Computer ratings for college are based on a margin-of-victory calculation and a 10-goal limit (correction). For high school, computer ratings are based on these two factors as well as a performance correction component and win-loss percentage. The margin-of-victory calculation is divided into two phases: local, or games played against in-league teams, and external, or games played outside a league, region, state, or division. The method has since added other components; however, only goal margin calculations are considered here.

As an example, Garden City (NY Section 8) plays local games against teams such as Floral Park and Wantagh and external games against NY Catholic (e.g., Chaminade) as well as teams from out of state.

Local Component

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.

(1) 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:

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

If Err-L > 0, then the designated team played above its computer rating.
If Err-L < 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 season's 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 of the local error = 0.00. In other words, the local power rating is the average of a designated team's 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.

External Component

External or non-local games have an error (Err-E) based on the same formula. However, an external correction factor> exclusive of the local margin of victory rating is computed by adding or subtracting the error for each game multiplied by 0.004.

Let's look at an example: Garden City in NY Section 8 for a previous season. Table 1 shows Garden City's schedule with opponent, score, opponent's power rating, and location (home, away or neutral site). The average home field advantage is 1.45 goals and is based on all games played by Section 8 teams.

The error for each game is computed in Table 2. Errors for each game are added to produce Table 3. Graph 1 provides a visual analysis of the results shown in Table 3. Note that the sum of all errors for the local games = 0.0. The sum of all errors for external games is 3.76. The local power rating (first component) is 99.75 and, when the second component is added (3.76/180.5) for games outside Section 8, the power rating for Garden City becomes 99.75 + 3.76/180.5 = 99.86.

Table 1: Schedule

   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) = ---- -1.40
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) = ---- +5.10
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

point 1 = 99.75 + 4.22 = 103.97
point 2 = 99.75 - 1.40 = 98.35
..... etc.


garden.jpg (20601 bytes)



Table 3: Combined Errors

   Opponent                 Score  Opp PR    Home   Err-L   Err-E

1 Lynbrook 15 6 93.52 1.45 4.22 0.00
2 Chaminade 14 12 96.35 0.00 0.00 -1.40 * 0.004
3 Manhasset 20 8 90.06 1.45 3.76 0.00
4 MacArthur 20 5 86.79 -1.45 0.59 0.00
5 Floral Park 15 0 87.53 1.45 4.23 0.00
6 Syosset 21 3 87.38 -1.45 4.18 0.00
7 Duxbury 9 3 97.40 1.45 0.00 5.10 * 0.004
8 Division-Levittown 20 2 82.66 1.45 2.35 0.00
9 Carey 24 2 81.37 -1.45 2.17 0.00
10 Great Neck No 18 3 80.48 1.45 -2.83 0.00
11 Wantagh 13 10 95.10 -1.45 -3.10 0.00
12 Port Washington 20 6 87.94 1.45 3.64 0.00
13 Lawrence 15 7 88.12 1.45 -2.18 0.00
14 Southside 17 2 85.26 -1.45 -0.94 0.00
15 Long Beach 11 3 87.02 1.45 -3.28 0.00
16 Southside 18 4 85.26 -1.45 -1.94 0.00
17 Floral Park 17 9 87.53 0.00 -4.22 0.00
18 Wantagh 8 10 95.10 0.00 -6.65 0.00
----- -----
0.00 3.70 * 0.004

Garden City ................. 99.75

The external adjustment is 3.70 * 0.004 or 0.136.

Based on the margin of victory, an accuracy for predicting the outcome of high school lacrosse games was found to be within three goals of the actual result.

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