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How much will Michigan improve this season? What predictions can we make based on three games?

Under new coach Jim Harbaugh, the Wolverines have lived up to expectations. They beat Oregon State and UNLV in games in which they were favored by the markets. However, they lost as an underdog at Utah in the season opener.

To get a deeper insight into their play, we must dig past the game results and into the passing and rushing numbers. Yards per play with sacks counted as pass plays is a useful efficiency metric.

Three games does not provide enough data for firm conclusions about Michigan. But by combining these numbers with preseason expectations, we can make useful predictions about the BYU game and beyond.

Let's start with the positives.

Michigan's biggest strength

Michigan's rush defense has been exceptional. Through three games, it has allowed a paltry 3.13 yards per carry, much less than the 4.98 average (calculated based on all games with FBS and FCS teams in 2014).

This strength carries over from last season. Despite an underwhelming 5-7 record, Michigan's defense allowed 4.04 yards per carry, 12th best in the nation.

In addition, they faced many of the country's top rush offenses (Ohio State, Indiana, Michigan State) in Big Ten play. After adjusting yards per carry for strength of schedule with my methods at The Power Rank, Michigan had the second-best rush defense in 2014.

It was reasonable to expect continued excellence in run defense because all of Michigan's starters at defensive tackle return for the 2015 season. (Brian Mone did suffer a season-ending injury in the preseason.)

The most pleasant surprise along this defensive front has been Ryan Glasgow. The former two-star recruit and walk-on started last season and earned a scholarship for this season. He continues to make life difficult for any opponent that attempts to run up the middle.

Glasgow gets help from defensive end Chris Wormley, who already has seven tackles for loss this season, and Willie Henry. Michigan's run defense should continue to excel throughout this season.

Overall, the defense has played very well, and even the last game against a supposedly poor UNLV shows this. Michigan's defense allowed 235 yards on 3.79 yards per play.

However, UNLV gained 493 yards on 5.67 yards per play against Northern Illinois in its opener. Ohio State had 298 yards on 4.52 yards per play against the same defense.

Michigan's biggest question

The pass offense has not excelled so far this season. Under the leadership of graduate transfer QB Jake Rudock, Michigan has thrown for 6.14 yards per attempt (this doesn't include three incompletions by Wilton Speight against UNLV). This pass efficiency is below the 6.24 college football average from 2014.

Rudock has completed 65 percent of his passes this season, above both his career and college football's average. However, many of these completions have resulted in short gains, which brings down the efficiency numbers. In addition, he has thrown five interceptions.

Rudock can't blame pass protection. Michigan has allowed one sack all season. It came against Oregon State when an unblocked defender caused a Rudock fumble.

This pass protection has been an unexpected surprise this season. Michigan has allowed sacks on 1 percent of pass attempts this season, much better than the 7.2 percent and 8.3 percent from 2014 and 2013, respectively.

In addition, the offensive line has held up against quality competition. Utah sacked the quarterback on 10.4 percent of pass attempts last season and returned all but one defensive linemen. However, Michigan's line gave Rudock enough time to finish his master's thesis before making some deep throws.

This protection hasn't resulted in an efficient pass offense as the offense seems out of sync. In the first half against Utah, Jehu Chesson appeared to slow down on a deep route that may have been a touchdown if he had run full speed.

Prediction for BYU

My numbers give Michigan a 5.5-point edge in this Saturday's home game against BYU, the same prediction as the markets in Vegas. This estimate is probably low.

BYU lost starting QB Taysom Hill to a season-ending injury in their opening game. Tanner Mangum took over and has led the Cougars to wins in two of three games as an underdog in each game.

However, luck played a big role in these wins. Mangum threw a 42-yard Hail Mary in the final seconds to beat Nebraska. He also had good fortune when Boise State allowed his receivers to get behind the secondary twice for big gains of 84 and 70 yards, although his scrambling ability helped make these opportunities.

It's unlikely Mangum has similar success with the deep ball against Michigan's defense. In addition, Rudock should have a solid game passing against a good but not great secondary.

Ed Feng has a Ph.D. in chemical engineering from Stanford and runs the sports analytics site The Power Rank. Email Ed Feng here.

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