Strength of Schedule (SOS) is a rating which applies to a team's schedule such that the stronger the opponents, the higher the SOS rating, or conversely, the weaker the opponents, the lower the SOS rating. In order to tabulate an SOS rating, the opponent's strength has to be evaluated.

Three common methods are used to do an SOS rating. The first uses an average of opponents' computer power ratings (PRs) to arrive at the SOS. A second method uses a weighted average of the PRs so that tougher games are not diluted by games against weaker teams. A third method employs the last two components of the Rating Percentage Index (RPI) method and examines the W-L record of the opponents and the W-L record of the opponents' opponents.

All three methods are demonstrated below with the advantages and disadvantages for each illustrated.

Consider the schedule of the Oklahoma football team though October 31 during the 2001 season. Their opponent's are listed along with their computer power ratings.

 North Carolina  (71.61)
Air Force (43.94)
North Texas (46.95)
Kansas State (70.70)
Texas (82.47)
Kansas (52.75)
Baylor (44.53)
Nebraska (84.16)

(1) Average of Opponents' Power Ratings

The average power rating would simply be the sum of all opponent power ratings divided by the number of games played. If the game was against a team outside Division I, then the game would not be included in the SOS rating. All games for Oklahoma were in Division I. Averaging the opponent's power ratings we get.

   71.61
43.94
46.95
70.70
82.47
52.75
44.53
84.16
-----
497.11 / 8 = 62.19

Advantages: Simple to understand and explain.

Disadvantages: Does not emphasize playing the best teams, penalizes for playing weaker teams, and requires computer ratings.


(2) Weighted Average of the Opponents' Power Ratings

   100 * ((71.61 / 100) ^ 2.5) = 43.39
100 * ((43.94 / 100) ^ 2.5) = 12.79
100 * ((46.95 / 100) ^ 2.5) = 15.10
100 * ((70.70 / 100) ^ 2.5) = 42.03
100 * ((82.47 / 100) ^ 2.5) = 61.76
100 * ((52.75 / 100) ^ 2.5) = 20.21
100 * ((44.53 / 100) ^ 2.5) = 13.23
100 * ((84.16 / 100) ^ 2.5) = 59.34
------
267.87 / 8 = 33.48

The weighted average is lower than the average, but the relative SOS is what is important, as shown below. If we want to give added weight to tougher games so that a team that plays a strong team (PR = 75.) and a weak team (PR = 25.) will have a higher rating than a team that plays two average teams (PR = 50). Let's consider two cases:

Team A plays two games against average teams (PR = 50), whereas Team B plays two games, one against a tough team (PR = 80) and one against a weak team (PR = 20). The SOS (average PR) for Team A is (50 + 50)/2 = 50. The average for Team B is (80 + 20)/2 = 50. Both teams have the same SOS when averaging. But what if we want the team that plays a stronger team (PR = 80) and a weaker team (PR = 20) to have a higher strength of schedule because we want to emphasize the stronger opponent and not significantly punish a team for playing a weaker opponent. Then, when we do the average, we use an exponential of the opponent's power ratings (here the exponent is 2.5).

   Team A's SOS = 100 * (((50/100)^2.5 + (50/100)^2.5)) / 2
= 100 * ((0.5^2.5 + 0.5^2.5)) / 2 = 17.67

Team B's SOS = 100 * (((80/100)^2.5 + (20/100)^2.5)) / 2
= 100 * ((0.8^2.5 + 0.2^2.5)) / 2 = 29.52

So instead of getting 50, for both, we now get 17.67 and 29.52, which means playing tougher opponents will yield a higher relative SOS than if weighted averaging is used.

Advantages: Emphasizes playing better teams while not penalizing for playing weaker teams.

Disadvantages: Not simple to understand or to explain; requires computer ratings.


(3) Ratings Percentage Index (RPI)

The RPI method, discussed in more detail elsewhere, is based on a team's record and its opponents' records and their opponents' records. The 2nd and 3rd components, when added, yield the strength of schedule. This method is based on wins and losses and not goal or point margins or other factors contained in the first two methods.

Consider this example of Team A's record and its opponents' and opponents' opponents records:

        Team Rec (1/4)    Opp Rec (1/2)     Opp-Opp Rec (1/4)
W/L PCT. W/L PCT. W/L PCT.
0.75 0.60 0.40

Using the second and third weights and values shown above, Team A's SOS would be 100 * ((0.50 * 0.60) + (0.25 * 0.40)) = 40.

Advantages: Uniformity throughout all NCAA Sports since it is based strictly on wins and losses. It is a straight forward calculation.

Disadvantages: Does not take into account margin of victory and if two regions are insulated from each other, where one is stronger than the other, the win-losses within in each region will generate essentially equal strenght of schedule ratings.

Overall, there is generally not a lot of large difference between the average and weighted average methods. However, there are noticeable differences between these two approaches and the RPI. In selecting a method, additional questions include: (1) Should only games played count in the SOS, or should all scheduled games count? (2) Should games outside a division count? (3) Should road and home games count equally? (4) Are point or goal margins (used with the averaging techniques but not RPI) important?

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