Many great running games are constructed around one play.
This might sound a little crazy. It is and it isn't. Obviously a team needs more than one play to win games; spamming the same run over and over without ever doing anything else won't move the ball for very long. So why would a coach base his offense around one play?
For any given play to work, the offense must be prepared to face every defense they will see and they must "keep the defense honest" in order to maintain the advantages that the rules of the game grant them. If the offense can correctly identify its assignments against any defense, and the defense doesn't know where the ball is going or when it is going there, the offense is in great shape.
Because of the immense amount of work that it takes to truly prepare to run a play, offenses usually benefit by slimming down the playbook to devote more time to each play. Think about everything that has to go into coaching a play: there are individual skills like foot and hand placement, there are small group skills like combination blocks between 2-3 players, and there is the team concept involving all 11 guys.
All of it must be taught, then repeated over and over so that skills are developed and refined. Once players acquire those individual skills, they need to practice them together to develop chemistry. Finally, they need to be practiced against real defensive looks so that the offense can identify its assignments against the NFL's plethora of defensive fronts.
If you have few enough plays in the playbook, you can focus on actually getting better running what you know instead of having to do a ton of work to merely get your offense off the ground. Less can do more.
What type of play will it take to win?
The variety of situations that an offense could potentially see makes it difficult to commit to fewer plays. An offense will have incredibly different goals inside of four minutes left in the game if it is ahead vs. if it is behind. It will have different goals on 1st down vs. 3rd down. The list goes on. To be prepared for all of these situations, offenses must have plays that work in each AND they must accrue practice repetitions for each of those plays.
Bill Walsh famously scripted a set of plays for each of these situations and practiced those plays throughout the week so that his offense would be prepared for every situation it could see in the game. But what if your offense is never ahead in the game and in position to run a 4 minute offense? What if you're never behind and in need of the two minute drill? All of the practice time you spent working on that specific set of plays was now wasted.
So, is it worse to be unprepared for a situation going in to a game, or to be prepared but for a situation you never see? If you have a small set of plays you might never have to find out. If you can run one play against every defense and have it be useful in every situation, you've used your preparation time to practice things you will actually use no matter how the game plays out.
Constraint and Efficiency
The offense always knows where the play is going and when it is going to go there. If you've ever seen a guy like Troy Polamalu hurdle the line at the snap and make a play in the backfield, you've seen the defense take one of these advantages away (knowing when the play will begin). If you've seen Ed Reed jump a route for an interception, you've seen the defense take one of these advantages away (knowing where the play will go).
In this game of inches, reaction is everything. A quarter second of reaction can turn a 4.30 ahh-thuhh-leete into a 4.55 plodder, and a quarter second of anticipation turns a 4.55 safety into a 4.30 nightmare. An offense that can make the defense unsure of what is coming is a dangerous offense.
The traditional way of throwing the defense off the scent is with constraint plays: if the defense cheats up to stop the run, the offense goes to a play action pass over their heads. The more plays in the playbook, the more constraint plays you need. If you intend to run 15 completely different plays, you really need at least 30 (including counters) or you risk tipping your hand to the defense.
Adding one new play to the playbook multiplies the amount of plays you need to keep the defense honest, and gives you less time to practice each of them.
Fewer plays in the playbook, more system efficiency
If you base your offense around one play, even if you adjust the formations (3WR vs. 3TE) or the wrinkles (how the fullback and tight end block, whether you run a QB option or not, etc.) there are things about that one play that remain the same. The OL blocks the same way. The QB's steps and fakes are the same. The runner's footwork and reads are the same. You can run the same play action pass with the same run fake.
The more things that are the same, the more efficient your practices become: if you're practicing those things you're truly preparing your team regardless of what happens during the game. You will run this play regardless of situation, and you can subtly adjust it to fit your shotgun 4 WR package, or your 3 TE "we need one yard" package. When your practices are more efficient, you have more time to install and practice each play as well as more time to focus on constraint plays.
The Zone Running System
This "system efficiency" has followed the Shannahans and Alex Gibbs around the NFL, and it is what truly transforms the Zone running plays into a Zone Running System. Gibbs is known as the Godfather of the Zone System (the saying goes "there are great coaches, there are legendary coaches, and then there's Alex Gibbs"), but he has been connected to the Shannahan coaching tree for a long time.
Gibbs' fingerprints have been all over the running games and thousand yard rushers in Denver (Terrelle Davis, Olandis Gary, Ruben Droughns, Mike Anderson, Tatum Bell, Clinton Portis), Atlanta (Warrick Dunn, Michael Vick), Houston (Arian Foster, Steve Slaton), Washington (Alfred Morris), and Seattle (Marshawn Lynch).
The play itself
For Alex Gibbs, the "one play" in his running game is Outside Zone.
Outside Zone is also known as "Stretch" or "Wide Zone." As the names suggest, the play will be zone blocked, it will aim to stretch the defense's front horizontally, and the action of the play will be aimed wide, away from where the ball is snapped. While a lot of teams run Outside Zone, not all of them run a zone blocked system. Here is Gibbs on why more teams don't run it:
"Everyone has a little piece, but very little. And they can't get it coordinated so they give up on it, which helps us. Because it is too hard to put it in with all those other plays. You see, if you put em in with other plays, guys, you can't do it. I mean you--you're fooling yourselves! You can't get it all taught. You can't.
So you know, when I make these trips I say ‘guys, I'll give you the stuff but I tell you right now if you put this stuff in with counters and powers, weak and strong? You can't stay on the f**kin' practice field long enough to do all the things we do! [...] Miami put the force game in, and hadn't stayed up with it, and they just changed that whole crew because they tried to do too many things. They couldn't be great at anything, and it hurt em."
There is nothing magical or revolutionary about the outside zone play, nor was Gibbs the originator of the play. The success that has followed Alex Gibbs and the Shannahans really has very little to do with the play itself. It has everything to do with the depth of preparation that they have been able to achieve due to focusing on one play and the way that play fits into and becomes a coherent offensive system.
If you put it in with counters and powers, weak and strong? You can't get it all taught.