College football returns in full force this week after a brief appetizer last weekend during “Week Zero.” A lot has changed in the offseason: athletes won the right to be paid for their likeness, the never-ending coaching carousel spun, vaccines became available as a tool to mitigate Covid-19 chaos and the latest round of conference realignment revved up.

But plenty is still the same. Teams still get in trouble for breaking any number of the rules in the NCAA’s esoteric 464-page rulebook. They have run-ins with the law and coaches are behaving badly in myriad ways. Their schools dig out from decades-old scandals.

In other words, the underbelly of college football remains as putrid as ever.

The WSJ Sports Grid of Shame is back after a one-year pandemic hiatus to help solve an always complex equation: How good your team is on the field versus how badly it behaves off it.

The horizontal axis shows how good each Power Five team should be on game days in 2021, calculated from a composite of objective rankings and subjective opinions of college football insiders. The further to the right a team appears, the more games it is expected to win.

The vertical axis is the “shame meter.” It’s a spicy indicator of how closely your team follows the rules, how athletes are doing in the classroom, how much the university subsidizes athletics at the expense of the general student body and whether students are excited enough to attend games.

To account for the changing landscape in college football, this year we’ve added a factor that can boost a school’s standing: team vaccination rate.

We boosted teams with the highest vaccination rates. The reason: It’s a competitive advantage. Most Conference health policies assign losses to teams unable to play games due to Covid-19 outbreaks, which happened dozens of times last season. All leagues encourage vaccinations and do not require quarantines for vaccinated players and staff who are identified as close contacts.

There are some aspects of college football that the data can’t capture. The “ick factor” helps account for these transgressions. Any university involved in a scandal, regardless of whether it happened during the offseason or directly implicated the football program, takes a hit. That explains why nearly 30% of the Big Ten is serving a long-term Grid penalty for its still-unresolved sexual-abuse scandals, and why Tennessee took a big hit for handing out Happy Meals full of cash to recruits.

Write to Laine Higgins at laine.higgins@wsj.com and Brian McGill at Brian.McGill@wsj.com