WOS87
01-06-2008, 01:35 PM
For those not interested in the workings of mathematical and statistical models, feel free to move on to the next thread. What I am putting forth here is just one of many ideas I have come up with and is derived using numbers alone. So please do not try to read any particular bias for or against any particular program(s) into this because there is none.
I have been forced to sit through several afternoons of mind-numbing academic seminars lately and it's become a habit of mine to work out various mathematical ideas in search of a better rating system (in place of just doodling randomly or trying to nap unnoticed). I came up with one that is very basic in how it works, yet resulted in a final ranking that actually looked fairly good.
My prior method of comparing performances between teams relied completely on margin of victory, and that is a major flaw, as there is not usually a linear correlation between increasing margins of victory and actual power of a team (due to most coaches working within the bounds of good sportsmanship and not running up scores or risking injuries to key players when they aren't needed).
As a way around this problem I concocted the following idea:
Instead of looking at actual margin of victory, look at relative performance compared to common opponents using ranking ordinals rather than points scored or allowed.
It's easier to explain by example than explanation. It works essentially like a preseason Coaches Poll for a district. Prior to each season beginning, each coach from each team in a district submits their votes on how they feel the teams in their district will rank that season. By combining the rankings submitted by all teams, you come up with a consensus poll.
I used the same idea, but instead of using the subjective opinions of individual people, I used the numbers that resulted from each game.
Going through the schedule of each 3A team, I assigned a ranking for Offense, Defense, and Overall Performance for each and every game played.
Using Celina as the example, and only counting games vs. 3A opponents to make the total number of calculations I was dealing with manageable:
Celina's 2007 Games vs. 3A Teams
Robinson scored 6 and allowed 19
Princeton 6 - 35
Frisco Wakeland 0-36
Pilot Point 6-56
Van Alstyne 0-62
Bonham 6-55
Prosper 14-62
Whitesboro 7-44
West 0-41
Emory Rains 6-48
Pittsburg 23-50
Glen Rose 21-70
Snyder 7-33
China Spring 14-21
Using only the above raw numbers the "votes" that Celina would turn in for their season would be as follows:
Offense:
1st - Pittsburg (23 pts scored)
2nd - Glen Rose (21 pts)
3rd - Prosper (14 pts)
3rd - China Spring (14 pts)
5th - Snyder (7 pts)
5th - Whitesboro (7 pts)
7th - Robinson (6 pts)
7th - Emory Rains (6 pts)
7th - Bonham (6 pts)
7th - Pilot Point (6 pts)
7th - Princeton (6 pts)
12th - Frisco Wakeland (0 pts)
12th - West (0 pts)
12th - Van Alstyne (0 pts)
You do the exact same thing for points allowed and for margins of victory.
Now the cool part. If you go through the above procedure for all 174 3A teams in the state and then sort through all of the ranks each team received from each of their opponents you would get the following (using Celina as the example).
How Celina's Opponents Would Rank Their Game with Celina compared to all other games played in 2007
(opponent - defense - offense - overall)
Robinson - 2nd - 6th - 4th
Translation: Celina held Robinson to the 2nd fewest pts of Robinson's season, Celina scored the 6th most points of any of Robinson's opponents and gave Robinson their 4th worst loss of the season.
Princeton - 5th - 5th - 3rd
Frisco Wakeland - 1st - 1st - 1st
Pilot Point - 3rd - 1st - 1st
Van Alstyne - 3rd - 1st - 1st
Bonham - 2nd - 1st - 1st
Prosper - 2nd - 1st - 1st
Whitesboro - 1st - 1st - 1st
West - 1st - 1st - 1st
Emory Rains - 1st - 3rd - 3rd
Pittsburg - 5th - 1st - 2nd
Glen Rose - 5th - 1st - 1st
Snyder - 1st - 4th - 1st
China Spring - 3rd - 5th - 2nd
So what the above translates to is (1) Celina scored the most points against 9 of the 14 3A opponents they played in 2007. (2) Celina held 5 of the 14 opponents to the fewest points scored in any game they played in 2007, (3) Celina gave 9 of their 14 opponents their worst loss of the season, looking at margin of victory.
If you average the rankings you get the following:
Celina's average offensive ranking = 2.29
Celina's average defensive ranking = 2.50
Celina's average overall ranking = 1.64
The Top 15 for Class 3A in each category:
Raw Offensive Rating
1. 1.62 - Liberty Hill
2. 2.00 - Dallas Roosvelt
3. 2.18 - Diboll
4. 2.21 - Cuero
5. 2.29 - Celina
6. 2.50 - Waco La Vega
7. 2.58 - Gilmer
8. 2.82 - Abilene Wylie
9. 2.91 - Royse City
10. 3.10 - West Orange-Stark
11. 3.18 - Snyder
12. 3.38 - Canyon
13. 3.56 - Jasper
14. 3.60 - Caldwell
15. 3.64 - Navasota
Raw Defensive Rating
1. 2.00 - West Orange-Stark
2. 2.50 - Celina
3. 2.85 - Liberty Hill
4. 3.09 - Graham
5. 3.13 - Rio Hondo
6. 3.22 - Giddings
7. 3.27 - Royse City
8. 3.33 - Waco La Vega
9. 3.36 - Abilene Wylie
10. 3.50 - Wills Point
11. 3.88 - China Spring
12t. 4.00 - Snyder
12t. 4.00 - Dallas Roosevelt
12t. 4.00 - Hidalgo
15. 4.11 - Port Isabel
Raw Overall Rating
1. 1.64 - Celina
2. 1.80 - West Orange-Stark
3. 1.85 - Liberty Hill
4. 1.88 - Dallas Roosevelt
5. 2.09 - Royse City
6. 2.17 - Waco La Vega
7. 2.18 - Abilene Wylie
8. 2.25 - Gilmer
9. 2.56 - Giddings
10. 2.57 - Cuero
11. 2.64 - Snyder
12. 3.22 - Carthage
13. 3.25 - Rio Hondo
14. 3.38 - Hidalgo
15. 3.44 - Argyle
Now before you start, I realize that that does not look quite right. Even I would not put WO-S over Liberty Hill if asked to do a similar ranking just from gut feeling.
There is a bias against teams who played more games in a season using the above method. (i.e. It's a lot tougher to get a 1st or 2nd place ranking against a team that has played 16 games compared to a team that only played 10 or less).
So what I did, is reverse the numbers, so that if you gave a team that played 16 games in the season their worst loss of the year, you would get 16 points rather than just 1. 1st place rankings, (instead of all just being averaged in as a 1.00, would vary in the amount of points they are worth, depending on how many games that opponent played.) This essentially builds a strength of schedule factor in to the system.
After making that change, you get the following results:
Adjusted Offensive Rating
1. 11.23 - Liberty Hill (in other words, on average, Liberty Hill's offensive output was better than 11 of each of their opponent's opponents.)
2. 10.86 - Cuero
3. 10.50 - Celina
4. 10.17 - Waco La Vega
5. 10.13 - Dallas Roosevelt
6. 9.91 - Abilene Wylie
7. 9.75 - Gilmer
8. 9.64 - Snyder
9. 9.64 - Diboll
10. 9.50 - Canyon
11. 9.18 - Royse City
12. 9.10 - West Orange-Stark
13. 9.00 - Breckenridge
14. 8.75 - Palacios
15. 8.67 - Port Isabel
Adjusted Defensive Rating
1. 10.29 - Celina
2. 10.20 - West Orange-Stark
3. 10.00 - Liberty Hill
4. 9.82 - Graham
5. 9.36 - Abilene Wylie
6. 9.33 - Waco La Vega
7. 9.13 - China Spring
8. 9.13 - Rio Hondo
9. 8.82 - Snyder
10. 8.82 - Royse City
11. 8.78 - Giddings
12. 8.71 - Liberty-Eylau
13. 8.63 - Clyde
14. 8.50 - Palacios
15. 8.40 - Wills Point
Adjusted Overall Rating
1. 11.14 - Celina
2. 11.00 - Liberty Hill
3. 10.55 - Abilene Wylie
4. 10.50 - Cuero
5. 10.50 - Waco La Vega
6. 10.40 - West Orange-Stark
7. 10.25 - Dallas Roosevelt
8. 10.18 - Snyder
9. 10.08 - Gilmer
10. 10.00 - Royse City
11. 9.44 - Giddings
12. 9.33 - Carthage
13. 9.27 - Graham
14. 9.13 - China Spring
15. 9.00 - Wimberley
While still having its flaws, I was surprised at how close it came to where I would probably place many individual teams.
I have been forced to sit through several afternoons of mind-numbing academic seminars lately and it's become a habit of mine to work out various mathematical ideas in search of a better rating system (in place of just doodling randomly or trying to nap unnoticed). I came up with one that is very basic in how it works, yet resulted in a final ranking that actually looked fairly good.
My prior method of comparing performances between teams relied completely on margin of victory, and that is a major flaw, as there is not usually a linear correlation between increasing margins of victory and actual power of a team (due to most coaches working within the bounds of good sportsmanship and not running up scores or risking injuries to key players when they aren't needed).
As a way around this problem I concocted the following idea:
Instead of looking at actual margin of victory, look at relative performance compared to common opponents using ranking ordinals rather than points scored or allowed.
It's easier to explain by example than explanation. It works essentially like a preseason Coaches Poll for a district. Prior to each season beginning, each coach from each team in a district submits their votes on how they feel the teams in their district will rank that season. By combining the rankings submitted by all teams, you come up with a consensus poll.
I used the same idea, but instead of using the subjective opinions of individual people, I used the numbers that resulted from each game.
Going through the schedule of each 3A team, I assigned a ranking for Offense, Defense, and Overall Performance for each and every game played.
Using Celina as the example, and only counting games vs. 3A opponents to make the total number of calculations I was dealing with manageable:
Celina's 2007 Games vs. 3A Teams
Robinson scored 6 and allowed 19
Princeton 6 - 35
Frisco Wakeland 0-36
Pilot Point 6-56
Van Alstyne 0-62
Bonham 6-55
Prosper 14-62
Whitesboro 7-44
West 0-41
Emory Rains 6-48
Pittsburg 23-50
Glen Rose 21-70
Snyder 7-33
China Spring 14-21
Using only the above raw numbers the "votes" that Celina would turn in for their season would be as follows:
Offense:
1st - Pittsburg (23 pts scored)
2nd - Glen Rose (21 pts)
3rd - Prosper (14 pts)
3rd - China Spring (14 pts)
5th - Snyder (7 pts)
5th - Whitesboro (7 pts)
7th - Robinson (6 pts)
7th - Emory Rains (6 pts)
7th - Bonham (6 pts)
7th - Pilot Point (6 pts)
7th - Princeton (6 pts)
12th - Frisco Wakeland (0 pts)
12th - West (0 pts)
12th - Van Alstyne (0 pts)
You do the exact same thing for points allowed and for margins of victory.
Now the cool part. If you go through the above procedure for all 174 3A teams in the state and then sort through all of the ranks each team received from each of their opponents you would get the following (using Celina as the example).
How Celina's Opponents Would Rank Their Game with Celina compared to all other games played in 2007
(opponent - defense - offense - overall)
Robinson - 2nd - 6th - 4th
Translation: Celina held Robinson to the 2nd fewest pts of Robinson's season, Celina scored the 6th most points of any of Robinson's opponents and gave Robinson their 4th worst loss of the season.
Princeton - 5th - 5th - 3rd
Frisco Wakeland - 1st - 1st - 1st
Pilot Point - 3rd - 1st - 1st
Van Alstyne - 3rd - 1st - 1st
Bonham - 2nd - 1st - 1st
Prosper - 2nd - 1st - 1st
Whitesboro - 1st - 1st - 1st
West - 1st - 1st - 1st
Emory Rains - 1st - 3rd - 3rd
Pittsburg - 5th - 1st - 2nd
Glen Rose - 5th - 1st - 1st
Snyder - 1st - 4th - 1st
China Spring - 3rd - 5th - 2nd
So what the above translates to is (1) Celina scored the most points against 9 of the 14 3A opponents they played in 2007. (2) Celina held 5 of the 14 opponents to the fewest points scored in any game they played in 2007, (3) Celina gave 9 of their 14 opponents their worst loss of the season, looking at margin of victory.
If you average the rankings you get the following:
Celina's average offensive ranking = 2.29
Celina's average defensive ranking = 2.50
Celina's average overall ranking = 1.64
The Top 15 for Class 3A in each category:
Raw Offensive Rating
1. 1.62 - Liberty Hill
2. 2.00 - Dallas Roosvelt
3. 2.18 - Diboll
4. 2.21 - Cuero
5. 2.29 - Celina
6. 2.50 - Waco La Vega
7. 2.58 - Gilmer
8. 2.82 - Abilene Wylie
9. 2.91 - Royse City
10. 3.10 - West Orange-Stark
11. 3.18 - Snyder
12. 3.38 - Canyon
13. 3.56 - Jasper
14. 3.60 - Caldwell
15. 3.64 - Navasota
Raw Defensive Rating
1. 2.00 - West Orange-Stark
2. 2.50 - Celina
3. 2.85 - Liberty Hill
4. 3.09 - Graham
5. 3.13 - Rio Hondo
6. 3.22 - Giddings
7. 3.27 - Royse City
8. 3.33 - Waco La Vega
9. 3.36 - Abilene Wylie
10. 3.50 - Wills Point
11. 3.88 - China Spring
12t. 4.00 - Snyder
12t. 4.00 - Dallas Roosevelt
12t. 4.00 - Hidalgo
15. 4.11 - Port Isabel
Raw Overall Rating
1. 1.64 - Celina
2. 1.80 - West Orange-Stark
3. 1.85 - Liberty Hill
4. 1.88 - Dallas Roosevelt
5. 2.09 - Royse City
6. 2.17 - Waco La Vega
7. 2.18 - Abilene Wylie
8. 2.25 - Gilmer
9. 2.56 - Giddings
10. 2.57 - Cuero
11. 2.64 - Snyder
12. 3.22 - Carthage
13. 3.25 - Rio Hondo
14. 3.38 - Hidalgo
15. 3.44 - Argyle
Now before you start, I realize that that does not look quite right. Even I would not put WO-S over Liberty Hill if asked to do a similar ranking just from gut feeling.
There is a bias against teams who played more games in a season using the above method. (i.e. It's a lot tougher to get a 1st or 2nd place ranking against a team that has played 16 games compared to a team that only played 10 or less).
So what I did, is reverse the numbers, so that if you gave a team that played 16 games in the season their worst loss of the year, you would get 16 points rather than just 1. 1st place rankings, (instead of all just being averaged in as a 1.00, would vary in the amount of points they are worth, depending on how many games that opponent played.) This essentially builds a strength of schedule factor in to the system.
After making that change, you get the following results:
Adjusted Offensive Rating
1. 11.23 - Liberty Hill (in other words, on average, Liberty Hill's offensive output was better than 11 of each of their opponent's opponents.)
2. 10.86 - Cuero
3. 10.50 - Celina
4. 10.17 - Waco La Vega
5. 10.13 - Dallas Roosevelt
6. 9.91 - Abilene Wylie
7. 9.75 - Gilmer
8. 9.64 - Snyder
9. 9.64 - Diboll
10. 9.50 - Canyon
11. 9.18 - Royse City
12. 9.10 - West Orange-Stark
13. 9.00 - Breckenridge
14. 8.75 - Palacios
15. 8.67 - Port Isabel
Adjusted Defensive Rating
1. 10.29 - Celina
2. 10.20 - West Orange-Stark
3. 10.00 - Liberty Hill
4. 9.82 - Graham
5. 9.36 - Abilene Wylie
6. 9.33 - Waco La Vega
7. 9.13 - China Spring
8. 9.13 - Rio Hondo
9. 8.82 - Snyder
10. 8.82 - Royse City
11. 8.78 - Giddings
12. 8.71 - Liberty-Eylau
13. 8.63 - Clyde
14. 8.50 - Palacios
15. 8.40 - Wills Point
Adjusted Overall Rating
1. 11.14 - Celina
2. 11.00 - Liberty Hill
3. 10.55 - Abilene Wylie
4. 10.50 - Cuero
5. 10.50 - Waco La Vega
6. 10.40 - West Orange-Stark
7. 10.25 - Dallas Roosevelt
8. 10.18 - Snyder
9. 10.08 - Gilmer
10. 10.00 - Royse City
11. 9.44 - Giddings
12. 9.33 - Carthage
13. 9.27 - Graham
14. 9.13 - China Spring
15. 9.00 - Wimberley
While still having its flaws, I was surprised at how close it came to where I would probably place many individual teams.