Which Teams Had the Nation's Hardest Schedules in 2013?

Much is made about which teams play the most difficult schedules in the country. Johns Hopkins even highlighted the need to keep a tough schedule in place as part of its conference alignment recommendations. The thing about simply playing a difficult schedule, though, isn't simply that a team played a tough slate; rather, it's what that difficult schedule means for a team relative to a handful of things. Pertinently, it provides some context to unadjusted statistics -- like goals scored and goals allowed per game -- and has a relationship to a team's regression or improvement in winning percentage from season to season.

To make some determinations around strength of schedule, I looked at four particular metrics: average strength of opposing offenses faced (based on adjusted offensive efficiencies); average strength of opposing defenses faced (based on adjusted defensive efficiencies); average strength of opponent adjusted efficiency margins (how many goals per 100 possessions a team is better than its opposition); and average opponent Pythagorean win expectation. The first two metrics provide a little context to what a team's offensive and defensive outputs were this year; the last two provide a little context on a particular team's overall effort was like in 2013. I care more about the second set of metrics than the first.

Some brief thoughts:

• Denver had the nation's most prolific offense in 2013 (no team scored goals at a more efficient rate than the Pioneers (adjusted for competition played)), but three teams had offensive seasons that deserve extra credit based on the defenses they faced: Princeton, which ranked eighth in the nation in goals per game; Duke, which ranked third in scoring offense; and North Carolina, which ranked fourth in the same metric. When adjusted for competition played and how efficiently teams score on a possession-by-possession basis, Carolina ranked second nationally, Duke tucked in behind the Tar Heels at fifth, and Princeton finished sixth in the country. These are three teams that had notable offensive years against some of the nation's best defenses.
• You can make an argument that Notre Dame's defense wasn't quite what it was in 2012, but staring at the Irish's scoring defense rank -- 10th at 8.31 goals per game -- doesn't necessarily make your point sing. Only one team -- Virginia -- faced a tougher slate of opposing offenses in 2013, and when you adjust Notre Dame's defensive performance for competition faced and scale to a possession-by-possession effort, the Irish's defensive performance ranks third nationally. The death of Gerry Byrne's defense was somewhat exaggerated.

Some brief thoughts:

• Bryant isn't included in the above table, but the Bulldogs experienced the second highest winning percentage drop from 2012 to 2013 (-35.67%) yet significantly improved their schedule from last year to 2013 (Bryant's schedule, based on average opponent efficient margin, ranked 57th in 2012; in 2013, the schedule ranked 38th in the same metric). Outside of some important roster losses from last year to this season, you can make a pretty decent argument that the Bulldogs' decreased winning percentage was partly attributable to playing a more difficult schedule (although, as noted, other things went on with Bryant in 2013 that differed from 2012).
• Princeton's schedule -- based on average opponent adjusted efficiency margin -- improved the most from 2012 to 2013, but, notably, the Tigers' winning percentage dropped 8.75 percent. Injuries were a big part of Princeton's season (as well as fabricating a defense), and the fact that the Tigers were able to hold everything together deserves some praise despite a nasty slate of games. Contrastingly, Yale upped its schedule from last season to this year (the improvement ranks ninth in the nation) and also had a small winning percentage improvement over 2012 (1.84 percent (30th in the country)). The Ivy League is a pretty ridiculous yacht club.
• Massachusetts' schedule improvement from 2012 to 2013 ranked as the nation's fourth most prominent increase, but the Minutemen's winning percentage drop -- -47.08 percent -- was the country's most drastic decrease. Knucklehead Theory^TM implies that Massachusetts was "a fraud" in 2012; that idea, though, is utter garbage that requires thinking for about a millisecond and then returning to Two and a Half Men reruns. Massachusetts was a horse last season, drawn into a tough first round game with Peter Baum and Colgate, and was one of the nation's best teams. The drop for the Minutemen from last season to this year was probably more attributable to Greg Cannella dealing with injuries, important roster turnover, and an inability to rekindle some of 2012's magic. The team's improved schedule played a role in Massachusetts' narrative in 2013, but it wasn't the biggest plot point.
• Over the last two seasons, Pennsylvania has played the nation's third-ranked schedules. These are brutal slates that Mike Murphy is putting together (of course, the Ivy League schedule isn't a decision that Murphy can make), but the Quakers responded in 2013: Pennsylvania increased its winning percentage by 10.59 percent over 2012, the 19th best mark in the nation. That's impressive and potentially grounds for throwing rose petals at the Quakers' feet before the 2014 season.
• Among the teams with top 10 schedules, Denver saw the greatest winning percentage improvement among the cohort, checking in at 12th in terms of winning percentage improvement (17.43 percent). The next highest was North Carolina at 18th (11.76 percent). In terms of positive winning percentage improvement among this group, only Pennsylvania (10.59, 19th), Maryland (4.76 percent, 28th), Yale (1.84 percent, 30th), and Duke (1.19 percent, 31st) made gains over 2012. I don't know exactly what that means, but you're free to speculate.