## Thursday, February 4, 2016

### Strength of Schedule for Carolina and Denver

Strength of Schedule for Carolina and Denver

The Carolina Panthers had one of the great regular season records of all time.   However, their regular season schedule appeared to be a bit weak compared to other teams including their Super Bowl Opponent the Denver Broncos.  Let’s test the hypothesis that the Panthers had a weak regular season schedule.

Question:  The table below has regular-season won/loss records for the opponent of the Carolina Panthers and the Denver Broncos.

Is the total win percentage of the opposition to Carolina significantly different from the total win percentage of the opposition to the Denver Broncos?

Discuss the limitations of this test and other things a statistician might do to assess the strength of schedule for the two Super Bowl Teams.

 Strength of Schedule Carolina Denver Opposition Wins Losses Wins Losses Jacksonville 5 11 Baltimore 5 11 Houston 9 7 Kansas City 10 5 New Orleans 7 9 Detroit 7 9 Tampa Bay 6 10 Minnesota 11 5 Seattle 10 6 Oakland 7 9 Philadelphia 7 9 Cleveland 3 13 Indianapolis 8 8 Green Bay 10 6 Green Bay 10 6 Indianapolis 8 8 Tennessee 3 13 Kansas City 10 5 Washington 9 7 Chicago 6 10 Dallas 4 12 New England 12 4 New Orleans 7 9 San Diego 4 12 Atlanta 8 8 Oakland 7 9 New York Giants 6 10 Pittsburgh 10 6 Atlanta 8 8 Cincinnati 12 4 Tampa Bay 6 10 San Diego 4 12 Total 113 143 Total 126 128

Analysis:   The aggregate win/loss records for the regular-season opponents of the two Super Bowl teams are presented in the table below.

 Total Regular Season Wins and Losses for Opponents of Carolina and Denver Carolina Opposition Denver Opposition Total Wins 113 126 239 Losses 143 128 271 Win Proportion 0.4414 0.4961 0.4686

The difference in the won-loss record for the two teams appears non-trivial but is it significant?

The answer to this question is No!

 t-test on  Difference in Regular Win Percentages for the Opponents of the Two Super Bowl Teams Diff -0.0272 SE 0.022096746 t-stat -1.232 Critical Value for .05 significance level -2.3

Discussion:  If we added playoff games of the two teams to the sample we would increase sample size and decrease standard error by around 15%.   This would make the test results a bit closer but still not significant.

I also very quickly looked at median wins for the opponents of the two teams.  Found it was 7.0 for Carolina and 7.5 for Denver.   This seems trivial.

Carolinas schedule does seem a bit weak but their record was impressive and you can only beat the teams that you play.

I do sense that Denver is the more tested team having played and beaten New England twice once in the regular season and the second time in the AFC championship game.   The counter argument is that Carolina beat Seattle twice but I Seattle had some hiccups this year.

I don’t believe Carolina has played against a defense as accomplished as Denver’s defense.   It might be useful to study defensive strength of the two teams opponents and attempt to determine whether Carolina can beat a truly great defense.

I don’t expect Denver to score much but I think Denver’s defense will also keep the score low.

Go Back to the home-field advantage hypothesis testing problems
http://www.dailymathproblem.com/p/home-field-hypothesis-testing-problems.html