Margin of Victory
The computer rating for college is based 'margin-of-victory' calculation and ten-goal
correction. For high school, the computer rating is based on the above two as well as
a performance correction component and win-loss percentage. Here we discuss 'margin-
of-victory.' The 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.
As an example, Garden City (NY Sec 11) plays "local" games against all "NY Sec 11"
teams (Floral Park, Carey, Southside, Long Beach, Wantagh, Syosset, etc. and
plays external games against NY Catholic (Chaminade), Massachustetts (Duxbury),
etc. The method has since added other components (SOS, RPI, W-L percentage, etc.);
however, for the purpose of discussing the method, only goal margin calculations
are considered here. Data for boy's HS lacrosse wiil serve as an example below.
(1) Power Ratings = Local Component + External Component
LOCAL COMPONENT
The local computer rating adheres to one criteria: The goal margin
of victory equals the difference in power ratings between the two
opponents when the game is played on a neutral field. When played
on the home field of one of the teams, then a home field advantage
(hfa) is added to that team. The home field advantage is determined by
averaging the home team scores - the away team scores for all games
played in the local region.
(2) PR1 - PR2 + hfa = score1 - score2
ERROR
Ideally, if you (1) subtract the power ratings of the two teams and
(2) add in the 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 rarely, if
ever occur and each game produces an error as follows:
(4) Err-L = (score1 - score2) - hfa - (PR1 - PR2)
If the Err-L > 0, than the designated team played above it's power rating.
If the Err-L < 0, than the designated team played below it's power rating.
Thus if team A plays team B and team A has a power rating of 90.0 and team B
has a power rating 80.0, then the power rating predicts A would beat B
by 10 goals if the game were played on 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 0.0.
All teams start even at the beginning of the season. Past performance is not
considered. Early in the season, the program has no knowledge of favorites or
underdogs and thus has no bias. However, it takes 5 to 6 weeks for ratings
to become meaningful so that an opponent's strength is within reason.
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.
Rephrasing this, 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 and the sum of external error divided by the total number of games
represents the second component.
EXAMPLE
Let's look at an example: Garden City in NY Section 8 (Nassau Co.) for the
year 2001. Table (1) shows Garden City's schedule with opponent, score,
opponent's power rating and location location (home, away or neutral site).
The average home field advantage is 1.45 goals and is based on all games
played by Nassau teams. The error for each game is computed in table 2.
The errors for each game are added to produce table 3. Graph 1 provides a
visual analysis of the results shown in table 3. Note 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 (3.76/18)*0.5 for games outside NY Sect 8, the power
rating for Garden City becomes 99.75 + 3.76/18*0.5 = 99.86.
Garden City ................. 99.75
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
Table 2
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 = 099.75 + 4.22 = 103.97
point 2 = 99.75 - 1.40 = 98.35
..... etc.
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
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
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
Garden City ................. 99.75 + 3.70/18 = 99.96
The influence of the external component may be reduced so the the term
"3.70/18" = 0.21 may be "3.70/18 * 0.5" = 0.105.
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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