SOS2

An Alternative Winning Percentage-based SOS

© Copyright 2006, Paul Kislanko

The NCAA's definitions of Strength of Schedule are not generally useful in compiling rankings, because in football (and to a lesser extent the other division 1 team sports) there is a large amount of duplicated data. This is because the Opponents' Opponents data double-counts games involving the team itself, and games between common opponents.

I have defined "SOS2" to more accurately reflect the true relationship of a team's schedule to that of the field as a whole.

The fields are:

SOS2= ( #OO × OWP + #O × OOWP ) / ( #O + #OO )
This essentially "weights" the OOWP by how many opponents connect the team to opponents' opponents, and OWP by the number of unique OOs that contribute to it. The denominator is just the total number of unique teams that contribute to this teams SOS.

WP= W / ( W + L )
W — the number of wins
L — the number of losses

This is just the standard definition of winning percentage,

OWP= OW / ( OW + OL )
OW — Sum of all opponents' wins not including games involving this team
OL — Sum of all opponents' losses not including games involving this team
The NCAA also does not include games against the team in question, but instead of the standard formula, it uses the average of the individual WPs for each opponent. For this report, we take the total Ws and Ls and apply the usual formula so the units are consistent.

OOWP= OOW / ( OOW + OOL )

OOW — Sum of all opponents' opponents wins not including games involving this team or any of this team's opponents
OOL — Sum of all opponents' opponents losses not including games involving this team or any of this team's opponents
This is the component that makes this definition more accurate than the NCAA's. Each game contributes to WP, OWP, OOWP or none of them, but only contributes to one. Counting games among opponents always adds to both OOW and OOL, which forces the ratio to be closer to .500 for all teams than it should be.

CI is just the Connectivity Index, the sum of #O (number of opponents) and #OO (number of opponents' opponents who are not also opponents.) This indicates how "connected" the team is to the field, and how connected the field is overall. Formula-based rating systems don't usually give accurate results until either half the field has a CI greater than 43, or 43 teams have a CI greater than 59.

GI is the sum of W, L, OW, OL, OOW and OOL. In other words, the total number of games that contribute to the SOS rating. This is possible because of the lack of duplication in the counts of wins and losses.

SOS2=	( #OO × OWP + #O × OOWP ) / ( #O + #OO ) This essentially "weights" the OOWP by how many opponents connect the team to opponents' opponents, and OWP by the number of unique OOs that contribute to it. The denominator is just the total number of unique teams that contribute to this teams SOS.
WP=	W / ( W + L ) W — the number of wins L — the number of losses This is just the standard definition of winning percentage,
OWP=	OW / ( OW + OL ) OW — Sum of all opponents' wins not including games involving this team OL — Sum of all opponents' losses not including games involving this team The NCAA also does not include games against the team in question, but instead of the standard formula, it uses the average of the individual WPs for each opponent. For this report, we take the total Ws and Ls and apply the usual formula so the units are consistent.
OOWP=	OOW / ( OOW + OOL ) OOW — Sum of all opponents' opponents wins not including games involving this team or any of this team's opponents OOL — Sum of all opponents' opponents losses not including games involving this team or any of this team's opponents This is the component that makes this definition more accurate than the NCAA's. Each game contributes to WP, OWP, OOWP or none of them, but only contributes to one. Counting games among opponents always adds to both OOW and OOL, which forces the ratio to be closer to .500 for all teams than it should be.
CI	is just the Connectivity Index, the sum of #O (number of opponents) and #OO (number of opponents' opponents who are not also opponents.) This indicates how "connected" the team is to the field, and how connected the field is overall. Formula-based rating systems don't usually give accurate results until either half the field has a CI greater than 43, or 43 teams have a CI greater than 59.
GI	is the sum of W, L, OW, OL, OOW and OOL. In other words, the total number of games that contribute to the SOS rating. This is possible because of the lack of duplication in the counts of wins and losses.