Sample Calculation

Here is a step by step sample of how I calculate my ratings. Below are some sample teams and the games they've played. Each row is a different team and each column shows who they played that week. Opponents shown in capital letters are games the team won, lower case represents a loss.

Team	1	2	3	4	5	6
A	D	E	G	I	H	J
B	E	D	F	J	I	H
C	J	H	I	G	F	e
D	a	b	E	F	G	I
E	b	a	d	H	J	C
F	H	I	b	d	c	G
G	I	J	a	c	d	f
H	f	c	J	e	a	b
I	g	f	c	a	b	d
J	c	g	h	b	e	a

1. Calculate Records

Each team's record is calculated by dividing the number of games they've won by the number of games they've played (when rating games from before the tiebreaker was introduced I counted a tie as half a win).

Team	1	2	3	4	5	6	Record
A	D	E	G	I	H	J	1.00000
B	E	D	F	J	I	H	1.00000
C	J	H	I	G	F	e	0.83333
D	a	b	E	F	G	I	0.66666
E	b	a	d	H	J	C	0.50000
F	H	I	b	d	c	G	0.50000
G	I	J	a	c	d	f	0.33333
H	f	c	J	e	a	b	0.16666
I	g	f	c	a	b	d	0.00000
J	c	g	h	b	e	a	0.00000

2. Calculate Opponents' Average Records

Next look up the record for each opponent a team has played. Add up all their records and divide by the number of teams played. For example, team A played teams D, E, G, I, H, and J, with records of 0.66, 0.50, 0.33, 0.00, 0.16, and 0.0 respectively. Add those up and you get 1.65. Now divide by the number of teams A has played (6) and you get 0.27.

Team	1	2	3	4	5	6	Record	Op Rec
A	D	E	G	I	H	J	1.00000	0.27778
B	E	D	F	J	I	H	1.00000	0.30556
C	J	H	I	G	F	e	0.83333	0.25000
D	a	b	E	F	G	I	0.66666	0.55556
E	b	a	d	H	J	C	0.50000	0.61111
F	H	I	b	d	c	G	0.50000	0.50000
G	I	J	a	c	d	f	0.33333	0.50000
H	f	c	J	e	a	b	0.16666	0.63889
I	g	f	c	a	b	d	0.00000	0.72222
J	c	g	h	b	e	a	0.00000	0.63889

3. Calculate Opponents' Opponents' Average Records

This is similar to how opponents' record was calculated. This time look up the opponents' record for everyone a team has played, add them up, and again divide by the number of teams played. Note how the numbers for opponents' opponents' record are more bunched up around 50% than record or opponents' record. This naturally lends more weight to factors like record, which are much more spread out.

Team	1	2	3	4	5	6	Record	Op Rec	Op Op Rec
A	D	E	G	I	H	J	1.00000	0.27778	0.61111
B	E	D	F	J	I	H	1.00000	0.30556	0.61111
C	J	H	I	G	F	e	0.83333	0.25000	0.60185
D	a	b	E	F	G	I	0.66666	0.55556	0.48611
E	b	a	d	H	J	C	0.50000	0.61111	0.44444
F	H	I	b	d	c	G	0.50000	0.50000	0.49537
G	I	J	a	c	d	f	0.33333	0.50000	0.49074
H	f	c	J	e	a	b	0.16666	0.63889	0.43056
I	g	f	c	a	b	d	0.00000	0.72222	0.39815
J	c	g	h	b	e	a	0.00000	0.63889	0.43056

4. Calculate Ratings

A team's rating is the average of the three numbers we've calculated. So add up each team's record, opponents' recored, and opponents' opponents' record and divide by three.

Team	1	2	3	4	5	6	Record	Op Rec	Op Op Rec	Rating
A	D	E	G	I	H	J	1.00000	0.27778	0.61111	0.62963
B	E	D	F	J	I	H	1.00000	0.30556	0.61111	0.63889
C	J	H	I	G	F	e	0.83333	0.25000	0.60185	0.56173
D	a	b	E	F	G	I	0.66666	0.55556	0.48611	0.56944
E	b	a	d	H	J	C	0.50000	0.61111	0.44444	0.51852
F	H	I	b	d	c	G	0.50000	0.50000	0.49537	0.49846
G	I	J	a	c	d	f	0.33333	0.50000	0.49074	0.44135
H	f	c	J	e	a	b	0.16666	0.63889	0.43056	0.41204
I	g	f	c	a	b	d	0.00000	0.72222	0.39815	0.37346
J	c	g	h	b	e	a	0.00000	0.63889	0.43056	0.35648

5. Sort By Ratings

Higher rating numbers are better than lower ones so sort the list in descending order of rating number.

Rank	Team	1	2	3	4	5	6	Record	Op Rec	Op Op Rec	Rating
1	B	E	D	F	J	I	H	1.00000	0.30556	0.61111	0.63889
2	A	D	E	G	I	H	J	1.00000	0.27778	0.61111	0.62963
3	D	a	b	E	F	G	I	0.66666	0.55556	0.48611	0.56944
4	C	J	H	I	G	F	e	0.83333	0.25000	0.60185	0.56173
5	E	b	a	d	H	J	C	0.50000	0.61111	0.44444	0.51852
6	F	H	I	b	d	c	G	0.50000	0.50000	0.49537	0.49846
7	G	I	J	a	c	d	f	0.33333	0.50000	0.49074	0.44135
8	H	f	c	J	e	a	b	0.16666	0.63889	0.43056	0.41204
9	I	g	f	c	a	b	d	0.00000	0.72222	0.39815	0.37346
10	J	c	g	h	b	e	a	0.00000	0.63889	0.43056	0.35648

Results

You can see that in general teams with good records rank higher than teams with lesser records. Teams A and B were both undefeated, but B played a tougher schedule than A did so B is given the number one spot. Notice also that team C had a better record than team D did, but D is ranked higher because they proved themselves against much tougher competition than C did (team D played both undefeated teams, while C played a one-win team and a winless one, also team D was able to beat team E and team C wasn't).