TL;DR - If BYU can finish drives, the outcome of this game will probably be similar to the outcome of the Michigan State game.

BYU according to the five factors

Explosiveness
Offense: #122 (down from #119)
Defense #62 (down from #59)

Efficiency
Offense #39 (down from #29)
Defense #82 (down from #74)

Field Position
Offense: #24 (up from #31)
Defense: #4 (up from #7)

Finishing Drives
Offense: #85 (up from #89)
Defense: #72 (up from #90)

Turnover Margin: #3 (up from #12)

Rush Offense/Defense
On offense, BYU is good at running the ball overall (#20) and at staying ahead of the down (#25), but average at generating big plays (#57).  They're bad in short yardage situations (#74).
On defense, BYU is good at stopping the run (#17), staying ahead of the down (#39), and limiting big plays (#6). They're above average in short yardage situations (#46).

Pass Offense/Defense
On offense, BYU is below average at passing the ball (#82) and average staying ahead of the down (#60).  The team is terrible at generating big plays in the passing game (#125).  The team does a bad job of protecting Taysom (#82).  On passing downs, the team is average (#51).
On defense, BYU is average overall (#65), terrible at staying ahead of the down (#120), and bad at preventing big plays (#94).  The team is average at getting to the QB (#57).  On passing downs, BYU's defense is terrible (#115).

By Quarter
On offense, BYU is average in the 1st (#55), terrible in the 2nd (#101), good in the third (#37), and above average in the fourth (#50).
On defense, BYU is below average in the 1st (#86), above average in the 2nd (#32), great in the third (#20), and good in the fourth (#33).

By Down
On offense, BYU is below average on 1st (#71), good on 2nd (#44), and good on 3rd (#44).
On defense, BYU is great on 1st (#15), above average on 2nd (#54), and bad on 3rd (#91).

Havoc (% of plays in which the defense recorded a TFL, forced a fumble, or defended a pass)
On defense, BYU's linebackers are elite in causing havoc (#3), however the DL (#118) and secondary (#117) have been terrible.

Cincinnati according to the five factors

Explosiveness
Offense: #87
Defense #27

Efficiency
Offense #74
Defense #73

Field Position
Offense: #116
Defense: #71

Finishing Drives
Offense: #84
Defense: #23

Turnover Margin: #35

Rush Offense/Defense
On offense, Cincinnati is bad at running the ball overall (#114), bad at staying ahead of the down (#109) and in generating big plays (#94).  They're good in short yardage situations (#19).
On defense, Cincinnati is below average at stopping the run overall (#70) and staying ahead of the down (#70).  However, they don't tend to give up big plays (#17) and they're bad at stopping teams in short yardage situations (#127)

Pass Offense/Defense
On offense, Cincinnati is an average passing team overall (#69), they're good at staying ahead of the down (#40), and bad at generating big plays (#97).  They're average at protecting the QB (#33).  On passing downs, Cincinnati's offense is good overall (#38).
On defense, Cincinnati is an below average team against the pass overall (#76), at staying ahead of the down (#76), and at eliminating big plays (#70).  They're average at getting to the QB (#68).  On passing downs, Cincinnati's defense is average overall (#69).

By Quarter
On offense, they're average in the 1st (#64), bad in the 2nd (#86), worse in the 3rd quarter (#93), and terrible in the 4th (#119).
On defense, they're good in the 1st (#33), bad in the 2nd (#88), average in the 3rd (#68), and bad in the 4th (#90).

By Down
On offense, they're bad on 1st down (#125), bad on second (#105), and great on third (#23).
On defense, they're average on 1st down (#59), below average on second (#84), and below average on third (#69).

Havoc
Their secondary is good at causing havoc (#38), their LBs (#51) and DL are average (#66).

Summary
This is the second worst team that BYU has faced (Arizona #90).  They're on par with Michigan State (#74), but they're fighting for bowl eligibility...so they could be dangerous.  Their best game this year was against Purdue where the offense performed well (70th percentile), but the defense was poor (37th percintile).  S&P+ has BYU favored by 8 points. 

Overall, they don't sustain drives, they're not efficient, and they give up terrible field position.  They're above average in turnover margin and they are pretty good at preventing teams from taking advantage of scoring opportunities (#23 on defense) where BYU has struggled (#85 on offense).  I think that this game looks a lot like the Michigan State game in that BYU will have some success running the ball.  BYU will generate yards but the key is to score points (where Cincy has been pretty good at stopping teams -- #23 in defense against finishing drives).