Strength of Schedule Strength of Schedule (SOS) is a rating which applies to a teams schedule where 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. A measure of an opponent's strength is its power rating or the record of its opponent and their opponents. The higher the rating, the stronger the team. There are three methods that come to mind when doing an SOS rating. The first method uses an average of all opponents PR's to arrive at the SOS. A second method uses a weighted average of the PR's so that 'tougher games' are not "diluted" by games against weaker teams. A third method uses the last two components of the Rating Percentage Index Method. It employs the W-L record of the opponents and the W-L record of the opponent's opponent. This method employs the Ratings Percentage Index (PRI). All three methods are demonstrated below with the advantages and disadvan- tages for each illustrated. The results of all three methods are shown for: (1) average, (2) weighted average and (3) RPI. We use the college football schedule for the year 2001 through Oct 31,2001 and use the game results of Oklahoma to derive the first and third calculations. Note that the results vary based on the method. -------------------------------------------------------------------------- Oklahoma has played 8 games (Power Ratings as of October 31 shown in parentheses): 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) The three methods are: (1) Average of the Opponent's 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 and penalizes for adding weaker teams or requires computer ratings. (2) Weighted Average of the Opponent's Power Ratings 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.). So lets consider two cases: Team A plays two games against average teams (PR = 50.), whereas Team B plays two games against a tough team (PR = 80.) and a weak team (PR = 20.). The average PR or average SOS of team A is (50. + 50.)/2. = 50.. The average of team B is (80. + 20.)/2. = 50.. So 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 do the exponential of the opponents power ratings using 2.5 as the exponent. Team A's SOS = ((50./100.) ** 2.5 + (50./100.) ** 2.5) * 100. = (0.5**2.5) + 0.5**2.5) * 100. = 35.35 Team B's SOS = ((80./100.) **2.5 + (20./100.) ** 2.5) * 100. = (0.8**2.5 + 0.2**2.5) * 100 = 59.03 So instead of getting 50. for both, we now get 35.35 and 59.03 which means player tougher opponents will yield a higher SOS. This technique is called weighted averaging. Advantages: Emphasizes playing the best team while not penalizing for adding weaker teams. Disadvantages: Not simple to understand or explain; requires computer ratings. (3) RPI Method The RPI Method is discussed at RPI and is based on a teams record and its opponent's record and their opponent's records. |
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