Morris is a member of a lengthy list of late-round running backs who have flourished in Shanahan's zone-blocking schemes. While many have maintained their initial success, more than one has proven to be little more than a flash in the pan.
But what evidence is there that Morris could become part of the latter group? There are two obvious points of concern.
The first involves the running style that helped Morris establish franchise records for rushing yards in a single season and touchdowns as a rookie in 2012.
Last preseason, what helped set a sixth-round pick from Florida Atlantic apart from a crowded rotation was his ability to make yards after initial contact.
Morris is a true bruiser who is never shy about throwing his shoulder into a would-be tackler. He will power and scrap his way for extra yards on every carry.
That is a commendable trait and one which certainly contributed to his average of 4.8 yards per carry in 2012. However, as much as a stubborn refusal to let the first hit drop him helped Morris dominate as a rookie, it could serve to shorten his overall career.
Running back is arguably the most demanding position in the NFL and most featured backs are absorbing some form of contact on every play.
Those who run with the kind of grueling style Morris does, expose themselves more quickly to natural wear and tear. Shanahan has experience with this kind of issue. Two of his milder successes at running back with the Denver Broncos fell victim to it.
Both Mike Anderson and Reuben Droughns were big-bodied zone-runners in the Morris mold for Shanahan's Broncos, although neither, technically, belongs in the category of one-season wonders.
Anderson rushed for 1,487 yards as a rookie in 2000, but injuries and poor form made the next four years a wash. Anderson did top the 1,000-yard mark for Shanahan one more time.
He managed 1,014 yards in 2005, but his average of 4.2 yards per carry was way down from the career-best performance of his first season.
Droughns was an even-more extreme example. He battered his way for 1,240 rushing yards in 2004 and was just eight yards shy of matching that total the next year as a free-agent capture for the Cleveland Browns.
But that was as good as it got for Droughns, who was out of football after the 2008 season. The toil of carrying the load ultimately proved too much for both Anderson and Droughns.
That problem is compounded for Morris because no other Redskins' runner has yet to emerge as a credible complement to share the load with him.
Morris ran the ball 335 times as a first-year starter. The next-most productive running back was Evan Royster with a meager 23 carries. That is a staggering difference, even if Morris is a willing workhorse.
The dynamic could change this season after Shanahan again indulged his habit for gambling on late-round running backs in the draft. He added Chris Thompson and Jawan Jamison in the fifth and seventh rounds, respectively.
They join Royster and Roy Helu Jr. in a crowded rotation. But the increased numbers do mean there is an even greater chance of finding someone able to split carries with Morris.
If that happens, the Redskins could employ more of a two-back system. That is something that has been a staple for Washington's NFC East rivals, the New York Giants, since 2008 and Shanahan is not averse to deploying a two-headed, or even three-headed backfield monster.
He did exactly that in 2006 when Tatum Bell split carries with Mike Bell. Tatum became the ultimate Shanahan one-year wonders.
Tatum rushed for 1,025 yards in 13 games, but was barely heard from again after that. Bell managed 677 yards in relief of Tatum that season and although that was his career-best mark, he did resurface as part of the rotation for the Super Bowl-winning New Orleans Saints in 2009.
Of course, as much as taking carries away from Morris would keep him fresh, it could also doom him to one-year wonder status. Shanahan has never been shy about rotating running backs and if a hotter hand other than Morris emerges, Morris could find himself looking on from the sidelines.
Yet splitting time with another runner is not the biggest threat to Morris enjoying continued success. The real danger for Morris is the potential for him not to refine his overall game.
For Morris to improve, that means becoming both a better blocker and a more productive receiver. According to Brian Tinsman of Redskins.com., Morris has been keen to improve himself as a pass-catcher this offseason:
Early indications out of training camp are that his offseason efforts could pay major dividends, as head coach Mike Shanahan praised his preparation, setting the bar high for his second season.
“A lot of people come out of college and they just don’t spend the time on catching the ball. He has spent a lot of time in the offseason catching the football, running routes and you can see that hard work has paid off because he’s a lot more natural,” Shanahan said. “It gives you another dimension.”
Thanks to his offseason dedication, Shanahan said Morris has a much better chance of staying in the game on third down, as he brings the most weapons to the huddle.
The idea of staying in the game longer obviously gives Morris ample opportunities to keep his production high. While his lack of polish as a receiver was not an issue in 2012, Morris cannot move forward without greater versatility.
If Shanahan chooses to lean on Morris the way he did with Terrell Davis in Denver during the late '90s, then Morris has to be able to do it all. Featured running backs must be complete backs, otherwise they are merely complementary parts.
Whatever role he takes, Morris is sure to be a target for defenses this season. That means durability could be the most important thing that prevents him from being a one-season wonder.
If he needs a cautionary tale from the Shanahan archives, Morris need only look at Olandis Gary. In 1999, Gary started 12 games and surprised everyone with a 1,159-yard season.
This was the start of the legend regarding Shanahan's ability to plug any runner into his system and have them succeed. Unfortunately, Gary only started four more games over the next five seasons and called it quits on his career in 2004.
Serious knee injuries wrecked Gary's NFL dream. While knee injuries can be the blight of any running back, that is especially true of those rushing in a zone-based system that demands quick one-cut moves.
Without wanting to jinx anything, the early signs from Morris concerning durability are good. He did not miss a beat for the Redskins during his debut campaign.
His own fitness is key, but the health of another player can also determine how successful Morris is in his second season. As with most things for the 2013 Redskins, production from Morris could depend on Griffin's fitness.
The reason is simple. A dual-threat quarterback always helps a running game, particularly a zone-based one.
The Patriots did it by blending their defensive fronts, crowding the line of scrimmage and blitzing the run. Teams cannot take that same approach if Griffin is healthy and retains a good measure of his multi-purpose skills.
His own threat as a runner forces opposing teams to play a passive brand of defense. That only serves to create even more room for Morris to exploit.
It will be interesting to see how Morris handles increased competition after having the position to himself in 2012. He must also expand his repertoire to maintain his hold on most of the snaps.
However, at this stage, it is smart to bet against last season's second-leading rusher being another one-year wonder in Shanahan's offense.