA 55,347 5.5% Evans Heritage (Conyers) Grovetown Lakeside (Evans)
AAAAAA 3 – AAAAAA 48,726 4.9% Heritage (Conyers) Evans Grovetown Greenbrier
AAAAAA 3 – AAAAAA 46,461 4.6% Heritage (Conyers) Evans Greenbrier Grovetown
AAAAAA 3 – AAAAAA 46,008 4.6% Heritage (Conyers) Evans Grovetown Alcovy
AAAAAA 3 – AAAAAA 42,354 4.2% Evans Heritage (Conyers) Grovetown Greenbrier
AAAAAA 3 – AAAAAA 41,270 4.1% Heritage (Conyers) Evans Lakeside (Evans) Grovetown
AAAAAA 3 – AAAAAA 39,724 4.0% Evans Heritage (Conyers) Grovetown Alcovy
AAAAAA 3 – AAAAAA 38,367 3.8% Evans Heritage (Conyers) Greenbrier Grovetown
AAAAAA 3 – AAAAAA 34,155 3.4% Evans Heritage (Conyers) Lakeside (Evans) Grovetown
AAAAAA 4 – AAAAAA 392,461 39.2% Tucker Lovejoy Stephenson Drew
AAAAAA 4 – AAAAAA 198,358 19.8% Tucker Lovejoy Drew Stephenson
AAAAAA 4 – AAAAAA 193,451 19.3% Tucker Lovejoy Stephenson Mundy’s Mill
AAAAAA 4 – AAAAAA 39,659 4.0% Lovejoy Tucker Stephenson Drew
AAAAAA 5 – AAAAAA 262,208 26.2% Mays Hughes Alexander Northgate
AAAAAA 5 – AAAAAA 204,843 20.5% Mays Alexander Hughes Northgate
AAAAAA 5 – AAAAAA 83,279 8.3% Mays Alexander Northgate Hughes
AAAAAA 5 – AAAAAA 59,622 6.0% Alexander Mays Hughes Northgate
AAAAAA 5 – AAAAAA 55,862 5.6% Alexander Mays Northgate Hughes
AAAAAA 5 – AAAAAA 33,958 3.4% Hughes Alexander Mays Northgate
AAAAAA 6 – AAAAAA 151,496 15.1% Harrison Dalton Allatoona Sequoyah
AAAAAA 6 – AAAAAA 101,626 10.2% Harrison Allatoona Dalton Sequoyah
AAAAAA 6 – AAAAAA 88,913 8.9% Dalton Harrison Allatoona Sequoyah
AAAAAA 6 – AAAAAA 61,134 6.1% Harrison Dalton Allatoona Sprayberry
AAAAAA 6 – AAAAAA 56,930 5.7% Harrison Dalton Sequoyah Allatoona
AAAAAA 6 – AAAAAA 43,951 4.4% Harrison Allatoona Dalton Sprayberry
AAAAAA 6 – AAAAAA 39,297 3.9% Harrison Dalton Allatoona Creekview
AAAAAA 6 – AAAAAA 34,654 3.5% Dalton Harrison Allatoona Sprayberry
AAAAAA 6 – AAAAAA 30,486 3.0% Harrison Dalton Sprayberry Allatoona
AAAAAA 7 – AAAAAA 229,599 23.0% Johns Creek Centennial Alpharetta Cambridge
AAAAAA 7 – AAAAAA 147,072 14.7% Centennial Alpharetta Cambridge Johns Creek
AAAAAA 7 – AAAAAA 129,949 13.0% Johns Creek Centennial Cambridge Alpharetta
AAAAAA 7 – AAAAAA 82,902 8.3% Centennial Cambridge Alpharetta Johns Creek
AAAAAA 7 – AAAAAA 65,190 6.5% Centennial Alpharetta Johns Creek Cambridge
AAAAAA 7 – AAAAAA 51,008 5.1% Centennial Cambridge Johns Creek Alpharetta
AAAAAA 7 – AAAAAA 44,402 4.4% Centennial Johns Creek Cambridge Alpharetta
AAAAAA 7 – AAAAAA 35,718 3.6% Cambridge Johns Creek Centennial Alpharetta
AAAAAA 8 – AAAAAA 94,954 9.5% Lanier Dacula Gainesville Winder-Barrow
AAAAAA 8 – AAAAAA 89,690 9.0% Dacula Lanier Gainesville Winder-Barrow
AAAAAA 8 – AAAAAA 82,424 8.2% Lanier Gainesville Dacula Winder-Barrow
AAAAAA 8 – AAAAAA 49,405 4.9% Lanier Dacula Gainesville Habersham Central
AAAAAA 8 – AAAAAA 47,003 4.7% Lanier Winder-Barrow Dacula Gainesville
AAAAAA 8 – AAAAAA 46,707 4.7% Dacula Lanier Gainesville Habersham Central
AAAAAA 8 – AAAAAA 43,703 4.4% Lanier Gainesville Dacula Habersham Central
AAAAAA 8 – AAAAAA 37,350 3.7% Lanier Dacula Winder-Barrow Habersham Central
AAAAAA 8 – AAAAAA 34,052 3.4% Lanier Dacula Winder-Barrow Gainesville
AAAAAA 8 – AAAAAA 33,967 3.4% Lanier Gainesville Winder-Barrow Dacula
AAAAAA 8 – AAAAAA 30,621 3.1% Gainesville Lanier Dacula Winder-Barrow
AAAAA 1 – AAAAA 90,478 9.0% Thomas County Central Bainbridge Warner Robins Veterans
AAAAA 1 – AAAAA 66,408 6.6% Thomas County Central Bainbridge Veterans Warner Robins
AAAAA 1 – AAAAA 65,120 6.5% Thomas County Central Bainbridge Warner Robins Harris County
AAAAA 1 – AAAAA 53,822 5.4% Thomas County Central Bainbridge Veterans Harris County
AAAAA 1 – AAAAA 47,109 4.7% Thomas County Central Bainbridge Harris County Warner Robins
AAAAA 1 – AAAAA 45,922 4.6% Bainbridge Thomas County Central Warner Robins Veterans
AAAAA 1 – AAAAA 45,219 4.5% Thomas County Central Warner Robins Bainbridge Veterans
AAAAA 1 – AAAAA 44,786 4.5% Thomas County Central Bainbridge Harris County Veterans
AAAAA 1 – AAAAA 36,643 3.7% Thomas County Central Veterans Bainbridge Warner Robins
AAAAA 1 – AAAAA 33,286 3.3% Bainbridge Thomas County Central Warner Robins Harris County
AAAAA 1 – AAAAA 32,491 3.2% Thomas County Central Warner Robins Bainbridge Harris County
AAAAA 2 – AAAAA 184,190 18.4% Ware County Wayne County South Effingham Statesboro
AAAAA 2 – AAAAA 178,251 17.8% Ware County Wayne County Statesboro South Effingham
AAAAA 2 – AAAAA 101,296 10.1% Ware County Statesboro Wayne County South Effingham
AAAAA 2 – AAAAA 90,844 9.1% Ware County South Effingham Wayne County Statesboro
AAAAA 2 – AAAAA 64,059 6.4% Ware County Wayne County Statesboro New Hampstead
AAAAA 2 – AAAAA 57,787 5.8% Ware County Wayne County South Effingham New Hampstead
AAAAA 2 – AAAAA 54,924 5.5% Ware County South Effingham Statesboro Wayne County
AAAAA 2 – AAAAA 52,358 5.2% Ware County Statesboro South Effingham Wayne County
AAAAA 2 – AAAAA 39,907 4.0% Ware County Statesboro Wayne County New Hampstead
AAAAA 3 – AAAAA 126,993 12.7% Starr’s Mill Griffin Riverdale Whitewater
AAAAA 3 – AAAAA 70,766 7.1% Starr’s Mill Griffin Whitewater Riverdale
AAAAA 3 – AAAAA 62,368 6.2% Riverdale Starr’s Mill Griffin Whitewater
AAAAA 3 – AAAAA 59,651 6.0% Starr’s Mill Griffin Riverdale Fayette County
AAAAA 3 – AAAAA 38,961 3.9% Starr’s Mill Riverdale Griffin Whitewater
AAAAA 3 – AAAAA 35,583 3.6% Griffin Whitewater Starr’s Mill Riverdale
AAAAA 3 – AAAAA 32,422 3.2% Griffin Riverdale Starr’s Mill Whitewater
AAAAA 4 – AAAAA 253,413 25.3% Stockbridge Woodland (Stockbridge) Jones County Locust Grove
AAAAA 4 – AAAAA 119,208 11.9% Stockbridge Woodland (Stockbridge) Jones County Ola
AAAAA 4 – AAAAA 93,495 9.3% Woodland (Stockbridge) Stockbridge Jones County Locust Grove
AAAAA 4 – AAAAA 80,452 8.0% Stockbridge Woodland (Stockbridge) Jones County Dutchtown
AAAAA 4 – AAAAA 42,561 4.3% Stockbridge Woodland (Stockbridge) Dutchtown Jones County
AAAAA 4 – AAAAA 39,985 4.0% Woodland (Stockbridge) Stockbridge Jones County Ola
AAAAA 4 – AAAAA 32,564 3.3% Stockbridge Woodland (Stockbridge) Ola Jones County
AAAAA 5 – AAAAA 102,721 10.3% Arabia Mountain Southwest DeKalb Lithonia Miller Grove
AAAAA 5 – AAAAA 101,042 10.1% Arabia Mountain Southwest DeKalb Lithonia Columbia
AAAAA 5 – AAAAA 87,007 8.7% Arabia Mountain Southwest DeKalb Miller Grove Lithonia
AAAAA 5 – AAAAA 61,756 6.2% Arabia Mountain Southwest DeKalb Columbia Lithonia
AAAAA 5 – AAAAA 51,468 5.1% Arabia Mountain Southwest DeKalb Miller Grove Columbia
AAAAA 5 – AAAAA 44,181 4.4% Arabia Mountain Lithonia Southwest DeKalb Miller Grove
AAAAA 5 – AAAAA 37,462 3.7% Arabia Mountain Lithonia Southwest DeKalb Columbia
AAAAA 5 – AAAAA 35,701 3.6% Arabia Mountain Southwest DeKalb Columbia Miller Grove
AAAAA 5 – AAAAA 34,693 3.5% Southwest DeKalb Arabia Mountain Lithonia Miller Grove
AAAAA 5 – AAAAA 32,700 3.3% Southwest DeKalb Arabia Mountain Lithonia Columbia
AAAAA 6 – AAAAA 353,030 35.3% Grady Carver (Atlanta) Banneker Riverwood
AAAAA 6 – AAAAA 131,482 13.1% Grady Carver (Atlanta) Banneker North Springs
AAAAA 6 – AAAAA 100,881 10.1% Grady Banneker Carver (Atlanta) Riverwood
AAAAA 6 – AAAAA 80,386 8.0% Grady Carver (Atlanta) North Springs Banneker
AAAAA 6 – AAAAA 67,017 6.7% Grady Carver (Atlanta) Riverwood North Springs
AAAAA 6 – AAAAA 52,545 5.3% Grady Carver (Atlanta) Riverwood Banneker
AAAAA 6 – AAAAA 46,574 4.7% Grady Carver (Atlanta) North Springs Riverwood
AAAAA 6 – AAAAA 34,190 3.4% Grady Banneker Carver (Atlanta) North Springs
AAAAA 7 – AAAAA 333,957 33.4% Kell Rome Carrollton Villa Rica
AAAAA 7 – AAAAA 178,566 17.9% Kell Rome Carrollton Cass
AAAAA 7 – AAAAA 85,856 8.6% Kell Rome Carrollton East Paulding
AAAAA 7 – AAAAA 56,902 5.7% Kell Rome Carrollton Paulding County
AAAAA 7 – AAAAA 47,067 4.7% Carrollton Kell Rome Villa Rica
AAAAA 7 – AAAAA 42,211 4.2% Kell Rome Villa Rica Carrollton
AAAAA 7 – AAAAA 30,077 3.0% Carrollton Rome Kell Villa Rica
AAAAA 8 – AAAAA 295,997 29.6% Buford Loganville Clarke Central Flowery Branch
AAAAA 8 – AAAAA 112,060 11.2% Buford Loganville Clarke Central Walnut Grove
AAAAA 8 – AAAAA 111,342 11.1% Buford Clarke Central Loganville Flowery Branch
AAAAA 8 – AAAAA 102,426 10.2% Buford Loganville Flowery Branch Clarke Central
AAAAA 8 – AAAAA 93,380 9.3% Buford Loganville Clarke Central Cedar Shoals
AAAAA 8 – AAAAA 46,410 4.6% Buford Clarke Central Loganville Walnut Grove
AAAAA 8 – AAAAA 44,095 4.4% Buford Loganville Walnut Grove Clarke Central
AAAA 1 – AAAA 93,754 9.4% Cairo Westover Carver (Columbus) Northside (Columbus)
AAAA 1 – AAAA 72,610 7.3% Cairo Westover Carver (Columbus) Hardaway
AAAA 1 – AAAA 60,069 6.0% Cairo Westover Hardaway Carver (Columbus)
AAAA 1 – AAAA 51,767 5.2% Cairo Americus-Sumter Westover Carver (Columbus)
AAAA 1 – AAAA 45,782 4.6% Cairo Carver (Columbus) Northside (Columbus) Americus-Sumter
AAAA 1 – AAAA 42,087 4.2% Cairo Westover Carver (Columbus) Americus-Sumter
AAAA 1 – AAAA 32,767 3.3% Cairo Carver (Columbus) Northside (Columbus) Westover
AAAA 1 – AAAA 31,088 3.1% Cairo Northside (Columbus) Americus-Sumter Westover
AAAA 2 – AAAA 96,305 9.6% Mary Persons West Laurens Spalding Upson-Lee
AAAA 2 – AAAA 95,666 9.6% Mary Persons Spalding West Laurens Upson-Lee
AAAA 2 – AAAA 65,850 6.6% West Laurens Mary Persons Spalding Upson-Lee
AAAA 2 – AAAA 59,719 6.0% Mary Persons Spalding West Laurens Perry
AAAA 2 – AAAA 57,796 5.8% Mary Persons West Laurens Spalding Perry
AAAA 2 – AAAA 52,785 5.3% Mary Persons Spalding Upson-Lee West Laurens
AAAA 2 – AAAA 44,928 4.5% Mary Persons West Laurens Upson-Lee Spalding
AAAA 2 – AAAA 44,841 4.5% Mary Persons Upson-Lee Spalding West Laurens
AAAA 2 – AAAA 41,734 4.2% Mary Persons Upson-Lee West Laurens Spalding
AAAA 2 – AAAA 40,086 4.0% West Laurens Mary Persons Spalding Perry
AAAA 2 – AAAA 35,202 3.5% West Laurens Mary Persons Upson-Lee Spalding
AAAA 3 – AAAA 279,272 27.9% Thomson Burke County Baldwin Richmond Academy
AAAA 3 – AAAA 229,717 23.0% Thomson Burke County Baldwin Cross Creek
AAAA 3 – AAAA 118,334 11.8% Thomson Burke County Richmond Academy Baldwin
AAAA 3 – AAAA 79,506 8.0% Thomson Burke County Cross Creek Baldwin
AAAA 3 – AAAA 50,570 5.1% Thomson Burke County Richmond Academy Cross Creek
AAAA 3 – AAAA 43,228 4.3% Thomson Burke County Cross Creek Richmond Academy
AAAA 3 – AAAA 37,420 3.7% Thomson Baldwin Burke County Richmond Academy
AAAA 3 – AAAA 32,589 3.3% Burke County Thomson Baldwin Richmond Academy
AAAA 3 – AAAA 31,065 3.1% Thomson Baldwin Burke County Cross Creek
AAAA 4 – AAAA 378,962 37.9% Woodward Academy Eastside Salem Luella
AAAA 4 – AAAA 162,783 16.3% Woodward Academy Eastside Salem North Clayton
AAAA 4 – AAAA 88,967 8.9% Woodward Academy Salem Eastside Luella
AAAA 4 – AAAA 78,156 7.8% Woodward Academy Eastside North Clayton Salem
AAAA 4 – AAAA 71,254 7.1% Eastside Woodward Academy Salem Luella
AAAA 4 – AAAA 40,169 4.0% Woodward Academy Salem Eastside North Clayton
AAAA 4 – AAAA 31,870 3.2% Eastside Woodward Academy Salem North Clayton
AAAA 5 – AAAA 255,411 25.5% Cartersville Troup Sandy Creek Cedartown
AAAA 5 – AAAA 125,453 12.5% Cartersville Troup Cedartown Sandy Creek
AAAA 5 – AAAA 122,141 12.2% Cartersville Cedartown Sandy Creek Troup
AAAA 5 – AAAA 121,200 12.1% Cartersville Cedartown Troup Sandy Creek
AAAA 5 – AAAA 42,944 4.3% Cartersville Troup Sandy Creek Chapel Hill
AAAA 5 – AAAA 35,194 3.5% Cartersville Sandy Creek Cedartown LaGrange
AAAA 6 – AAAA 276,907 27.7% Ridgeland Northwest Whitfield Pickens Heritage (Ringgold)
AAAA 6 – AAAA 174,101 17.4% Ridgeland Pickens Northwest Whitfield Heritage (Ringgold)
AAAA 6 – AAAA 132,967 13.3% Ridgeland Northwest Whitfield Heritage (Ringgold) Pickens
AAAA 6 – AAAA 66,082 6.6% Ridgeland Pickens Heritage (Ringgold) Northwest Whitfield
AAAA 6 – AAAA 66,050 6.6% Pickens Ridgeland Northwest Whitfield Heritage (Ringgold)
AAAA 6 – AAAA 56,195 5.6% Ridgeland Heritage (Ringgold) Northwest Whitfield Pickens
AAAA 6 – AAAA 37,983 3.8% Ridgeland Heritage (Ringgold) Pickens Northwest Whitfield
AAAA 6 – AAAA 31,767 3.2% Pickens Ridgeland Heritage (Ringgold) Northwest Whitfield
AAAA 7 – AAAA 145,124 14.5% Blessed Trinity Marist West Hall Chestatee
AAAA 7 – AAAA 143,818 14.4% Marist Blessed Trinity West Hall Chestatee
AAAA 7 – AAAA 129,913 13.0% Blessed Trinity Marist West Hall White County
AAAA 7 – AAAA 127,020 12.7% Marist Blessed Trinity West Hall White County
AAAA 7 – AAAA 83,126 8.3% Blessed Trinity West Hall Marist Chestatee
AAAA 7 – AAAA 74,316 7.4% Blessed Trinity West Hall Marist White County
AAAA 7 – AAAA 41,190 4.1% Marist Blessed Trinity Chestatee West Hall
AAAA 7 – AAAA 39,100 3.9% Blessed Trinity Marist Chestatee West Hall
AAAA 8 – AAAA 101,639 10.2% Jefferson Stephens County Oconee County St. Pius X
AAAA 8 – AAAA 56,526 5.7% Jefferson Stephens County Madison County Oconee County
AAAA 8 – AAAA 55,352 5.5% Stephens County Jefferson Oconee County St. Pius X
AAAA 8 – AAAA 45,596 4.6% Jefferson Stephens County Oconee County Madison County
AAAA 8 – AAAA 44,968 4.5% Jefferson Oconee County Stephens County St. Pius X
AAAA 8 – AAAA 37,539 3.8% Stephens County Oconee County Jefferson St. Pius X
AAAA 8 – AAAA 37,241 3.7% Jefferson Stephens County St. Pius X Oconee County
AAAA 8 – AAAA 36,701 3.7% Jefferson Oconee County Stephens County Madison County
AAAA 8 – AAAA 35,310 3.5% Stephens County Jefferson Oconee County Madison County
AAA 1 – AAA 119,422 11.9% Crisp County Worth County Cook Monroe
AAA 1 – AAA 108,280 10.8% Crisp County Cook Worth County Monroe
AAA 1 – AAA 83,122 8.3% Crisp County Worth County Monroe Cook
AAA 1 – AAA 66,307 6.6% Crisp County Cook Monroe Worth County
AAA 1 – AAA 55,940 5.6% Crisp County Monroe Worth County Cook
AAA 1 – AAA 50,704 5.1% Crisp County Monroe Cook Worth County
AAA 1 – AAA 48,705 4.9% Crisp County Worth County Cook Dougherty
AAA 1 – AAA 45,693 4.6% Worth County Crisp County Cook Monroe
AAA 1 – AAA 44,729 4.5% Crisp County Cook Worth County Dougherty
AAA 1 – AAA 36,498 3.6% Worth County Crisp County Monroe Cook
AAA 2 – AAA 90,583 9.1% Liberty County Pierce County Appling County Tattnall County
AAA 2 – AAA 83,139 8.3% Liberty County Pierce County Appling County Brantley County
AAA 2 – AAA 71,523 7.2% Pierce County Liberty County Appling County Tattnall County
AAA 2 – AAA 64,437 6.4% Pierce County Liberty County Appling County Brantley County
AAA 2 – AAA 63,171 6.3% Liberty County Appling County Pierce County Tattnall County
AAA 2 – AAA 49,373 4.9% Liberty County Appling County Pierce County Brantley County
AAA 2 – AAA 37,768 3.8% Appling County Liberty County Pierce County Tattnall County
AAA 2 – AAA 35,338 3.5% Liberty County Pierce County Tattnall County Appling County
AAA 2 – AAA 33,195 3.3% Appling County Liberty County Pierce County Brantley County
AAA 2 – AAA 30,636 3.1% Liberty County Pierce County Brantley County Appling County
AAA 3 – AAA 426,539 42.7% Jenkins Southeast Bulloch Savannah Windsor Forest
AAA 3 – AAA 205,276 20.5% Jenkins Southeast Bulloch Windsor Forest Savannah
AAA 3 – AAA 101,598 10.2% Jenkins Savannah Southeast Bulloch Windsor Forest
AAA 3 – AAA 63,535 6.4% Jenkins Southeast Bulloch Savannah Islands
AAA 4 – AAA 169,798 17.0% Peach County Jackson Westside (Macon) Pike County
AAA 4 – AAA 143,950 14.4% Peach County Jackson Pike County Westside (Macon)
AAA 4 – AAA 110,830 11.1% Peach County Jackson Pike County Central (Macon)
AAA 4 – AAA 58,873 5.9% Peach County Pike County Jackson Westside (Macon)
AAA 4 – AAA 54,809 5.5% Jackson Peach County Westside (Macon) Pike County
AAA 4 – AAA 53,093 5.3% Peach County Pike County Jackson Central (Macon)
AAA 4 – AAA 47,510 4.8% Jackson Peach County Pike County Westside (Macon)
AAA 4 – AAA 41,657 4.2% Jackson Peach County Pike County Central (Macon)
AAA 5 – AAA 245,944 24.6% Westminster (Atlanta) Pace Academy Cedar Grove Lovett
AAA 5 – AAA 212,584 21.3% Westminster (Atlanta) Cedar Grove Pace Academy Lovett
AAA 5 – AAA 129,995 13.0% Westminster (Atlanta) Cedar Grove Lovett Pace Academy
AAA 5 – AAA 119,034 11.9% Pace Academy Westminster (Atlanta) Cedar Grove Lovett
AAA 5 – AAA 36,015 3.6% Pace Academy Cedar Grove Westminster (Atlanta) Lovett
AAA 5 – AAA 30,763 3.1% Westminster (Atlanta) Pace Academy Cedar Grove Redan
AAA 6 – AAA 117,984 11.8% Calhoun Sonoraville Bremen Adairsville
AAA 6 – AAA 110,020 11.0% Calhoun Sonoraville Adairsville Bremen
AAA 6 – AAA 62,906 6.3% Calhoun Adairsville Sonoraville Bremen
AAA 6 – AAA 51,315 5.1% Calhoun North Murray Sonoraville Bremen
AAA 6 – AAA 48,004 4.8% Calhoun North Murray Sonoraville Adairsville
AAA 6 – AAA 39,888 4.0% Sonoraville Calhoun Bremen Adairsville
AAA 7 – AAA 214,195 21.4% Greater Atlanta Christian Dawson County North Hall Union County
AAA 7 – AAA 150,200 15.0% Greater Atlanta Christian Dawson County North Hall Lumpkin County
AAA 7 – AAA 119,031 11.9% Greater Atlanta Christian Dawson County Union County North Hall
AAA 7 – AAA 97,134 9.7% Greater Atlanta Christian Dawson County Lumpkin County North Hall
AAA 7 – AAA 75,161 7.5% Greater Atlanta Christian Dawson County Lumpkin County Union County
AAA 7 – AAA 61,127 6.1% Greater Atlanta Christian Dawson County Union County Lumpkin County
AAA 7 – AAA 46,271 4.6% Greater Atlanta Christian Union County Dawson County North Hall
AAA 8 – AAA 197,787 19.8% Hart County Morgan County Franklin County Jackson County
AAA 8 – AAA 137,287 13.7% Morgan County Hart County Franklin County Jackson County
AAA 8 – AAA 131,994 13.2% Hart County Franklin County Morgan County Jackson County
AAA 8 – AAA 68,162 6.8% Hart County Morgan County Jackson County Franklin County
AAA 8 – AAA 59,716 6.0% Morgan County Hart County Jackson County Franklin County
AAA 8 – AAA 38,056 3.8% Hart County Morgan County Franklin County East Jackson
AA 1 – AA 373,956 37.4% Fitzgerald Brooks County Thomasville Berrien
AA 1 – AA 143,113 14.3% Brooks County Fitzgerald Thomasville Berrien
AA 1 – AA 111,305 11.1% Fitzgerald Thomasville Brooks County Berrien
AA 1 – AA 100,998 10.1% Fitzgerald Brooks County Berrien Thomasville
AA 1 – AA 38,958 3.9% Brooks County Fitzgerald Berrien Thomasville
AA 1 – AA 37,221 3.7% Fitzgerald Brooks County Berrien Early County
AA 2 – AA 385,921 38.6% Benedictine Vidalia Toombs County Bryan County
AA 2 – AA 183,147 18.3% Benedictine Toombs County Vidalia Bryan County
AA 2 – AA 110,437 11.0% Benedictine Vidalia Toombs County Bacon County
AA 2 – AA 52,646 5.3% Benedictine Toombs County Vidalia Bacon County
AA 2 – AA 52,612 5.3% Benedictine Vidalia Toombs County Swainsboro
AA 2 – AA 40,822 4.1% Benedictine Vidalia Swainsboro Toombs County
AA 2 – AA 35,497 3.5% Benedictine Toombs County Bryan County Vidalia
AA 2 – AA 35,192 3.5% Benedictine Toombs County Vidalia Swainsboro
AA 3 – AA 171,817 17.2% Washington County Dublin Southwest Dodge County
AA 3 – AA 125,671 12.6% Washington County Southwest Dodge County Dublin
AA 3 – AA 112,216 11.2% Washington County Southwest Dublin Dodge County
AA 3 – AA 84,191 8.4% Dublin Washington County Southwest Dodge County
AA 3 – AA 64,745 6.5% Southwest Washington County Dodge County Dublin
AA 3 – AA 50,501 5.1% Dublin Southwest Washington County Dodge County
AA 3 – AA 43,244 4.3% Southwest Dublin Washington County Dodge County
AA 3 – AA 33,951 3.4% Dodge County Washington County Dublin Southwest
AA 3 – AA 32,852 3.3% Southwest Washington County Dublin Dodge County
AA 3 – AA 30,846 3.1% Southwest Dodge County Washington County Dublin
AA 4 – AA 274,482 27.4% Jefferson County Screven County Laney Josey
AA 4 – AA 156,510 15.7% Jefferson County Screven County Laney Glenn Hills
AA 4 – AA 131,185 13.1% Jefferson County Screven County Laney Harlem
AA 4 – AA 109,805 11.0% Jefferson County Screven County Laney Butler
AA 4 – AA 67,536 6.8% Screven County Jefferson County Laney Josey
AA 4 – AA 41,471 4.1% Jefferson County Screven County Josey Laney
AA 4 – AA 38,562 3.9% Screven County Jefferson County Laney Glenn Hills
AA 4 – AA 32,126 3.2% Screven County Jefferson County Laney Harlem
AA 5 – AA 177,495 17.7% Callaway Lamar County Heard County Spencer
AA 5 – AA 176,703 17.7% Callaway Heard County Lamar County Spencer
AA 5 – AA 106,238 10.6% Callaway Lamar County Spencer Heard County
AA 5 – AA 89,660 9.0% Callaway Spencer Heard County Lamar County
AA 5 – AA 85,424 8.5% Callaway Spencer Lamar County Heard County
AA 5 – AA 80,365 8.0% Callaway Heard County Spencer Lamar County
AA 6 – AA 79,483 7.9% Hapeville Charter B.E.S.T. Academy Douglass K.I.P.P. Atlanta Collegiate
AA 6 – AA 57,815 5.8% Hapeville Charter B.E.S.T. Academy K.I.P.P. Atlanta Collegiate Douglass
AA 6 – AA 53,536 5.4% Hapeville Charter K.I.P.P. Atlanta Collegiate B.E.S.T. Academy Douglass
AA 6 – AA 43,081 4.3% Hapeville Charter Douglass K.I.P.P. Atlanta Collegiate B.E.S.T. Academy
AA 6 – AA 30,105 3.0% Hapeville Charter Douglass Washington K.I.P.P. Atlanta Collegiate
AA 7 – AA 480,901 48.1% Pepperell Model Rockmart Chattooga
AA 7 – AA 133,532 13.4% Pepperell Rockmart Model Chattooga
AA 7 – AA 108,024 10.8% Pepperell Model Rockmart Dade County
AA 7 – AA 39,411 3.9% Rockmart Pepperell Model Chattooga
AA 8 – AA 225,451 22.5% Rabun County Elbert County Putnam County Banks County
AA 8 – AA 199,918 20.0% Rabun County Elbert County Banks County Putnam County
AA 8 – AA 188,429 18.8% Rabun County Elbert County Banks County Monticello
AA 8 – AA 43,583 4.4% Rabun County Elbert County Banks County Social Circle
AA 8 – AA 41,519 4.2% Elbert County Rabun County Putnam County Banks County
AA 8 – AA 36,636 3.7% Elbert County Rabun County Banks County Putnam County
AA 8 – AA 36,121 3.6% Elbert County Rabun County Banks County Monticello
AA 8 – AA 35,667 3.6% Rabun County Elbert County Monticello Putnam County

Using the more detailed output such as shown above, it’s possible to consider some other measures of just how open some region races actually are.

The first measure could be to simply see how often the modal playoff seeding is realized in the simulation. For example, the modal playoff seeding for 7-AAAAAAA has a 49.2% chance of occurring. Another measure can be how many each of the possible permutations is eventually realized in the simulation. For example, Region 2-AA has 8 teams and so 1,680 permutations. Of those only 104 were realized during the 1,000,000 simulations. We might conclude the Region 2-AA race is fairly close with perhaps only a small handful of games remaining that will decide the playoff seeding. We can also see that Regions 1-AAA, 1-AAAAA, 1-AAAAAA, and 1-AAAAAAA all had 100% of their permutations realized in 1,000,000 simulations, so it appears those regions are still very much up for grabs.

But a final measure which I think nicely captures what we’re looking for is what I will refer to as a “Parity Index”, which shows the probability of the exact same playoff seeding being realized twice in a row in the simulations. Here we’ll see that Region 6-AA might be the one to get the popcorn out for:

Classification Region Teams Modal Pct Permutations Realized Parity Index Classification Region Teams Modal Pct Permutations Realized Parity Index
AAAAAAA 7 – AAAAAAA 7 49.2% 58 of 840 = 6.9% 0.328 AA 5 – AA 6 17.7% 211 of 360 = 58.6% 0.099
AA 7 – AA 8 48.1% 141 of 1680 = 8.4% 0.266 AAAA 7 – AAAA 5 14.5% 109 of 120 = 90.8% 0.094
AAA 3 – AAA 8 42.7% 200 of 1680 = 11.9% 0.241 AAA 8 – AAA 6 19.8% 251 of 360 = 69.7% 0.090
AAAAAA 4 – AAAAAA 8 39.2% 131 of 1680 = 7.8% 0.234 AAAAAA 2 – AAAAAA 5 17.1% 114 of 120 = 95.0% 0.086
AA 2 – AA 8 38.6% 104 of 1680 = 6.2% 0.205 AA 3 – AA 7 17.2% 247 of 840 = 29.4% 0.080
AAAAAAA 6 – AAAAAAA 7 31.3% 82 of 840 = 9.8% 0.197 AAA 4 – AAA 7 17.0% 290 of 840 = 34.5% 0.079
AAAA 4 – AAAA 7 37.9% 129 of 840 = 15.4% 0.194 AAAAAAA 2 – AAAAAAA 6 17.6% 233 of 360 = 64.7% 0.073
AA 1 – AA 6 37.4% 173 of 360 = 48.1% 0.188 AAAAAAA 3 – AAAAAAA 6 19.1% 256 of 360 = 71.1% 0.070
AAAAAAA 1 – AAAAAAA 4 32.9% 24 of 24 = 100.0% 0.186 AAAAAA 6 – AAAAAA 8 15.1% 314 of 1680 = 18.7% 0.061
AAAAA 6 – AAAAA 8 35.3% 149 of 1680 = 8.9% 0.171 AAA 1 – AAA 5 11.9% 120 of 120 = 100.0% 0.055
AAAAA 7 – AAAAA 9 33.4% 248 of 3024 = 8.2% 0.162 AAAAAAA 4 – AAAAAAA 6 12.6% 258 of 360 = 71.7% 0.054
AAAA 3 – AAAA 6 27.9% 96 of 360 = 26.7% 0.160 AAAAA 5 – AAAAA 6 10.3% 319 of 360 = 88.6% 0.047
AAA 5 – AAA 8 24.6% 148 of 1680 = 8.8% 0.142 AAAA 2 – AAAA 6 9.6% 286 of 360 = 79.4% 0.045
AAAA 6 – AAAA 7 27.7% 217 of 840 = 25.8% 0.140 AAA 6 – AAA 10 11.8% 724 of 1920 = 37.7% 0.043
AA 4 – AA 8 27.4% 132 of 1680 = 7.9% 0.140 AAAAAA 8 – AAAAAA 6 9.5% 265 of 360 = 73.6% 0.042
AAAAA 8 – AAAAA 7 29.6% 129 of 840 = 15.4% 0.139 AAA 2 – AAA 6 9.1% 311 of 360 = 86.4% 0.042
AAAAAAA 8 – AAAAAAA 6 30.8% 177 of 360 = 49.2% 0.137 AAAAA 3 – AAAAA 7 12.7% 331 of 840 = 39.4% 0.040
AA 8 – AA 7 22.5% 136 of 840 = 16.2% 0.136 AAAAA 1 – AAAAA 5 9.0% 120 of 120 = 100.0% 0.037
AAAAAA 5 – AAAAAA 9 26.2% 248 of 3024 = 8.2% 0.130 AAAA 8 – AAAA 6 10.2% 281 of 360 = 78.1% 0.034
AAAA 5 – AAAA 7 25.5% 224 of 840 = 26.7% 0.118 AAAAAA 1 – AAAAAA 5 8.3% 120 of 120 = 100.0% 0.033
AAAAAA 7 – AAAAAA 9 23.0% 337 of 3024 = 11.1% 0.110 AAAA 1 – AAAA 8 9.4% 590 of 1680 = 35.1% 0.032
AAA 7 – AAA 7 21.4% 189 of 840 = 22.5% 0.106 AAAAAA 3 – AAAAAA 6 6.5% 352 of 360 = 97.8% 0.026
AAAAA 4 – AAAAA 9 25.3% 234 of 3024 = 7.7% 0.103 AAAAAAA 5 – AAAAAAA 6 7.0% 351 of 360 = 97.5% 0.025
AAAAA 2 – AAAAA 5 18.4% 85 of 120 = 70.8% 0.101 AA 6 – AA 7 7.9% 410 of 840 = 48.8% 0.024

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