Explanation of Power Ratings

Computer ratings for college and high school are based on a margin-of-victory calculation and a 10-goal limit (correction).

Goal Margin The local computer rating adheres to one criterion: The goal margin of victory equals the difference in power ratings between the two opponents if the game were to be played on a neutral field. When played at the site of one of the teams, a home field advantage (HFA) is added for that team. HFA is determined by averaging the home minus away scores for all games played in the local region.

PR1 - PR2 + HFA = score1 - score2

Error Ideally, if you (a) subtract the power ratings of the two teams and (b) account for home field advantage ('+' if the designated team is at home and '-' if the designated team is away), the result should be equal to difference in the actual game score. This will only seldom occur, of course, and each game produces an error as follows:

Err = (score1 - score2) - HFA - (PR1 - PR2)

If Err > 0, then the designated team played above its computer rating. If Err < 0, then the designated team played below its computer rating. Thus, if Team A plays Team B, and Team A has a power rating of 90 and team B has a power rating 80, then A would be predicted to beat B by 10 goals if the game were played at a neutral site. The power ratings are based on all games a team plays and averaged for total performance. The computer program iterates on all teams for all games such that the average error for all teams goes to zero. All teams start even at the beginning of the season. Past seasons performance is not considered. Early in the year, the program has no knowledge of favorites or underdogs and thus has no bias. However, it takes 5 to 6 weeks for the computations to become meaningful. The objective of the computer rating scheme is to insure that the iterative final power rating for all teams produces a sum over all games for each team such that the sum of the local error = 0.00. In other words, the power rating is the average of a designated teams performance over all games and the magnitude of the '+'s and '-'s balances out as the sum of errors goes to zero when all local games a team plays are considered.

   Opponent                 Score  Opp PR    Home
 
1  Lynbrook                 15  6   93.52    away
2  Chaminade                14 12   96.35    neut
3  Manhasset                20  8   90.06    away
4  MacArthur                20  5   86.79    home
5  Floral Park              15  0   87.53    away
6  Syosset                  21  3   87.38    home
7  Duxbury                   9  3   97.40    away
8  Division-Levittown       20  2   82.66    away
9  Carey                    24  2   81.37    home
10 Great Neck No            18  3   80.48    away
11 Wantagh                  13 10   95.10    home
12 Port Washington          20  6   87.94    away
13 Lawrence                 15  7   88.12    away
14 Southside                17  2   85.26    home
15 Long Beach               11  3   87.02    away
16 Southside                18  4   85.26    home
17 Floral Park              17  9   87.53    neut
18 Wantagh                   8 10   95.10    neut

Home field advantage = 1.45 goals. Chaminade and Duxbury are non-local games.

Table 2: Error Analysis
1  Lynbrook           Error = (15- 6) + 1.45 - (99.75 - 93.52) =  4.22
2  Chaminade          Error = (14-12) + 0.00 - (99.75 - 96.35) =  
3  Manhasset          Error = (20- 8) + 1.45 - (99.75 - 90.06) =  3.76
4  MacArthur          Error = (20- 5) - 1.45 - (99.75 - 86.79) =  0.59
5  Floral Park        Error = (15- 0) + 1.45 - (99.75 - 87.53) =  4.23
6  Syosset            Error = (21- 3) - 1.45 - (99.75 - 87.38) =  4.18
7  Duxbury            Error = ( 9- 3) + 1.45 - (99.75 - 97.40) =   
8  Division-Levittown Error = (20- 2) + 1.45 - (99.75 - 82.66) =  2.35
9  Carey              Error = (24- 2) - 1.45 - (99.75 - 81.37) =  2.17
10 Great Neck No      Error = (18- 3) + 1.45 - (99.75 - 80.48) = -2.83
11 Wantagh            Error = (13-10) - 1.45 - (99.75 - 95.10) = -3.10
12 Port Washington    Error = (20- 6) + 1.45 - (99.75 - 87.94) =  3.64
13 Lawrence           Error = (15- 7) + 1.45 - (99.75 - 88.12) = -2.18
14 Southside          Error = (17- 2) - 1.45 - (99.75 - 85.26) = -0.94
15 Long Beach         Error = (11- 3) + 1.45 - (99.75 - 87.02) = -3.28
16 Southside          Error = (18- 4) - 1.45 - (99.75 - 85.26) = -1.94
17 Floral Park        Error = (17- 9) + 0.00 - (99.75 - 87.53) = -4.22
18 Wantagh            Error = ( 8-10) + 0.00 - (99.75 - 95.10) = -6.65
   home field = 0.0 means the game was played on a neutral site

Table 3: Combined Errors
   Opponent                 Score  Opp PR    Home   Err 
1  Lynbrook                 15  6   93.52    1.45    4.22    
2  Chaminade                14 12   96.35    0.00    0.00   
3  Manhasset                20  8   90.06    1.45    3.76    
4  MacArthur                20  5   86.79   -1.45    0.59    
5  Floral Park              15  0   87.53    1.45    4.23    
6  Syosset                  21  3   87.38   -1.45    4.18    
7  Duxbury                   9  3   97.40    1.45    0.00    
8  Division-Levittown       20  2   82.66    1.45    2.35    
9  Carey                    24  2   81.37   -1.45    2.17    
10 Great Neck No            18  3   80.48    1.45   -2.83    
11 Wantagh                  13 10   95.10   -1.45   -3.10    
12 Port Washington          20  6   87.94    1.45    3.64    
13 Lawrence                 15  7   88.12    1.45   -2.18    
14 Southside                17  2   85.26   -1.45   -0.94    
15 Long Beach               11  3   87.02    1.45   -3.28    
16 Southside                18  4   85.26   -1.45   -1.94    
17 Floral Park              17  9   87.53    0.00   -4.22   
18 Wantagh                   8 10   95.10    0.00   -6.65    
                                                    -----   
                                                     0.00    
   Garden City             .................   99.75

Thus we have computed gthe power rating for Garden City such that the sum of all errors is 0.0.