Playoff Team Advanced Stat Profiles
D3Football.com does a great job of previewing each team in the NCAA tournament (which is partially why I'm going to copy their format), but for stat-heads like myself, I found it frustrating trying to compare your typical NCAA counting stats for conferences I didn't follow closely. Herein lies (what I hope to be) your answer. Below I describe the opponent-adjusted scoring offenses & defenses, as well as the adjusted rushing and passing efficiency ratings for each team. These metrics are all adjusted for opponent strength so you can better compare across conference, regions, and between varying styles.
If you're unaccustomed to my methods, feel free to check out my Ratings Explanation page, but the gyst of it is that every stat is rate-adjusted to tell you how the team would be expected to perform against an average DIII team (Millikin was the most average team in the country this season). I'm going to mostly focus on Points/Game (PPG) and Yards/Play (YPP), which are pretty self-explainatory. The other stat you're probably going to need a primer on is Adjusted Net Yards/Attempt (ANY/A). ANY/A is very similar to YPP, but it also includes turnovers and touchdowns. Turnovers are worth approximately 45 yards of field position, and touchdowns are worth an equivalent of about 20 yards.
Let's begin.
Mary Hardin-Baylor Bracket
Mary Hardin-Baylor

Redlands

Hardin-Simmons

Linfield

Wheaton

Huntingdon

North Central

Rose-Hulman

Mary Hardin-Baylor is the hands-down favorite in this bracket, but it definitely seems that Hardin-Simmons has figured them out a bit over the last couple seasons. If I was UMHB, I would be pleased to know Linfield is favored over HSU in the first round.
Rose-Hulman and Redlands are the only teams in the bracket that don't rate in the Top 25 in scoring margin, so most games should be competitive. I wouldn't be surprised to see North Central and Wheaton give the Cru a good fight; teams with higher efficiency margins than scoring margins tend to over-perform their spreads.
Alfred Bracket
Alfred

Bridgewater State

Western New England

Husson

Hobart

Mount Union

Johns Hopkins

Randolph-Macon

Alfred may be the top seed in this bracket (it also might be Johns Hopkins, it's honestly hard to tell), but Mount Union is the favorite. Despite their loss to John Carroll, Mount Union has dominated the rest of the schedule to the point they're still the #2 team in the country in adjusted scoring margin. Alfred and Johns Hopkins are the next best teams in the bracket at #19 & #18. With Alfred ranking in the Top 10 in most efficiency categories, and with only one unit of their pod-mates' cracking the Top 40 (Western New England's defense), Alfred should waltz to the quarterfinals.
Just like in the preseason, where I felt RMC wasn't getting very much credit for their returning talent, I wouldn't be surprised to see them beat JHU, and give Mount Union a run for their money. If Hobart somehow beats UMU, it'll undoubtedly be through the air. Hobart ranks #28 nationally in YPP, but #12 in ANY/A in passing offense, and Mount Union's secondary is potentially their worst unit (though still #16 nationally in YPP & #34 in ANY/A). In a Hobart vs. Randolph-Macon second-round matchup, I think the slight edge would go to RMC, even on the road.
St. Thomas Bracket
St. Thomas

Northwestern Minn.

Coe

Monmouth

St. John's

UW-Platteville

UW-Oshkosh

Washington U.

This bracket... is stacked. The UMHB bracket may have more proven playoff contenders, but this is one of the most loaded groups of eight in the history of the 32-team format. St. John's has the hardest path to the semis since 2005. St. Thomas is the favorite, though mostly because they play the worst team in the tournament (and one of the worst ever) in the first round.
My biggest beef with this bracket though is that I probably don't get to see if my numbers were right about Monmouth. After beating Wartburg in their non-conference, they didn't just run the table in the MWC, the absolutely destroyed people. Consider this: the MWC is the 22nd-ranked conference in the country, with no other teams cracking the Top 50 nationally in Scoring Margin or Net efficiency. Monmouth ranks 12th in Scoring Margin and #3/#4 in Net Efficiency after adjusting for their weak schedule! Being in the West, it was unlikely they were going to get a first round home game, and they got one of the weaker conference champions (Coe won all of their games, but not by the sort of margins a true contender typically would), so I'm hoping to see them stack up against St. Thomas.
UW-Whitewater Bracket
John Carroll

Olivet

Wesley

Stevenson

Thomas More

Wittenberg

UW-Whitewater

Lakeland

The reason I included ANY/A with the efficiency metrics instead of displaying YPP only is for teams like UW-Whitewater. They're #41 nationally in YPP on defense, but #4 in ANY/A. What's that mean? The Warhawks can give up big plays and will let teams sustain some drives, but those drives probably aren't going to finish with any points, and they're very possibly going to finish with UWW taking the ball away from you. The rushing defense is still elite, and the secondary makes enough big plays to rank #12 in ANY/A, but the offense has been unable to find an identity all season.
Elsewhere, Thomas More, John Carroll, and Wesley all rank in the Top 15 in Scoring Margin, and in the Top 25 in Net Efficiency. John Carroll has been pretty firmly entrenched in my Top 10 all season, and a big reason why is their defense, which ranks #1 nationally in YPP and in the top 4 for everything else. If they make it past the Wesley/Stevenson winner into the quarterfinals, I wouldn't expect a lot of points in a UWW/JCU game.
If you're interested in checking out other teams' stat profiles, I developed a Google Sheet with every team in the country included. Since it's a Google sheet, and not a fancy-schmancy application like my other interactive charts, only one person can edit at a time. So if you log on and see someone else using it, please play nice. You can access the document here.