ORCHARD PARK, N.Y. -- When the Buffalo Bills dealt Tyrod Taylor and later traded up to select Josh Allen with the No. 7 pick, their goal was to develop a passer who could raise the team to greater heights than Taylor was able to achieve with his arm.

Although the Bills (2-3) escaped with a much-needed, 13-12 win over the Tennessee Titans on Sunday, their path to victory with Allen followed the same sort of conservative approach that once protected Taylor's weaknesses from being exposed.

Four games into Allen's career as the Bills' starter, that strategy should come with at least some level of concern. Instead of expanding the offense as Allen grows into his role, the Bills retreated into the protective shell of a ground-and-pound game plan. In the few instances when Allen poked out his head to take a chance, the results were lacking.

Buffalo ran the ball 43 times and attempted only 20 passes (including a desperation heave by holder Corey Bojorquez during a botched fake field-goal attempt), tied with a Redskins win in Week 3 for the fewest passes thrown by a team this season.

Sunday's game had the feel of Taylor's 2015-17 tenure in Buffalo. He was under center for six of the 38 NFL games during that span in which 20 or fewer passes were attempted. Much like how Allen scored on a 14-yard scramble on Sunday, Taylor made impressive plays with his legs and won all six of those games in which the Bills attempted 20 or fewer passes.

However, the evidence that Taylor could win when the game was on his shoulders was lacking. He was a statistically poor passer when attempting to come from behind in close games, situations that often exposed his accuracy issues and produced his few interceptions.

Allen is supposed to be something bigger and better for Buffalo. His off-the-charts arm strength should make defenses cover every blade of grass on the field. Expecting Allen to be that sort of prolific passer immediately in his career is certainly unrealistic, but he could have come up bigger in the limited moments Sunday when the Bills gave him a chance to showcase his arm.

Offensive coordinator Brian Daboll scripted a flea-flicker to Allen on Buffalo's first offensive play, but Allen's pass sailed over tight coverage on wide receiver Kelvin Benjamin and had little chance of success. Allen's best throw came on a 12-yard dart to tight end Charles Clay in the second quarter, but he later fired a laser to Benjamin's feet on third-and-10 in the third quarter.

"There were a couple of throws I wish I could have back that would've made it a lot easier [to win]," Allen said, noting his miss to Benjamin.

When the Bills trailed 12-10 and needed to drive for a game-winning field goal late in the fourth quarter, Daboll told Allen that the team would lean on its offensive line. Allen attempted only two passes for a total of minus-4 air yards.

Allen was also intercepted earlier in the fourth quarter on a pass that was on target and should have been caught by wide receiver Andre Holmes. He finished with 82 passing yards and a 42.0 passer rating. His leading receiver was running back LeSean McCoy, who had 23 yards, and Allen's longest gain came on a 13-yard pass to McCoy that was caught at the line of scrimmage.

There seemed to be an effort by the Bills to reel in Allen after he turned the ball over three times and was sacked seven times in a shutout loss to the Packers last week. Allen recklessly launched a pass that resulted in an interception in that game, two weeks after inexplicably tossing a pick to the Los Angeles Chargers while being wrapped up by defenders.

"You stress it at practice that every play is not going to be an 80-yard bomb," Daboll said Monday.

Added Allen on Wednesday: "I have to be better. I have to understand and respect the league, getting the ball from my hands, whether throwing it away or finding my checkdown and just allowing us to live another play."

The Bills' method for making Allen better on Sunday was to keep the ball out of his hands, which is a fair strategy for dealing with a rookie quarterback. That was good enough for the victory over the Titans, as Buffalo, which entered the game allowing a staggering 21 sacks through four games, gave up only one on Sunday.

But what happens when the Bills decide to open up their offense or are forced to do so? Allen's performance through four games should raise questions.

Coach Sean McDermott indicated Sunday that the team will continue to lean on its running game in upcoming road games at Houston and Indianapolis.

"I just think it's establishing the offensive line and the line of scrimmage," McDermott said. "Without giving away too much strategy for next week, I'm just going to leave it at that."

Eventually, the Bills will need Allen to win games that Buffalo is not able to control with the running game and defense.

"Offensively, you got to make sure you can put up points," McDermott told WGR 550 on Monday. "It's a quarterback-driven league. That was part of the investment in Josh, and developing him is critical to our success."