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Statistically Speaking: The Teams You Beat

Saturday, July 14, 2007

The Teams You Beat



The impetus for this blog comes from some astute posting over at Kermit the Blog in regards to the relative paucity in quality opposition in Big East scheduling. The question I want to address here is whether a weak schedule can help us predict what will happen the following season. Is a team that beat up on patsies more likely to decline the following season than a team that played and won against a tough schedule? To answer this question, I performed two sets of regression analyses.

First I looked at the wins of all 65 BCS teams (plus Notre Dame) in 2005 and took the record against BCS teams (plus Notre Dame) of teams they had beaten (wins against non-Division IA teams excluded). Confused? Here's an example. In 2005, the Pittsburgh Panthers finished 5-6 under first year coach Dave Wannstedt. Their five wins were against Youngstown State, Cincinnati, South Florida, Syracuse, and Connecticut. The Youngstown State game gets thrown out since we are only concerned with games against Division IA teams. The first team they beat, Cincinnati, was 2-6 against other BCS teams (beating only Connecticut and Syracuse), South Florida was 4-5, Syracuse was 0-10, and Connecticut was 2-6. Combined, the teams Pitt beat finished 8-27 against BCS teams for a rather low winning percentage of .229. This number is our dependent variable and we will see how well it predicts the next season's (2006) winning percentage and conference winning percentage for each BCS team.

r squared value for predicting next season's winning percentage: .0946

r squared value for predicting next season's conference winning percentage: .0901

Both relationships are positive indicating that as defeated opponent's record against BCS teams goes up, so does both conference and overall winning percentage. Defeated opponent's combined record against BCS teams appears to be a consistent, albeit poor predictor of team's finish the following season. The r squared value is practically identical for both record and conference record the next season, but only a little more than 9% of the variation is explained.

While compiling each team's defeated opponent's record against BCS teams I noticed that winning percentage against BCS teams can have sample size issues. Therefore, I also decided to use total wins against BCS teams by defeated opponents as an independent variable. An example from 2005 between two Pac 10 schools can illustrate the dramatic effect sample size can have. In 2005, the Oregon Ducks had a fantastic regular season finishing 10-1. Their 10 wins were against Houston (1-1 versus BCS schools), Montana (non-Division IA), Fresno State (0-2), Stanford (4-5), Arizona State (5-5), Washington (1-8), Arizona (2-7), Cal (5-4), Washington State (1-7), and Oregon State (3-6). Combined, their defeated opponents finished 22-45 against BCS schools for a winning percentage of .328. That same season the Arizona Wildcats finished a disappointing 3-8. Their wins were against Northern Arizona (non-Division IA), Oregon State (3-6), and UCLA (7-2). Combined, their defeated opponents finished 10-8 for a winning percentage of .556. That's nearly 23 percentage points higher than Oregon's defeated opponents. However, their defeated opponents have less than half as many wins as Oregon's. Here are the r squared values for total wins.

r squared value for predicting next season's winning percentage: .2456

r squared value for predicting next season's conference winning percentage: .2183

Both relationships are positive indicating that as defeated opponent's total wins against BCS teams goes up, so does both conference and overall winning percentage. Again both relationships appear to be relatively consistent in regards to both conference and overall winning percentage. However, the predictive ability for total wins is over twice as high as winning percentage.

What does this all mean? While it certainly does matter to some extent how 'good' a team's wins were when predicting how they will fare the following season, it is certainly not the best indicator for future success. Instead of using it to predict how good a team will be, its best used to quantify how good a team was.

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