Opponent-adjusted metrics: Part 2, college football score margin

Introduction

In the last post, a general procedure for calculating opponent-adjusted metric was presented. This was described as:

• Calculate the raw metric for each team/player
• Calculate the expected value of this metric, if an average team/player had played the same schedule
• From these two pieces of information, an adjusted metric is calculated which satisfies these crucial criteria:
• If a team matches the expected value of an average team, it is therefore average and the opponent adjusted metric will reflect this
• If a team exceeds the expected value, it is above average
• If a team does not meet the expected value, it is below average

This method was then used to rank the Division 1 college football teams from the 2012 season (after bowl games). In this post, the same principals will be used to calculated an opponent-adjusted average score margin.

Method

As in the last post, a relationship must be defined to calculate the adjusted average score margin from the raw average score margin and the expected average score margin. Last time, the adjusted record was required to be no more than 1.000 and no less than 0.000. This time, however, the adjusted average score margin can (in theory, at least) take any real value. Because of this, the equation this time is simpler:

Adjusted average margin = Raw average margin - Expected average margin

Results

The adjusted average margin for each of the 124 Division 1 team is shown below:

The teams of interest here are those whose position in the opponent-adjusted average margin ranking is significantly different from that in the previous post's opponent-adjusted record. In this case, it may be surmised that the team in question was inconsistent during the season, exceeding expectations one week while failing to live up to them the next. However, a team which wins by less than expected is still credited with a win and likewise, a team which loses by less than expected is still credited with a loss. So the opponent-adjusted ranking is less affected by these performances than the opponent-adjusted average score margin.

Conclusion

At first glance, this metric does not appear to be as useful as the opponent-adjusted record of the last post: there are teams which appear to be badly-ranked, for example Southern Cal, who finished the season with a 7-6 but who find themselves above 12-0 Ohio State. However, as mentioned, consistency plays a part here.

It would be of interest to calculate, for each team, a standard deviation of the opponent-adjusted margin along with the average presented here. From that, if a team's outcome is assumed to follow a normal distribution, it would be possible, for any game, to calculate the probability of each team winning. While the team with the higher average opponent adjusted score margin will be more likely to win, this probability will decrease as the standard deviation of that team increases. This may form the basis of a future post.

Another point of interest is to investigate whether certain teams perform better when playing against teams of a certain ability. Some teams thrive on big games against the big teams, but stutter against weaker opposition; others beat up small teams but struggle against better teams. By plotting game-by-game adjusted score margin against the opponent's average adjusted score margin, team's tendencies in this regard could be revealed.