Perhaps you have noticed, many teams, including the Buckeyes, have been using three defensive linemen in their nickel package when facing a passing down. Have you ever wondered why?  It turns out, if you know a little math, it makes perfect sense. (Maybe math is a big no-no for you....but I swear it is easy.)

Here is a standard 4-3 look with four defensive linemen, three linebackers and four defensive backs.

When faced with a passing down, defensive coordinators sometimes choose to put an extra defensive back on the field.  The fifth defensive back is what triggers the name "nickel" package.  But the question arises, which player comes off the field?  Do you remove a linebacker and play a 4-2-5 (4 DLs, 2 LBs, 5 DBs) or do you remove a defensive lineman and play a 3-3-5 (3 DLs, 3 LBs, 5 DBs)? 

Both of the defenses have their strengths and weaknesses, but if your goal is to cause the most confusion for the offensive line pass protection schemes and you understand a little bit about the branch of mathematics called combinatorics, your best bet may be the 3-3-5 alignment.

Let's make a few assumptions.

1. Defensive linemen generally rush the passer when it is a pass play.  There are a few times during the game when a d-lineman will drop into pass coverage on a zone blitz, but you cannot become predictable when you do this or opposing teams will exploit your pass dropping lineman.  Let's face it, do we really want someone like Nick Bosa trying to cover someone like Curtis Samuel?  No.
2. Linebackers are players that can drop in coverage and rush the passer with efficiency at both.
3. Defensive backs generally cover receivers when it is a pass play.  Using the same reasoning as above, DBs will occasionally rush the passer, but, again, you cannot become predictable when you do this or opposing teams will exploit you.

Let's take a look at a 4-2-5 alignment.

If we assume all d-linemen rush and all d-backs cover, then the defensive coordinator can alter the play of the two LBs in order to blitz, to cover or a combination of the two in order to create confusion among the offensive players.  Let's count the number of different things d-coordinator can do (this is the math part.)

1. Blitz no LBs.
2. Blitz all LBs.
3. Blitz LB-1 only.
4. Blitz LB-2 only.

So now we know...we counted the different things which can be done and there are only four possible outcomes.  Sure, there are lots different places to send each linebacker or d-lineman, but the offensive line only needs to prepare for the four different scenarios listed above.  It seems simple, because it is.

Here is a look at the 3-3-5 alignment.

Just like last time, assume all d-linemen rush and all d-backs cover, now the defensive coordinator can alter the play of three LBs in order to blitz, to cover or a combination of the two in order to create confusion among the offensive players. Let's count the possible scenarios like we did above.

1. Blitz no LBs.
2. Blitz all LBs.
3. Blitz LB-1 only.
4. Blitz LB-2 only.
5. Blitz LB-3 only.
6. Blitz LB-1 & LB-2.
7. Blitz LB-1 & LB-3.
8. Blitz LB-2 & LB-3.

You can see there are twice as many scenarios for which the offensive linemen must be prepared.  And defensive coordinators are using this fact to create special "rush" packages, which include stunts with the defensive linemen and linebackers, for hundreds and hundreds of possible different looks to cause confusion and favorable match-ups.  

Linebackers will sometimes show they are blitzing and drop and vice versa.  In case you are wondering, all of this is choreographed and it is not random.  The defense is purposely trying to manipulate the offensive line pass blocking scheme pre-snap. If you know how the opponent will react, you can plan for your mismatches.  And this manipulation is sometimes easier to do from a 3-3-5 alignment because there are twice as many possible scenarios the offensive line must deal with versus a 4-2-5 alignment.

This is by no means a comprehensive look into any defense.  Just some food for thought on why coaches do the things they do.

EDIT

Here is a perfect example of what I mean by creating confusion. We all remember this play...Ohio State shows a pre-snap look of rushing six defenders.  Oklahoma recognizes something and you can see them change either change the play or change the blocking scheme (as an outsider, it is impossible to know what truly happened.)  But in the end, Ohio State rushes only three defenders vs. five blockers and gets an unblocked defender directly to the QB.